So this is lecture 14. It's already 9, no? Okay. So a couple of things before we continue. So one thing I probably should have emphasized more carefully even at the beginning which I think I did but I didn't do it very explicitly. It's this fact that we have to keep the picture that we had for our communication system. So we always said I have n bits which I map into, map into some symbol, some a plus jb belonging to the constellation and then I do a multiplication with phi of t. So this is a picture that we have so far, 0 to t, 1 by root t and then you transmit. This is for mqam. So this goes through a channel and all that. So I've implicitly assumed so now I'm okay. So one more thing I should say. So for such a system I'm going to say what is going to be my bit rate? I'm expecting my bit rate to be n bits per t second. So once I see, once I say this, what does it mean? If I want this to be my bit rate, I should be able to operate this transmission continuously without any stopping. So like every t seconds I should be repeating it without any breaks or delay or waiting for something to happen or anything. So only then I can say I have a continuous bit rate of n by t. So when I say my bit rate is n by t, I'm implicitly assuming that I'm doing, I'm operating this every t seconds continuously. I'm not stopping. So is that feasible is a question that we had be quietly sidestepped? How did we nicely sidestep that? We said there's really no channel. The channel we assume to be, right? What is the channel that we assume? Assume this to be delta pretty much, right? Ideal. So you've got bandwidth is so large that my channel response is almost a delta. That was our assumption. So once you come up with this assumption approximately delta, then whatever you put out is exactly available here, right? So if you have xab t here, the same xab t here is available after your channel and you add noise to it and you continue. So what happens from t to 2t? Another thing will happen and there will be no interference between the signal from t to 2t and 0 to t. The reason is assume the h of t to be delta. So obviously there's no question of interference. All these things don't arise. The moment you relax this assumption and look at h of t not being delta, some strange things will happen. So one needs to look at it carefully. So if the thing I talked about towards the end of last class about inter-symbol interference was not clear, maybe this is a bit more another way of viewing it. So far we didn't worry about it because I assume my channel was delta. This is a very, very ideal large bandwidth assumption. Once I assume that there is no question of any interference of anything. What I put out from 0 to t, right? The signal y of t, if you look at y of t, y of t from 0 to t will depend only on x of t from 0 to t. y of t from t to 2t will depend only on x of t from t to 2t. There's no other dependence. There's no question of the signal corresponding to one symbol interfering with the signal corresponding to some other symbol. So that never arises in our ideal picture. I want to relax this assumption a little bit and assume h of t is not quite a delta but that's very sharply concentrated. Support is very, very small so that the bandwidth is very large compared to t. So the support of h of t is very, very small compared to my t. So if I assume that is the case, we'll see for BPSK I'll show you an illustration of how it will actually work and how ISI doesn't really play a role. So I'll show you this illustration in a slightly non-ideal scenario just to emphasize this point because this is important. I think one needs to see where this is coming from. So I'll spend some time on this. So I'll take BPSK. So BPSK is just one bit, 0 and 1 mapping to plus 1 and minus 1 and I'll assume I'm operating it continuously. So my x of t might look something like this. I'll probably look. So maybe I shouldn't draw my y axis so low below. My x of t might look something like this. This could be an x of t. So 0 to t then 2t here, 3t here, 4t here, 5t here. So this is when I'm operating continuously. So every t seconds I'm putting out one bit. I'm doing it on the transmitter. So what am I assuming my channel to be? My channel I'm saying as very, very large bandwidth compared to t. So if I draw both these guys on the same scale then how should h of t look? Yeah, very small compared to t. So it will look something like, so maybe if you want to draw it causally, just to be sure, it'll look something like this. It'll be very, very small, much smaller than this. I'm just drawing this little bit exaggerated. Very, very small in the same scale. So if you take 0 here and t here, it's extremely small. So that's how my h of t is going to be. So this is much more slightly more practical than saying delta. Delta is a very ideal theoretical type assumption. This is slightly more practical. What will happen if I convolve these two? If I convolve a very small, tiny support signal with this square, what should happen? It'll always be a square again. So it'll almost be a square wave, except that those corners will be a little bit rounded that's all. So you can visualize this convolution. But since I'm drawing it causally, there'll also be an overall delay, but that delay will adjust. We'll say that delay is known at the receiver and it adjusts. So maybe it adjusts for it in some way. So once you do that, you'll see when you convolve here, in the ideal case, you'll get the exact x of t if you say h of t is delta. But if it's not so ideal, even then it's not too bad. It's going to look something like this. It's going to look something like this. There's no real reason why it'll look anything else. So it's going to look definitely something like this. So remember, so it's an okay assumption to say that this is equal to x of t. And then you can process. So if you do, for instance, if when you do integration from 0 to t, the part that because of the small curve here and there will not really contribute anything. The bulk is what's going to really contribute the whole thing. And then when you threshold with zero, it'll be very clear whether it's positive or negative. So this little thing here will not contribute. If there's no noise, of course, there's noise, then noise will do something. That's a different thing. But the signal itself is pure as far as correlation is concerned. So even when I operate with a bunch of pitch together, as long as my time scales are so that the support for H of t is really, really tiny compared to my signaling interval t. So what's the interpretation of this in the frequency domain? The support being very small. The bandwidth of the channel is very, very large compared to the signaling bandwidth that I'm using for my x of t. So those things are all equal and not equal and concepts can be viewed in both things, both domains and convince yourself that that's true. So even when I operate continuously a bit after another, as long as my timing is, I mean, my assumption of large bandwidth is true, I can think of the resulting convolut, the received signal as being just x of t itself. So what does it mean? This is was a crucial step here. Now remember, when I say y of t is x of t plus n of t, x of t, I'm assuming is the signal at the receiver after the convolution has happened. And then when I do my, what is the first step at the receiver to go from continuous time to discrete view to correlate, correlate with an orthonormal basis. How do you find the orthonormal basis? You find it for x of t, you don't find it for x of t convoluted with h of t. Actually, what should you find it for? x of t convolved with h of t, that's what you really need to find it for. But since I know my x of t is pretty much the same, I'm correlating with the orthonormal basis for x of t itself. So even when I operate continuously, say I send 10 bits at a time, when I want to decode all 10 bits together, what should I do? I should look at the signals corresponding to all the 10 bits. I'll have 2 power 10 possibilities. I have to find the orthonormal basis for that and then go about doing it. But that problem will break out, break down into a symbol by symbol detection problem because of the orthonormal I'll go through that once again, you'll see what I mean. So but remember the assumption we made is very crucial in the receiver. I'm assuming my orthonormal basis can be used as if it's for x of t itself without worrying about the convolution. So that's a crucial thing. So ideally, you'll have to take care of the convolution and then find your orthonormal basis because that's your reception. So hopefully, this picture is clear in your mind. So this is what I mean when I say, so for instance, people were talking about, I'm assuming infinite bandwidth, what's the band pass equivalent. So this is the way to picture all that. So you think of this, approximately as working out in this portion. Any questions? Well, this is a baseband picture. You can also think of a passband picture. What will happen in passband? This will be the envelope of your passband. So you'll have a real part, imaginary part, sine and cos. So the signal will look more passbandish. The envelope will be this. All right. So it's clear now. So what's the next question? The logical next question to ask is what happens when I want to shrink my t? How small can I make my t in relation to the support of h of t? So I want to keep reducing my t. So what am I doing in terms of bandwidth? I'm using more and more bandwidth. I want to use more and more bandwidth because as you learn soon when this 3G auction happens, bandwidth is a very, very precious commodity. You pay a lot of money for it. So you want to use as much of the bandwidth as it's out there. So when you want to decrease t, but you can see clearly when you decrease t, when t becomes comparable to the support of h of t, what will happen? The convolution will hardly look like x of t. So I mean, I have a depiction here. You can try this in MATLAB if you want. It's not too difficult to picture. When my support for h of t becomes close to t, when I decrease t to close to h of t, then my x of t convolved with h of t will look drastically different from x of t. And you cannot run the same receiver as you had before. You can't just happily use the orthonormal basis according to x of t. So things have to change there. So that kind of a situation is a situation where ISI happens. Y of t from t to 2t will depend on x of t for you can say pretty much all t depending on how your h of t is. So maybe if it's causal, then you can think of all the previous symbols will be involved and all that. So that's the crucial picture to keep in mind. So when t becomes comparable to support of, t is comparable to support of h of t. This is in time domain. What is the equivalent notion in frequency domain? Bandwidth of x of t becomes comparable to bandwidth of h of t. Then you will see y of t from t to 2t, for instance, will depend on all x of t I'll say. So because the reason is x of t convolved with h of t and h of t extends beyond t. So it's going to influence a lot of things. So this results in what's called ISI or Intersymbol Interference. So the signal that you put out corresponding to the symbol from 0 to t will also play a role in y of t from t to 2t which you actually expect only for symbol 2. So it will again affect that. So that's Intersymbol Interference and that fundamentally changes your receiver. The reason is why you have to now do orthonormal basis for x of t convolved with h of t. You can't just happily do orthonormal basis for x of t itself and you can't treat each symbol individually. You