Error modeling schemes for fading channels in wireless communications: A survey
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paper_title: A trace-based approach for modeling wireless channel behavior

paper_content:

The loss behavior of wireless networks has become the focus of many recent research efforts. Although it is generally agreed that wireless communications experience higher error rates than wireline, the nature of these lossy links is not fully understood. This paper describes an effort to characterize the loss behavior of the AT&T WaveLAN, a popular in-building wireless interface. Using a trace-based approach, packet loss information is recorded, analyzed, and validated. Our results indicate that WaveLAN experiences an average packet error rate of 2 to 3 percent. Further analysis reveals that these errors are not independent, making it hard to model them with a simple two-state Markov chain. We derive another model based on the distributions of the error and error-free length of the packet streams. For validation, we modulate both the error models and the traces in a simulator. Trace-driven simulations yield an average TCP throughput of about 5 percent less than simulations using our best error model.
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paper_title: Measurement and analysis of the error characteristics of an in-building wireless network

paper_content:

There is general belief that networks based on wireless technologies have much higher error rates than those based on more traditional technologies such as optical fiber, coaxial cable, or twisted pair wiring. This difference has motivated research on new protocol suites specifically for wireless networks. While the error characteristics of wired networks have been well documented, less experimental data is available for wireless LANs.In this paper we report the results of a study characterizing the error environment provided by AT&T WaveLAN, a commercial product designed for constructing 2 Mb/s in-building wireless networks. We evaluated the effects of interfering radiation sources, and of attenuation due to distance and obstacles, on the packet loss rate and bit error rate. We found that under many conditions the error rate of this physical layer is comparable to that of wired links. We analyze the implications of our results on today's CSMA/CA based wireless LANs and on future pico-cellular shared-medium reservation-based wireless networks.
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paper_title: Mobile Communications Design Fundamentals

paper_content:

From the Publisher: ::: The most recent addition to William C. Y. Lee's acclaimed series on mobile and cellular communications, Mobile Communications Design Fundamentals, Second Edition offers designers, researchers, and students an up-to-date, invaluable guide to the theoretical framework of mobile radio communications and how such systems are designed. With an abundance of new material, this Second Edition covers leading-edge Personal Communications Service (PCS), microcell, and CDMA systems, providing all the theoretical and design knowledge and know-how needed to design with both present and future technology. Useful as a professional handbook or as a senior/graduate level text, the book provides complete coverage of the differences between fixed and wireless radio systems, up to and including the new FCC-promoted PCS systems; an authoritative description of the mobile radio environment that gives engineers the necessary technical background to confidently select the appropriate radio technology; definitive, clearly presented design parameters for both the base and mobile units; troubleshooting approaches that help you anticipate the problems associated with each system and solve them when they arise; comprehensive guidelines for how to develop the system design and frequency plan and how to tackle all capacity issues, and new information on CDMA, a hot broadband radio technology...boosting microcell technology capacity with system planning...built in prediction...analyzing digital communication systems...and covering noncellular mobile radio systems, including those for data communication. With more than half of the material in this new edition based on the author's own widely recognized research work, Mobile Communications Design Fundamentals is a book no one interested in the new wave in mobile communications can afford to miss.
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paper_title: Characteristics of a digital mobile radio channel

paper_content:

A field test has been made in order to better understand the digital mobile radio channel. At the mobile receiver (450