have to group all the symbols together and then look at it. Hopefully that's also clear. So each symbol individually cannot be done because one symbol is going to interfere with the other symbol. So you can't do it independently like we did before. You have to look at everything together. So I'm going to talk about this why we did each symbol independently in the previous case next. I'll write it down carefully and then show to you why we could get away with doing each symbol independently before when we had this last bandwidth assumption. Okay, so let me do that. Yes. Yeah, I'm going there. That's where I'm going. Eventually I'll get to that. Okay, so I'll get to that. So I mean I wanted to continue there and then I realized this notion of continuously operating. I didn't emphasize before. I didn't point out some of the intricacies involved in that. So I thought I should spend some more time on that. I'll come to that as soon as we get there. So far when we correlated, we treated each symbol independently. We did have to look at 10. If you're sending 10 symbols one after the other, we never really bothered to look at all 10 together. The reason is because you'll see why. So it's very easy to see why that happens. So let me illustrate that once again. So this is again an illustration for continuous operation in the previous case. Okay, so in the previous case, what is the previous case in the ideal large bandwidth case? Okay, intuitively it's clear. I think it's very clear, but I want to make sure that even from an orthonormal basis point of view, it's going to work out. Okay, so why did that happen? Suppose now in my picture, I have a sequence of N bit vectors. Okay, so B0, B1, all the way to B, L minus 1. So this is N times L bits. Okay, grouped N bits at a time. Okay, and then I map it to... Okay, so I'm going to illustrate it for MQAM. Okay, so anything else also remains the same. I'm going to map it to a sequence S of K of symbols. Okay, AK plus JBK, K will run from 0 to L minus 1. Okay, so this is the sequence of symbols. Okay, so this is my bit sequence, N times L bits. I'm using a... What kind of... I don't know. So if I did N... So I don't know. So you'll have to use like 2 power N QAM. Right, so that's what you'll have to use here. Right, so 2 power N QAM is the case I'm considering. Am I right? It's 2 power N QAM. Okay, so you've got capital L symbols. So you have 2 power NL possibilities here. So same 2 power NL possibilities will be here as well. Okay, and then what did I do? I did. So I'm going to show what actually happens here. So I'll say I'm kind of filtering by phi of t. Okay, so what is this phi of t? From 0 to t it is 1 by root t. Okay, so I'm filtering with an impulse response phi of t. So what will I get out? Okay, my transmit symbol X of t will be summation K equals 0 to L minus 1. Remember there is... This is a discrete time sequence at every t seconds. Okay, so this is going to be S of K what? Phi of t minus K. Right, so that is my signal that is going out. Okay, according to my ideal assumption, what is my channel? Channel is delta. Right, so it doesn't matter. It's just the same thing. And then noise gets added. Okay, since my channel is delta, I know at Y of t is going to be what? Exactly equal to X of t plus N of t. So when I want to correlate at the receiver, I can do orthonormal basis with respect to X of t. Okay, so how many possible X of t do I have? This is now 2 power NL possibilities. Okay. Right, it seems like a huge number, but how many bases will you need? 1? It can't be 1. Okay. So if you do Gram-Schmidt on all these 2 power NL X of t's, what will be the bases that you should get? What if L equals 1? If L equals 1, what's the basis? Phi of t. So L is 2, what needs to be the bases? Yeah, just the shifted versions.  What are the L basis elements? Phi of t, phi of t minus t, phi of t minus 2t, so on. Okay, that is crucial. The fact that your basis elements are time shifts of each other is extremely crucial. Okay, and that happened because I took phi of t this way. Okay, so it's an important point here. So I want to emphasize that. The orthonormal basis works out to be phi of t minus kt for k between 0 and L minus 1. Okay, convince yourself that this is true. Okay, so and this is very important. Okay, so once the orthonormal basis works out to be this, everything else we did is justified. Okay, so we can treat each symbol separate. Okay, so you can simply correlate with t minus kt. Do you see why that is true? Right? Yeah, so when I correlate with phi of t, what will happen? All the other symbols will pretty much drop out. I will be only doing the first symbol. So I might as well do it after t seconds. I don't have to wait for LT seconds to do that. Right? After t seconds, I can correlate with phi of t. After 2t seconds, I can correlate with phi of t minus t. And what I get will only be s of 2. Okay, so you see that? That's the nice thing about the way we've worked. Okay, this y of t when you receive it. And if you imagine running it through a set of correlators, phi of t. Okay, this is correlation. Okay, so I don't know. I should be careful here. Okay, if I imagine correlating with phi of t, correlating with phi of t minus t and all that, so on correlating with phi of t minus l minus 1t. Okay, what will you get out? Here you will get nothing but s of 1 plus noise. Okay, if you want n of 1. Okay, so s of 2 plus noise. And what will be the PDF of all these guys? The noise PDFs, they'll all be IAD Gaussian with zero mean and variance n naught by 2, which is the level of the PST. So all these things you can show, there's no problem. Okay, this will be s of k, s of l minus 1, I'm sorry, plus noise. And you can run detectors independently. Okay, they're all independent. So detectors can be run independently. Well, all this is really, really intuitive. But I just want to show the pure mathematical basis for this whole thing, if you will. No, I mean, it's very intuitive why each symbol is independent when once I make the delta of t assumption. So it's very easy to do that. But just want to show that even if you do orthonormal basis for a bunch of symbols together, you pretty much get the independent basis for each symbol. So there's no problem. Okay, and if you look closely, you'll see you don't need to have all these correlators as independent circuits. The same circuit can be reused every t seconds, because phi of t will pretty much do only from 0 to t and then t minus t will come only from t to 2 t. So you can happily reuse the same circuitry. So you simplify the circuitry. Okay, so many things depended on the basis becoming phi of t minus k t. Okay, phi of t and its shifted versions became an orthonormal basis. And because of that, first of all, the decoding problem was simplified. And well, it became independent. Okay, so it's very crucial. Okay, and right now it seems like we can do this only when h of t is delta or in a more practical way h of t has a huge bandwidth compared to x of t. Okay, so but it turns out one can look at this same system very closely and allow h of t to have a general bandwidth. And then find out if there exists a phi of t, which will fit into the bandwidth of h of t more closely, but still have phi of t and phi of t minus 2 t and t of t minus t and phi of t minus k t being orthonormal. If that is the case, then I can repeat the same thing. Okay, so basically the ISI case is a generalization of the above. Okay, so you will see we will generalize this and we will try to fit it into a finite bandwidth. Okay, so if you understood why the ideal case with delta of t as a channel response split into symbol wise, you will also it will also be clear to you why the ISI case will split into some ways. Okay, so it's possible definitely for the ideal channel assumption. Okay, the ideal finite bandwidth channel assumption is definitely possible. Any questions on this? It's clear? I'll come to that. Maybe at that time I'll answer this question. So when I deal with the ISI case, I'll come to that. Okay, so this your question is kind of like about this capital L, right? It will become irrelevant. The way we choose it, we can allow L to be any number. So it doesn't matter. But maybe you want to optimize and do something else. That's a different question. But the way we do it will be L can be any number. Okay, so I want to convince, I want you to convince yourself of a couple of things now. Okay, so if you look at the picture in time domain, it's very clear and obvious why phi of t and phi of t minus kt, like phi of t minus kt is an orthonormal basis. Okay, can you convince yourself of the same thing in the frequency domain? Right, Fourier transform, this is all L2 function. So Fourier transform is inner product preserving. So if we take Fourier transform of phi of t minus kt, what should I definitely get? I should get a set of orthonormal functions again. Okay, so what will happen if I take Fourier transforms? Yeah, so you'll get sinc but sinc with e power minus j different phases multiplying. Are all of them orthonormal? Yeah. Okay, so you should know you should be comfortable with the fact that all of them will be orthonormal. Okay, so it's a little bit of a non trivial fact. It may not be very trivial like in the time domain case. Okay, but try to think about it that way. Okay, so that's useful. So the reason is we will see designing orthonormal signals in this case in the time domain was very, very easy. But when you want to optimize your bandwidth, you'll want to design it in the frequency domain. Okay, so there you should have some reasonable comfort with going back and forth. All right. Okay, so if there are no more questions, let me proceed. Okay, so if I have to summarize, okay, so in the ISI case, my phi of t, okay, in this case, I could happily pick it to have infinite and large pieces. It'll be different. It'll be different. The way we do it is different. It's not the same thing. It's okay. I just wanted people to think about it. The way we do the orthonomality will be different. We'll convert it into discrete time and we'll do it very comfortably. Okay. All right, so the phi of t in the ISI case has to see in the in the in the large bandwidth case, I only had to worry about orthonomality. I didn't have to worry about bandwidth of phi of t itself. Bandwidth of phi of t could be very, very large. There is no problem because my channel bandwidth is much, much, much larger than that. Okay. But if I want to bring my channel band bandwidth of phi of t close to bandwidth of h of t and constrain it with that, then I have to worry about bandwidth here. Okay, so in the in the case that we are going to consider now, what is the case we are considering my h of f is going to be what? Okay, minus w by 2 to w by 2. Okay, so if I say finite bandwidth, whatever I do to phi of t, phi of t must fit inside this bandwidth and preferably be fully filling. Okay, so if I take only very small bandwidth, I know how to do it. I can pretty much take it to be flat. I don't have to really choose anything phi of t very carefully, but I don't want to choose it as flat. Okay, because I want to occupy more and more bandwidth. Okay, so I want phi of t to have bandwidth. I will say close to okay, I am putting tilde, but it is close to w by 2. I want to push the bandwidth as high as possible. Okay, so that is the significant change from what I did before. If I did not change that, then I might as well pick it to be flat and pick my t to be really, really large compared to 1 by w and then I will be happy. Okay, I don't want to do that. I want to pick my bandwidth to be tending to that, but still have what? But still have phi of t minus kt orthonormal. Okay, is this possible? Can this be done? What is the largest bandwidth of phi of t for which this can be done? All these things are questions which are answered by what is called the Nyquist criterion. Is there a question? Yeah, well the way I am defining bandwidth for baseband signals is the largest positive frequency. Okay, so for passband, I will define it differently. So it will be, bandwidth will be defined only for positive frequencies. I don't, I mean I don't want to say I have amusing bandwidth from minus 100 to 0. You can use it in theory, but in practice you don't pay for the negative frequencies. So your bandwidth is only positive frequencies. Okay, so I think maybe our minister will be successful, but it's very difficult to sell negative bandwidth to companies. They won't buy it. So we will define bandwidth as only positive frequencies. So for baseband, it will become w by 2 and for passband, it will naturally become w. Okay. So I want my bandwidth to be as high as possible. So once I want to increase my bandwidth, you'll see there's more stringent requirements, but it's possible. It's still possible. There's no problem. We'll see how this can be done and that's answered by what's called the Nyquist criterion. Okay, so we'll see that next. And am I doing anything else before that? Okay, so I'll do the setup a little bit more carefully because soon enough we'll extend it to other cases and I want to do, I want to be able to do that. Okay. So let me repeat the setup once again. The setup is quite important, so that grasp it very carefully. Okay, so now instead of looking at 1B vector, I will look at B0, B12, B, L minus 1. I know I'm repeating it, but I think it's fairly important. Okay. So you have n times L bits. Okay. And okay, so this is some map into a signal constellation. Okay, the signal constellation should have size what? 2 power n, right? The signal constellation size should be 2 power n. It goes and mapping n bits into the constellation point. So that's the only condition on my signal map. Okay, and I'll say it's a 2D map. It's just a complex number. Okay, it puts out a complex number. And those complex numbers, I'll collect them into what I'll call a symbol sequence. Okay, so this will be S of k. Okay, remember this is complex, k between 0 and L minus 1. Okay, so this picture we'll use several times in this course, so I want you to get used to it. And then I'll use, I'll call this a transmit filter. So this V of t, we've been always thinking of it as a basis function before. What I'm going to write down also as a, can be thought of as a basis function, but you'll see in the general case once you convolve with H of t, it doesn't make sense to call or think of this alone as a base function. So to give it a general name, I'll call it as a transmit filter. Okay, so I'll use this notation G of t for that. So this is my transmit filter. Okay, so it might turn out to be the basis or it might play a role in the basis. Okay, so that might happen, but in general, it's just a transmit filter. Okay, so what am I expecting from the transmit filter? I'll treat this as actually like an impulse train. Okay, separated at t. Okay, so I'll think of this as in continuous time as S k t minus k t. Okay, this is what I'll think of this as. And then I'll filter it. When I filter, what will I get? Yeah, so this will be my transmit signal X of t. So I need a notation for it. So for that, I'll call this entire vector capital B and I'll index this with B. Okay, is that fine? X B of t, this will be what? Summation k equals 0 to L minus 1 S of k G of t minus k t. Okay, all right. So that is my transmitter in complex baseband. Okay, right now I'm in complex baseband. Okay, so you might say maybe G of t you want it to be complex, but typically people choose G of t to be real. Okay, what will be complex? S of k will be complex. That's good enough. Okay, maybe if you're, maybe in future somebody will come up with a clever method where G of t itself becomes complex. So far, it's not really necessary. So G of t can be chosen to be real. Okay, so notice one thing. First thing I will not insist on, I will not insist on support of G of t between being between 0 and t. Okay, why is that true? So once I start insisting on that, I know my bandwidth is going to become much, much larger. And to support all those things, it'll be very difficult. So I'll allow my G of t to have a general support, I will not insist on anything about support. Okay, but I will definitely insist on bandwidth for G of t. Okay, so I'll say bandwidth for G of t should be what? Definitely within W by 2. That's the only thing else. Okay, so we won't insist on anything on the support. We'll say bandwidth for G of t should be less than or equal to W by 2. Okay, so the reason is this is going through my channel, which has a bandwidth W by 2, so I don't want to exceed that. Okay, so that's one thing. The other thing is the word about implementation. I want to point out that also. So in reality, today, what you do is these transmit filters, easiest thing to do is to have a very powerful processor for this transmit filter. Okay, so the whole thing can be built into a processor, gets the bits as input, converts it into a complex number, just two real numbers, a plus jb, it's very easy to do that. And then what you do is you multiply a by G of t, b by G of t, that's what you do when you do this a plus jb times G of t. And G of t is kind of over sampled by the processor very heavily to get samples of G of t at very, very close intervals. You over sample it because your processor probably works at some gigahertz clock today. I don't know, maybe not gigahertz, but definitely tens of megahertz and you can afford to over sample your G of t, which is a baseband signal. So you over sample it and then put out say an 8 bit version for each sample of G of t. And then you have a d2a, maybe in fact many processors have d2a built into them. So you have a d2a, which will convert the 8 bit and sample and hold. So you see it's a very processor type implementation. You don't have to actually worry about G of t, no. So now G of t can be an arbitrary shape. I know any arbitrary shape G of t can be implemented in baseband easily with this processor and d2a combined. So I don't have to restrict myself to a specific form for G of t, which can be implemented in analog with some filters and all. So that's going to restrain you. So I won't restrain that way. So I'll say any G of t, any waveform is fine with me. And in terms of implementation, I'll have this processor backed idea in my mind to do that. So you don't even need a processor. Actually just spreading out these, I mean just store it in a RAM and then read it out. I mean it's not that difficult today. So it's very easy to do this. One d2a is pretty much enough. So don't worry about if I give you a complicated expression for G of t involving several terms. It can be done very easily today in almost like a software situation, even though in hardware. Okay. All right. So that's my X B of t. So pretty much the only constraint is bandwidth. Of course, there'll be power constraints. Okay. The power constraints will always be there, but we'll think of G of t as normalized. Okay. So once you think of G of t as normalized, what's the advantage? If G of t minus kt is also orthonormal and all that, then the power of S of t, no, actually if it's normalized, S of k times G of t will have the same power as S of k itself, expected value of X of k. So my constellation energy will map to that. So we'll think of G of t normalized in that way, but that's not too important. Okay. So typically you pick norm to be one. Okay. So that's a good pick, good way of doing that. All right. So that's my, that's the way I'm going to think about my thing. Okay. So once these things are true, okay, if my, if my X of t goes through a H of t and what is my response here, filter response here, it's flat between minus W by 2, W by 2. Okay. And I'll have to insist on a linear phase because I'm drawing only the magnitude response here. I'm saying it's flat. I'll say my linear phase, my phase can be linear. Okay. Linear phase will only cause a delay and I can adjust for the delay without any problems. Okay. But I can't have weird phase making my response look very bad. Okay. So that has to happen. Okay. So once that is there, everything is fine. So once phase is linear and you have constant magnitude, what will happen to Y of t? What will be outside here? It'll pretty much be equal to X B of t. Right. With the delay, but I'm going to say I'll adjust for any delay. Okay. So no problem. We don't worry about the delay. So once I have this and this condition is satisfied for the bandwidth, right, this after the filter will come through unharmed. Okay. And that's crucial. Why is that crucial for the receiver? Yeah, the receiver you can do correlation with the normal basis for X B of t itself and not worrying about the convolution with H of t. Okay. So that's the crucial part. So to this noise gets added and then you do your receiver. So you do your receiver correlation. We'll find this as we go along. Okay. So one assumption you need in the design of G of t is knowledge of W by 2 and knowledge of the channel. Knowing that the channel is flat in your band, you should know that. Okay. So in practice, how would you know something like that? Right. It's not very easy to find out, right. So what people do is they sound the channel from the transmitter, go to the receiver, the receiver will use a really low rate communication to tell the transmitter kind of what the channel looks like. So from there, you make a choice and then you decide what the G of t is. So you can do all these things. So some training can be done. So these things are practical and can be done. So in the information, you don't need that much. But if you know your channel is fixed and it's not going to change too much, you can calculate it ahead of time and then design for a certain specific type of H of t. Okay. So but you have to know it's magnitude response flat and phase response linear to proceed. Okay. So phase response linear is a typical assumption you can make. I think well it's those kind of things but magnitude response has to be flat and you should know that. Okay. Is that clear? Okay. So the next thing we'll do. So once you know the received signal is just simply XB of t. That is good news. But now I want so what's the step next? The next step is always easy. Okay. So there's no confusion here. The way to do it is take all your XB of t, find a orthonormal basis. Okay. You might get certain number of orthonormal basis and then you correlate Y of t with that and based on what you get, you build a detector, you find your pdf, join pdf and proceed. Okay. But that can get quickly complicated. Okay. Suppose I have n equals 6, which is 64 QAM. Okay. And then I want to do is like 1000 bits. Okay. So immediately everything goes out of the window. Right. You can't expect to do Gram-Schmidt over such a huge number of things and you can't pick any, you can't come up with any rule for picking G of t that way. Okay. So we'll again go back to a previous case and use that as our motivation. In the previous case, everything simplified because G of t minus kt formed an orthonormal set of signals and that simplified everything. Okay. So now I'm going to ask the question. Suppose I want G of t minus kt to be an orthonormal set of signals. Okay. Is that possible? Can I design G of t so that G of t minus kt is an orthonormal set for k equals 0 to L minus 1. Okay. So is that possible? Once I do that everything becomes dirt cheap. Okay. I only have to do correlations with G of t and G of t minus kt. In fact, my circuits can be repeated because I'm doing only the same correlation over and over again. I'll show you how to make that happen. It's a little bit more involved here, but it can be done. All those simplifications happen and everything becomes easy. Okay. You can almost do symbol by symbol. Don't have to worry about ISI at all. Okay. Is there any question? Decides t. I'm going to come to it. This orthonormality condition will determine t. So we haven't come to that yet. Okay. So right now I've just picked a symbol time t every so capital T determines this guy, right? How often do you put a new symbol out? Okay. And then everything else follows. And how do you determine capital T? Capital T will turn out to be determined by this orthonormality condition. There will be a certain maximum certain minimum t that you can possibly pick. Okay. Any other question? Okay. So what's the condition? It's just from here, it's just simple signal signals and systems type analysis. What do we want? The condition we want is G of t minus kt. Okay. Inner product with G of t minus LT should be what? Should be 0 if k is not equal to l. Maybe it's 1 if k equals l. Okay. That's fine. So now over all possible k and all possible l I want to vary, but that's the same as varying. Okay. This condition is equivalent to G of t, G of t minus LT, l equals 1 to l minus 1. Is that okay? Okay. See those are the only shifts that are really relevant to me and you can show these two are the same. Okay. So I'll in fact want that. Okay. So instead of restricting ourselves to l minus 1, you'll see this will be, this will not give us readily easy answers. So we'll say simply l not equal to 0. Okay. And we'll say this goes on and on and on. We'll ask that for all l not equal to 0. Okay. So it seems like a most stringent condition, but it will give you a nice clean closed form answer which is much better than looking at just 1 to l minus 1. Okay. And also another thing is this capital L may not be something that you fix ahead of time. Okay. Sometimes we might want to send 100 symbols. Sometimes we might want to send 1000 symbols or maybe 10,000 symbols continuously. Right. And you want to be able to adjust to all of that without worrying about this ISI and auto normality condition. So if you require for all l not equal to 0, then it simplifies both the analysis and the practice. So you probably want to pick that. Okay. So once you look at this, let's write this out in integral form. Integral t equals minus infinity to infinity g of t, g of t minus l t. Okay. dt equals 0. You know correlation can be also written down as convolution with the matched filter thing. So this thing will work out to g of t convolved with g star of minus t. I mean I have been saying g star will be real but just to be complete will be g star of minus t evaluated at l t to be 0. Of course for l not equal to 0. Okay. So all these things. Right. So looks like this signal is important to me. g of t convolved with g star of minus t. When I sample that signal, what should I get? Okay. Suppose I define this gate to be c of t. What should I get when I sample this signal? If I define c of l as c of l t, it should be delta l. Right. So if c of l, so c of t, c of t would, what would be the Fourier transform of c of t? c of f would be mod g of f squared. Okay. So now c of l, what would be the Fourier transform for the, yeah, Fourier, discrete time Fourier transform for c l. It is going to be 1 by t summation m equals minus infinity to infinity c of f minus m by t. Right. This will be the same as what I would call as e part j 2 pi f t. Right. In the discrete time domain. This has to be what? The discrete time Fourier transform of delta. What is that? 1 for all f. That is it. That is your Nyquist criteria. Okay. If your g of t is such that mod g of f squared when aliased with respect to 1 by t, okay, gives you a flat response. Okay. So remember, then what will happen? Then g of t, t and g of t minus t and g of t minus 2t and all these things will be orthonormal with respect to each other. That is an if and only if and all these conditions have to be satisfied. Is that okay? Okay. So all this 1 by t and 1 and all that is okay. It is relevant and important to be strictly mathematically accurate, but up to certain constants you can say that. So all you need is mod g of f squared aliased with 1 by t should be flat. Then you can normalize and adjust and get everything else you want. Okay. So this is what I meant I said when I said frequency domain type constant. It is a different way of doing it. It is not the same thing as that. Okay. Everybody is happy. Everybody is convinced to understand what this means. Okay. So the first thing you should check to get used to this is to check that the phi of t we had before satisfies this condition. What was the phi of t we had before? One between 0 and t and 0 else. Okay. That one definitely is orthonormal but t of t minus 2t is orthonormal. So in the frequency domain do you think you can convince yourself that this is true? What is the Fourier transform of that? It is a sinc. Okay. Then mod square is what? Sinc squared. And then when that is aliased will you get 1? Okay. Well there you go. That is an answer for you. So if you did not follow that you better go and work that out. So that might be a good lesson in getting used to all these DTFTs and Fourier transforms and aliasing and all that. Okay. So does that work out is something you have to check. Okay. So it is easy to check that at least for that case it has to work. Okay. But that may not be the only case. Okay. There are so many other situations possible. Okay. So there was a question about choice of t. This tells me something about choice of t. Okay. So notice g of f vanishes outside of w by 2. Okay. What is my g of f going to look like? Assuming I have a real signal. It is going to be something but it is going to be symmetric about 0. Okay. Okay. And it vanishes outside of w by 2 and minus w by 2. And what do I want? What will happen if I do mod g of f square? That will also vanish outside of minus w by 2 and w by 2. And then when I want to shift and add by 1 by t, what am I required? What am I requiring? That it should become flat. Okay. So if I choose my t, my 1 by t to be greater than w, what will happen? If my 1 by t, okay, suppose w is here. If 1 by t is greater than w, what will happen? There is no way I can satisfy the no ISI condition. Okay. The orthogonality, Nyquist orthogonality condition cannot be satisfied. Nyquist criteria will be while later. Okay. So any g of t which is band limited to w by 2 cannot satisfy the Nyquist criteria if 1 by t is greater than w. So this automatically gives you a constraint on how fast you can, your symbol rate can be. So that implies simple rate less than or equal to w for bandwidth w by 2. Okay. Remember this is base band. So you should be careful. Okay. So that is your way of fixing w. Okay. So the next question to ask is what is the next question to ask? Suppose I say symbol rate is less than or equal to w, what would you desire? Equal to w, right? So you want the fastest symbol rate that can possibly happen. So can you have symbol rate equal to w? If symbol rate is equal to w, what is the only possible g of f? Flat between minus w by 2 and w by 2. Okay. So there you go. That is the way you keep constricting these things. And then you try to relax that and see if you can get something better. So we will do that in the next class.


challenge on getting it, getting good quality care, getting enough of it, and actually, I think in the previous panel mentioned when care has been reduced to meet budgetary needs or capacity needs has meant outcomes for that person are far poorer than they should be, in particular with regard to their own rights and their human rights. Thanks for that. Henry, do you have anything to add on there? I can't hear you at the moment. Hang on a minute. No, I'm not sure what's going on there. Maybe while you're trying to figure that out, we can come back to you once we get your audio sorted out. I'll add my other question that I had. The committee has heard that we've had evidence sessions already on the national care service, and we've heard from previous witnesses that the bill, as proposed, is a disproportionate solution to the challenges that we face. Are you keen to hear your views on whether we actually need legislation to bring about the improvements? Maybe Adam, I'll start with you. I think that we're at a position now where legislation is what we've got. If you look across the piece in social care, how disparate it can be in terms of the receipt of it and the different systems that will be in place. We've talked in the past, and everyone has talked about those who hear from people who receive social care or their families about this postcode lottery idea. We've got huge numbers of different integrated joint boards, health and social care partnerships and how the NHS does this and local authorities. I think that this has been a helpful step. If you're going to try and reform social care, then you probably need a useful mechanism to do that, and legislation will be this. Underpinning all of this is about accountability, as much as anything, and responsibility for social care. I was listening to the last panel session there, and the question was put about the Cabinet Secretary for Health and Social Care actually having responsibility for that. My goodness, that's exactly the type of thing that we need from the Scottish Government, so it's not just in name only social care, because if you go back to the beginning of the Covid-19 pandemic and the instances of people's social care packages being removed from them, I'm told that they'll have to go without people be waiting days in their own beds without being fed or washed or anything, the things that they need, there was nobody really held accountable for that in a crisis. Now, while that wasn't a crisis, that demonstrated absolute necessity. The Scottish Government had no levers essentially to fix this. Local authorities or IJBs or health services partnerships were wholly remote from public accountability. I think if you had that in the health system, which is equally as necessary to somebody's wellbeing as social care if you're receiving it, so I think underpinning that, having that responsibility is necessary and actually trying to reform social care is important. That will mean many things to many different people, of course. A lot of this will be about money and resources and how this is used effectively as the best outcomes for people. So we've got a natural care service proposed and we wholeheartedly support such a thing, at least in the broadest concept of it, but I want to bring that back to the accountability and responsibility that is massively important and doing so through legislation as much as anything is vital. Thanks, Adam. Hannah, you've integrated. Do you want to come in? Yeah, I would agree with Adam's comments there. I would also say that I think there are parts of the system that we can be working on to improve outwith the legislative framework and that that should be happening, but that's not a fixal. We know that the structure of, say, the SDS legislation does not deal with the problems that we have with our little bit of criteria, which is one of the most pressing reasons why people don't receive early intervention care and why things reach the point of crisis intervention. I do use that word very specifically because I think that that is frequently the case that people are in by the time they actually have access to social care in many instances now. I would also flag that all the legislation isn't a fix in all ways, and I would particularly say that the Alliance and our membership do have concerns about framework bill approach. There are things we would really wish to see change in that within primary legislation more on that later, but an example of legislative protection is working well when there were problems with accountability would be during the pandemic. We know that some local authorities temporarily suspended complaint systems. Now that's not in line with their duties as public bodies and when that was raised, I would assume out of ignorance and relative lack of support for extremely overworked individuals. I'm not trying to knock front line and look at local authority colleagues by saying this, but functionally they were not fulfilling their statutory duties and when that was raised and aired with them, the problem was actually dealt with pretty promptly because there was the legislative accountability and because there was a process of place to go, that's not great and here's why. To have something that can provide similar assurances would be beneficial if done right and that's a pretty significant cortisol. Thanks very much, Hannah. Henry, I'm going to try to bring you in again and if you can just respond or add anything to both the question about from the Alzheimer's Scotland perspective kind of the problems with the way that social care is delivered and the postcode lottery piece, but also do we actually need to bring in legislation to bring about the improvement? Can you hear me okay? Yes, we can, fantastic. I think that in terms of the I can answer the necessity question first of all that there's no doubt I think that as a country we're still reeling from the changes that were made back in 1996 on the days of regional councils and we've never really quite been able to deliver consistent variation across the two local authorities of what affected social care, so our view is very much that when you're faced with the challenges of the scale of dementia and if you look across the piece everyone today has told you how difficult it is to access good quality social care, but I think what's more important is that there's some big strategic plans that have been made over the past 12 years particularly around dementia, the national dementia strategy, but around about probably 35 to 40 commitments and all of them rely on local delivery and very few of them have actually been delivered consistently, so I think I can understand this from two sides, I can understand when a local authority is dealing with their own issues and trying to work out how best to serve their communities and the challenges that they've got there and then a Government who puts together some of the best perhaps the most comprehensive and innovative policies around dementia that we certainly think could go on the table, these two things don't well build together, so we've got national visions, national strategies, national agreements that would transform the lives of people who were mentioned from the point of diagnosis through to integrated and advanced care that have never really been delivered, so when you ask us if that were under the governance and direction of a national peer service with peer boards that were working to a consistent framework to give everyone across the piece the same quality of care, we would say yes that makes enough lot of sense because what we have tried to do today has just been very difficult, and I think that the agibs, when we bring two shugging bodies together with very little funds to meet the needs that's already out there, I think that the right at the start they were about saving money and trying to make better resources, and we never reached the point about really meaningful prevention work, and I think that the thing that Derek Feeley highlighted and we were very supportive of all was the sense of moving forward, thinking about prevention, thinking about prevention earlier, and even at the time of crisis that we need to really move everything forward and think through how we can avoid so much of the difficulties we experience now, and I think that's again something that needs to come from a national perspective driven through the care boards to local people. Thanks very much. I'm now going to move on to questions from Willie Coffey. Thanks very much again, convener, and good afternoon to everybody on the panel. I just wanted to go back to Derek Feeley's report, of course, and one of the key standouts for me, and I've read many times now, is that Derek said that the driving focus should be consistency of quality and equity of care and support by service users. That's at the heart of the Feeley review. Do you think, in your opinion, does the national care service provide the instrument to enable us to deliver this consistency of service across Scotland, and I'll ask Adam, if he would pitch in with an answer to that, please. I think it could. Obviously, detail is lacking, and a lot of the things how it actually happened. Of course, it's being co-designed and the co-production underlying the secondary part of legislation, but I think that when you consider the lack of consistency, and that's highlighted by the fact that anyone is coming forward to say that they're having poor social care or not receiving it at all, and it's not meant at those who are delivering it, because you look across the piece, for those who are working in social care, that consistency for them, as well, is lacking. It was mentioned in the last panel about different terms and conditions for doing the same type of work, but depending on who's being commissioned to undertake this, that some suppliers or suppliers may have to withdraw entirely from delivering social care because financially it's not sustainable. We've had before this latest round of energy crisis care homes closing because of financial model. It's an expensive business care, and often good things cost money, but I think that this is really important, and I feel that it's absolutely right in that report.  Then that is absolutely right in this, and it's not consistent. So the care service could do all of these things, and Dev will be in the detail, of course, and that's what we don't really have right now, to be able to properly scrutinise. Thank you for that. Can I have a brief comment from Henry and from Hannah as well, please, on that? Is this the instrument that we need to deliver that consistency across the country? I think that the truth will be that there will be variations in performance. I think that if you look across to our national care service, for example, we don't achieve consistency despite having a very clear direction, a very clear guidance, because performance is always an issue in their management and their thoughts. I think that what we will have is a consistent set of principles, a consistent set of standards, a consistent set of both their rights and expectations that can be delivered and measured against, but I do think that, given the challenges that are going on in any social care structure of this scale, we'll always see some depth of inconsistency, but he asked me about the values and the principles in this driving position. Yeah, we need a national care service that's got all of that at the front. That should determine the structures that come behind it, and then, I think, the performance delivery will need an awful lot of very end-depth monitoring to ensure that we achieve that consistency. I would echo Adam's conditional response and that of Henry as well. I think that if I can summarise it that way, I guess that if I was getting into the T's and Z's, I'd say that the national care service has more organisational capacity, potentially, to do that in certain areas than current systems, but I'm not sure that that's the same thing as saying the National Care Service, Bracket Scotland and Clothes Brackets Bill does. I suppose that talking specifically about the data collection came up during the last panel, particularly around problems with the flags used around local learning disabilities. Our national approach to data collection would be proper intersectional analysis, both from our different population groups and how they're accessing social care, and something outcomes-focused that could be managed nationally, so the same questions and same data sets are being compared. To highlight where things are working well and that practice is shared, as well as highlighting problems, I think could be a really key part of being the usefulness of some areas of national analysis alongside that local delivery part that is also very important and has been raised by colleagues. If you don't have that, you don't know what you don't know, you can't meet the problem. I would also say that, although I would agree that there are clearly issues with varied provision within the NHS, the NHS does not vary its eligibility criteria in different local authorities and social care does. There are some areas where, under the current system, there are very clear distinctions in practice and that, bluntly, they are not human rights-based approaches by default. The very well-conceptions in section 1 of the bill prioritising human rights-based approaches could see that play through in a more equitable, in a more equal fashion. I have more detail, please. Okay, thanks for that, Hannah. Just another question that led the previous panel on the question of accountability. Do you agree or not that the ultimate accountability should rest with the cabinet secretary in the Scottish Government? Adam Snowding. That goes to myself first. Sorry, I had been left unmuted, so I wasn't sure. I think that ministerial accountability is a good concept. I think that it is useful to be able to have not marking your own homework, if I can put it in those terms. Sometimes, at the moment, when people are submitting complaints that we're hearing again and again that we're not sure who's dealing with the transparency isn't there, we don't know where to go, if we haven't got anywhere, there's something that is more devolved and has its benefits. But we do also question the longevity of some of that and whether there also needs to be a system that ensures anti-political changeover does not affect people's access to accountability structures. Yes, I think that it actually reflects what the public needs to be reduced at the present time. I think that if you look at probably minister's inboxes, you'll see lots and lots of people writing to them asking for them to fix and solve all the issues and difficulties in social care. So I think that in general public tend to think that the minister is responsible for social care. What I would say is that I think that the challenges of social care have been very difficult for many local authorities and IJBs to deal with. For me, this has to be about an inclusive engagement with everyone, this transition moving forward. Ultimately, I think that it's the right way to go, but I don't think it's simply because the system can be really appalled and I think that general public are keen for their government to be responsible for things that are not supposed to be. Okay, thanks very much for that. Thank you very much, Willie. We're now going to move to question from Miles Briggs. Thank you, convener. Good morning to the panel. Thanks for joining us today. It's my understanding that Lord Brailsford, the new chair of the Scottish Public Inquiry into the handling of the Covid-19 pandemic will meet with families today and I welcome that. I wanted to ask specificly, with regard to your organisations, whether or not you feel that Ann's law has been captured and embedded into legislation. I don't think that if you asked those who are initially calling for Ann's law, I don't speak for them to say, is this what we intended or what we needed, they would say is. I think that it's also a pretty complicated business getting it with all the different elements that are required. I mean, we're really supportive of it, have been through the whole pandemic. The really sad thing, and this is necessary at all, that essentially people's human rights were not realised to do this and what we didn't have often was a system in which people said, how can we make this happen? As opposed to defence, defence will close the doors, we need to make sure that this virus is stopped. There are lots of really good examples of that, I don't want to draw on too long apologies, but I think that there are a lot of very good things about the principles of this. Part of the concern I think is, and I know that there are some legitives of timeframes, is that how long it will take for this to be realised. At a meeting with the Guards implementation of care home visiting, which I'm part of, I think was a couple of weeks ago, there are still inconsistencies. Doors are closed for different reasons because of no virus or some other things that will be necessary in the future as much as a result of Covid, but Covid is much better managed now than it was before. We're meeting in person, there's no masks, these types of things, we're in a much better place vaccination programme, PPE is being used and available, so this is a really, I think, quite sad state of affairs that we're still not at a place where residents who read this and family members and carers are able to get exactly what they need everywhere. So until this bill is passed, that won't be law, but I think broadly speaking it's doing the right things, but I don't think it's as strong as some who've been calling for it would like. Does Henry or Hannah want to come in on that question? Yeah, thanks. I think there's some really fundamentally challenging issues associated with Anne's law that we have to look at too, and we can't just look at its integration. The first thing is that part of the reason that these relatives can't access the premises is because of the very nature, size and scale of the premises. We know that 1,600 people with dementia probably died as a consequence of living in a large scale regarding environments. Going forward, we have to say, is that the right model? Is that the way that we think we can deal with a future pandemic? Because at the time when everything really evolved, most people placed their trust in public girls' understanding of how to handle and deal with this pandemic. Very few people knew how to challenge that from the student safety challenge, whereas I think that the campaigners and the care home relative group have made the point, they've made the case, they've won that argument and we can never go back the way on that just now. And I think that, as it stands, the option again comes back to public health making decisions now. That needs to be challenged. There's other evidence, there's counter evidence, there's a merchant song theories that have probably eaten a few fish to get to this, you know. So I think that we're in a different place for a different debate, and some of what we, public health, just held all the cards and made all the decisions and never quite understood perhaps the impact that that had on those families and individuals, and perhaps still don't. I feel that we need a bigger public debate about the future of that long-term care estate. We need to question it, consider it, and we never can have families in that position ever again. So it's not just about Anne's Law, it's about the whole position, as far as we are concerned, as we will follow. Thank you. Hannah, did I see your hand up previously? Yeah, just building on Henry's points, which I think we would be very much in agreement there with, would be the imperative to take that learning from the pandemic about process, as well about the specifics, and use that to inform these discussions. So that could also include around discussions around the right to rehabilitation, right to independent living, and the way in which consistently throughout the early stages of the pandemic, we did not see disabled people, people living in long-term conditions or unpaid carers, having input in decision making. I think that that has particular relevance to the post framework bill in terms of the material around care board representation, but also the ministerial intervention case of emergencies, that there's no statement up present about a duty to have respect or to pay attention to the principles of co-production, the principles of human rights outlined in the early sections of the act. I would be really keen to see that there, because that is the functional threading through of some of that learning that's being referred to there and the impetus to not go back that colleagues have just commented on. Thank you. In your evidence to committees, the Alliance has suggested that there should be scope within the bill for creation of an independent authority to be able to hold ministers to account for their decisions. I just wonder if you could outline what you would see that looking like legally and what legal standing that would have as well. I should preface this for saying that I'm not a legal professional. That is really centred around the concept that it is really important that people can trust in the process. Trust in ministerial oversight, absolutely, but also trust that someone has the capacity to be properly looking out for what is working and what isn't working, because ministerial accountability bestwill in the world is not going to involve one person who's the capsaic with the capacity to go, what is happening in the data we are receiving, what gaps do we have, where do we not know what standard of care people are receiving, what is being done to combat that, what progress has been made, that has to be done by a team of researchers bluntly, or some variation on that thing. Part of our proposal for the independent role of that is to reinforce, to support public trust around that process, but also to provide a really useful resource that ministers can draw on as part of that ministerial responsibility role, as well as being held to account. It's a two-directional process that would be the proposal. I also think that I'll expect some of the early comments made around complaints, which is if you have an independent body, they can be part of a more proactive approach to problem solving. In the same way that, say, the Care Inspectorate's reports, I like good practice. They're not all about saying, you know, we're putting you into special measures that far from it. So, certainly, they can really straddle that space and also be available both for disabled people and people access and services to be aware of, but also staff and the workforce, so that they can be raising concerns and suggestions and flagging items. That's helpful. Thank you. I don't know if anyone else wants to make any points about that suggestion. If not, I'm happy to hand back. Nobody has indicated. Thanks, Miles. Okay, so I'm just going to say again, if members can direct their questions and please just allow the panel to indicate they want to come in on that question and please everybody keep your questions and responses succinct. We're now going to move to questions from Marie McNair, who's joining us online. Thank you. Good afternoon, panel. Thank you very much for your time this morning. I'm going to follow with the same line of questions from the previous panel. It's obviously, I just want to know about the impacts of integrated joint boards. I want to tease out, do you think that the model has had enough time to bed and make a difference? What are the implications of replacing them with care boards? I know there's been a bit of discussion about that already, but maybe if you could come in with an expand on that a wee bit, Hannah, if you don't mind. I would say that IJBs, whether they've had long enough, I don't have the same breadth of experience as previous colleagues who were involved in the 2014 setup, but we have clear evidence that they are not meeting the needs of disabled people, people living in long-term areas on a consistent basis. Part of that is due to the legislative framing of integration, so the key example that I would give that I think care boards have the potential to meet the problem would be around representation of lived experience and of the third and independent sectors in that we see real variants between boards that do and don't have those posts in IJBs and those that do don't. Maybe they have the available posts, but it's not filled or functionally. The order of business is 9am meetings. We've got to read 50 pages over the weekend, which people with unpaid care responsibilities etc. We've frequently heard, I can't do a 9am slot because that's when the support is coming in. The nuts and bolts and the system is not designed to engage properly with people with lived experience of accessing services. If care boards are from the outset, it is prerequisite that people with lived experience are part of them in order for decisions to be quarried. That's a very different political landscape at that point in terms of the language of co-production and input on decisions, which is a really key part of that definition. We'd like to see that fed throughout the whole process of wider health and social care design. Although it's very welcome that the bill in its current state acknowledges that possibility and highlights the possibility of paying people properly for their time rather than just expenses, which is another problem in the current system, it's not listed as an essential. Best way in the world if something is not a requirement, it will be the first thing that goes when people are under pressure. That would be something that we would really like to see changed in current ill structure. However, if care boards can learn from things such as the people-led policy panel and the success of some of the really good work that happened around social security and co-production, that would be really welcome and could potentially be a much more meaningful engagement with co-production on an on-going basis than we see in IJBs. I don't think that IJBs have worked. I think that there's a number of very important and significant issues of that song that have been mentioned. One of the areas that I would point to is that the process of commissioning a subsequent procurement through IJBs has led us into a state of the crisis in social care. Where I would just separately highlight that would be the non-committal framework in the agreement that IJBs have adopted across the country. I would support enough to chair and inquire on behalf of the Fair Work Convention. We looked very carefully at all of that, and we made some recommendations in 2019, one of which was to see that the IJBs have driven, through the framework agreements, many organisations and indeed many of the employees within that to carry the burden of risk in the burden of the variability within social care. That, for me, is a failure of planning, it's a failure of proper commissioning. That's what leads to organisations having zero-year contract workers and not knowing how many years are going to be required. All of that then feeds into the actual willingness and desire of someone to work within social care. We've got 1,000 organisations, we've got 200,000 staff, 89 per cent of women, and we don't have any collective voice for that group of workforce at all. That, for me, is where social care has started to become more and more under pressure, more greater difficulties and that lack of really significant planning, proper commissioning and making sure that organisations are given the right level of contract with the right number of staff to deliver the needs that's led to where we are in terms of crisis. That's one area that IGIBs have struggled with. I don't think that the cultures have ever really emerged. We've got a name and we've got a logo and we've got a label, but have we really got one culture between all that was put into the individual IGIBs? Probably not. Moving forward, the idea of not having two different line management structures and two different report and procedures and having one national peer service seems to make sense, but there's a lot of work to be done to deliver on that. Thanks, Henry. In following up, do you recognise the situation that was expressed by the minister last week that currently people feel they've been pushed from pillar to post if they, for example, have a complaint or concerns about the service? You share that view. Yeah, well, I think what happens is that it's very difficult, first of all, to find out who to complain to, how to complain, where to go to. I think that my experience of people is that they really only complain when things get really serious and really significant and I would certainly support that. I think that that's very fair and a true and active reflection of what's happening with the industry. Thank you. Very briefly, does anyone else want to come in on that question? Adam? I will be really brief. If you look at accountability for IGIBs, there isn't that much in terms of the public. If you ask the public who are on the IGPs, what do they do? I think that there's very low understanding. I'll refer back to a report from Audit Scotland a couple of years ago where we were talking about how they just haven't worked yet. It's a very good question about whether they need more time, but do we have time to wait for that? Will that in itself fix social care? If it's such a broad kind of ask, in a sense it's fixed social care is pretty tricky, isn't it? If you're going to look at a national care service, there's a model to support that through care boards, but I think that IGIBs, despite a lot of good work, have been maybe even commissioning work. It's been a race to the bottom in terms of the cheapest costs for people to deliver, to procure care. I think that there's a lot more that they could do and I don't think that we've got time to see if that settles. Hannah, you wanted to come back in on the people being moved from pillar to post question. Just on that second question, yes they are, but I think one specific area I'd like to flag that I think is often not a lot of attention is paid for too, is the need for a complaint system and that sort of redress situation to be accessible to family and friends of people who access care or wish to access care and have since passed away. At the moment, the current system essentially investigation ceases in many cases after an individual has died and that is not fair on those families, it's not fair on those individuals, it also sets a really poor precedent in terms of learning and the ability to build upon when things don't work. So we would strongly welcome material that would alter that current state of play. Thank you, Mary, and thanks Hannah for flagging up that aspect. Mark, you've got some questions. We've heard concerns from local authorities and trade unions about the prospect of a wholesale transfer of staff and assets to a new national service and the minister last week tried to allay those by saying that it would only be as a provider of last resort in result of a failure. I just wanted to come to Hannah first and ask if you know what's led to that level of confusion, why was there such a concern amongst the sector about a wholesale transfer of staff and what your view actually would have been if that comes to pass? I think that this is responding on the hoof but I have not and a number of colleagues have not read the bill in the same way that has since been outlined by the minister. The understanding had been that there is the possibility of wholesale movement of staff and that that caused understandable concern, particularly among other areas in the bits where sections where it was explicit that NHS staff would not be moved and questioning, well what does that mean for NHS Highland who provides social care via for adult services? So there was some significant confusion amongst third sector colleagues around those sections. If, as the minister outlines, the transfer of staff will only happen in emergency, then I would return to my comments about being clear on the definition of an emergency, the length of time, whether something is permanent or short term, and how the human rights of both people accessing services and workforce and their work embedded throughout that are going to be respected throughout any such process. I think that material on that would reassure because at the moment it's considerable uncertainty in this sector that is already doggling and under considerable pressures and so stress is not a desirable addition in that context. Does that make sense? Yeah, yeah, thanks. I don't know if Adam or Henry wanted to come in. No. No, okay, that's fine. My other question was just around trust. The review report said that trust is not currently in plentiful supply and social care support when they're whether you'd agree with that, whether you would recognise that there is a difference in trust in social care in the NHS and why you think that might be. Come to Adam first. I think there's certainly an issue of trust and it's both sides, I think, for those who receive social care and those who are delivering social care. I think a lot of folks, in terms of like key workers in social care, might have a lack of trust in the system or in the, maybe, their employers or what they are getting themselves in terms of not just the kind of pay but conditions and training and all the types of things that support this. You've got unpaid carers who've got an extraordinary heavy burden on them to try and pick up everything when it comes to making sure that their loved one is in the best, the best healthy can possibly be. But I think if you looked at the last two and a half years to three years and social care has had probably the worst period of PR it could ever have had, not for what I've tried to do a really good job. It has been faced with a crisis in the beginning of Covid when care homes are essentially and social care providers left on their own to try and find PPE. You know, we've heard these stories, we can't forget that, that people were going on Amazon to try and find anything, but it was channeled broadly speaking to the NHS. Now, whether this was a decision that might all come out in the wash within the independent inquiry, UK and Scottish, but how these things happened, so response and what happened in social care meant that it was hard to deliver it because of these types of things. So, it felt like, if you're talking about trust, it felt like the NHS was protected for more than social care. I think that's an incredible hangover from that. As people had their social care packages removed with no warning or indeed not returned to levels that were initially assessed as their need, so that's the point. It's not as if what you get now is at some point you've been assessed as needing, this hate is care, and then all of a sudden you no longer need that much care. So, I think there is, there are big challenges there, and it's a lot of this about resource and making sure you can access it when you need it and as much as you need it. Thank you, thanks, I don't know if there's anyone on me. Oh yes, so Henry, you'd like to come in and I think you wanted to come in on the previous question as well, so if you can pull that in, that would be great. In terms of the trust issue, I think what's really important to understand is that the majority of the public get a surprise when they start to require social care services because they end up in this form of financial assessment, they end up having to contribute, having to pay for it, and that has been very big across 32 different authorities, but particularly for our people who are most concerned about when people reach the advanced stage of dementia, they might need to go to a care home, they're then facing bills of £1,200 per week, so they think that care is going to be free, the public generally thinks that care is going to be free, and when you enter the social care arena and you realise it isn't, obviously it will affect your perception of that, it's almost a damaged psychological contract that we've got that you work your whole life and all of a sudden you need something that you have to pay, either a component or for all of that, so that really impacts in my opinion on the trust, whereas with NHS, you never experience that and you tend to receive the care that you require, albeit that you may have to wait sometimes in various associations for it, so we've got two very different approaches and very different structures, but actually a very similar perspective around that, and that ultimately leads to a significant damage of trust, and indeed we have got a campaign that's targeting the inequalities around that which I won't get introduced now, but I really do think that that's something that you must bear in mind, that social care has always had this means-tested charring ability that actually makes people very confused and causes a trust failure. Thanks, Henry. Okay, we're going to move on to questions from Paul MacLennan. Yeah, thank you, convener. A couple of questions, I think, for me. On, we've talked about before in the previous session as well, and about, can you mean discussing about the framework, this is the framework element off the bill, and it's kind of moving on to the co-design would be the next stage, just to ask the panel what they would see their part in the co-design or what they would like to see as their part in the co-design process as we move forward. In the second question, the minister mentioned last week that the national care service represents the greatest opportunity as it existed for the profession for a very long time. Just your thoughts on that comment as well. I'll open it up probably to yourself, Hannah, first of all, and then open it up beyond that. I mean, first up, the alliance is very interested in being involved in co-production work so that we can share as many opportunities as widely as possible with our membership. What I would say the feedback we have had from them thus far is that the existing structures around the co-production work or by much of it is really good are not transparent, and that goes back to those questions about trusts that have just been outlined. I think that we could be seeing on-going improvement also in terms of inclusive communication and access. Hannah, just on that point, you're saying not transparent. What would you like to see in case of more transparency? So, off the top of my head, it's really welcome that you've got the lived experience expert panels. It wasn't clear from the information shared whether this was selective, whether everybody who wanted to be involved would be involved, just kind of basic columns essentially. But also a lot of the information is shared online only. What does that do around digital choice and digital access and what paid population groups and just not going to hear about stuff? There are a lot of material there. I think also there are concerns we have heard from within our membership at the timescales, particularly given the different developments across one of the core mainstream national care service work and the questions about whether to include justice services and children and young people services. Real concerns about making sure we don't retrofit children and young people services are included because a retrofitted system is not the way for purpose, it's not the way properly co-produced, but making sure that co-production work is fully inclusive of all potential groups from the very outset because universal accessibility is no bad thing even if things and even if those parts of the system are not in the end included. With regard to opportunity, the mention is a fair worker really welcome but not having a lot of detail has raised some concerns. There's the potential for this to be an opportunity. At the moment we know that yes there was a pay-up lift for social care staff but pay-up lift doesn't come with an ongoing promotional track in the way that NHS have, so something that could do that would be really welcome. Similarly that uplift did not apply to children and young people's social care workers but there are some existing disparities that are still being perpetuated, can that be addressed? We've also heard substantially from colleagues for example within the sensory loss sector who talk about the level of expertise required to be a guide communicator and that that is not noticed or acknowledged within the current systems either in terms of continued professional development or in terms of pay or conditions. So lots of scope to improve whether the bill will improve that is another question but the opportunity is welcome particularly if there's a real drive to get into that and lots of bolt stuff and see meaningful improvement for the sector. Henry wants to come in on that one. I think that the national care service has to have a national agreed body that represents social care workers alongside it. We need standard terms and conditions, we need to move away from the variety that we've got across the whole sector and give us people a sense of security. Again that was recommended by the Fair Work Convention's report and it's not happening yet but it really does need to happen. In terms of sort of co-design, I think that it would be very difficult to co-design the next stage of this bill including everyone and I think it's got to be chunked down in its specific bits of work, bits of any areas and people need to be brought in and engaged from the beginning but perhaps more depth across different pieces. So for example the ways of organisation have been campaign working with members for 40 years. We've got many thousands of members, we've got active voice groups, they all want to be part of this and we have to find a way I think at the right point in time using that skill and that expertise and using the line I think on the third sector because the third sector exists to do the very thing that now wants to be done. Something that the Government needs to create a new methodology on what we can do but quite frankly decades. I think that there's a lot to learn from our sector and we can do a lot more in partnership as opposed to create some new structures that perhaps they need a lot of help from but central component but there's a lot out there, a lot of organisations out there that can really be engaged and supported. However that does require some investment, it requires some funding, it requires some thought. I think the first part there was with regard to involvement. I think there is a lot of insight from older people, carers, family members that Age Scotland's helpline will have collated over many many many years that advises on that, we'll know what people are calling about in terms of what is good, what's not so good. I think that that's something that we would want to offer in terms of that kind of general public take on it. They've also got elements of work which they support people with experience of dementia which we'll have, eth minority older people, LGBTQ plus older people as well to making sure that their voices, their experiences, indeed their aspirations for social care are heard. I think that this is as much about the future as it is about today and fixing, you know, the national care service isn't going to fix the problems we're facing in social care today, tomorrow but we're looking into the future. We want to make sure that as more people may need it and whoever you are and whatever you might need wherever you are that that is fully recognised and understood and also for organisations like Age Scotland and many many others to test the ideas and to scrutinise some of the ideas that are coming out of co-design and co-production to actually work out in reality. Do we think that this will work or not? I think that that's another part is that we often have this to the Government about let's have a blank sheet paper and all come together and create this thing. Actually sometimes we want a little bit of leadership as well from the Government, say this is how it will work in actual practice, this is the framework that we've got, this is how the world operates. What do you think could improve that or where do you think they kind of blocks to this happening or? Okay. Thank you for that. Can you come to the time? So that's me. Thanks Paul. So that we've come to the end of our questions and I thank you all for joining us and giving evidence today. I think it's been useful for the committee to hear your reflections on the national care service bill. And as we agreed at the start of the meeting to take the next two items in private, there's no more public business today and I now close the public part of the meeting.


Everyone welcome to today's day trading recap Tuesday February 9th another green day keeping the green streak alive plus 1200 even today Took a little bit of a roundabout way to get there is a little wild wild ride in the markets this morning But ended up positive on the mighty 90 front. We just did two trades both of those were losers Boba minus 160 Microsoft 370 and Then we took a pairs trade I put it in pre-market, and then I actually added to it after the market opened It just kept going against me So I ended up just bailing took a pretty decent loss as far as what I do usually do on pairs trades minus 5 79 So the morning did not start out the greatest But it ended up very well as the runners came roaring back. I did four runners all four winners plus 2309 so net net for all trades plus 1200 on the day Airbnb plus 270 Boeing was my biggest winner plus 1123 Netflix which was just testing everybody's in the community's patience today Ended a book in the nice 640 and then Walmart 276. So let's check these out Start with the losers start with the mighty 90s Baba let me get to Baba here So with Baba had this nice nice volume spike here. We were looking for a point of exhaustion Actually waited a little bit got short here Started to come down. I was trying to get out of part of it And it just didn't quite get there and it ripped higher and so when it finally rolled over a little bit We just bailed on the rest of it about right down here So I ended up taking a small loss of minus 160 on Baba and then Microsoft kind of a similar situation. We were in these somewhat similar timeframe here Got this volume spike Started to roll over but it was pretty strong at that point and just ripped higher on us So we waited waited waited waited and finally when it came down here We just got out and took a loss on on Microsoft onto the runners Airbnb Airbnb is not one we trade a lot But this was actually called out by somebody in the community, which is awesome. That is what I love about the community I can't see everything at all times and so love having people Call out certain things that they see once they learn the strategy So had this big push-up big second volume bar on this pullback We got long right here and this thing was just a quick winner just ripped up I did leave I took off about right here left some on the table because we did have another extension higher But still booked 270 on that one Boeing my biggest winner See where's Boeing So Boeing Another one that kind of tested our patience, but worked out really well. So I had this had this initial push-up Big spike in volume and then it just started to chop around in positive territory chop chop chop Look like it's gonna flush us out a couple times two three four or five times and then finally Gave us the pay dirt and just ripped higher. I got out about right here on these big volume spikes I was looking for it to potentially pull back a little bit and I was gonna get back in But so I got out of all of it right there I did give us a little bit more. I know some people stayed in for a little bit more profit, but still booked $1,123 on the trade so nice trade in Boeing and then Netflix Netflix was a beast today for us Both and get in a bad way so Netflix Had this initial strength and massive volume coming in So we were looking for a pullback for a potential continuation with more strength Well, we got into our first first little bit right here I scaled into a little bit more right here and then this thing just kept bleeding bleeding bleeding bleeding and and Really the goal was here I mean it was never given us a reason to get out and so and and the volume was low It was just kind of bleeding sideways to lower and finally when it got down to this orange line yesterday's open kind of a key level we jumped in with a little bit more and I think it was on yeah So then set through even more chop more chop and then finally when we got this bounce I closed out that ad booked a nice profit on that piece was hoping for a Continuation higher to get out of the rest, but it started rolling over so we sat through all this chop I didn't add back in again I was pretty much done for the day in fact if it would have broken below this level here I was just gonna bail and take a loss on the trade But it held and then finally boom right at the end of the day We got out of everything by 11 30 I usually like to be done by by 10 or 10 30 central So we played a little overtime this morning, but it paid off ended up booking 640 on that next Netflix trade and then Walmart booked 276 Let's take a look at Walmart another runner So Walmart big big volume bar here, so we're waiting for a pullback We got long after just this little pullback here right right about there and this thing pushed up force nicely Got out of most of it at this point when it started to pull back back down towards the blue line In fact, I didn't even let it get all the way down there I thought it was gonna keep going up and so I ended up adding back in right here Did get a bounce, but then it just kind of rolled over and so when it got down to here I Didn't add it. I was just holding my original position and finally we got this got this relief rally and I ended up I was trying to get out of half my position right here But I put the order in incorrectly into my platform So I ended up closing the whole thing out right there Actually, it was right here ended up closing it all I meant to close half But ended up closing it all out right there, but still book 276 left some chips on the table just from a Personal error, but that's okay Plus 1200 for the day. So keeping the green streak alive. We'll be back streaming live tomorrow. We'll catch you there. Cheers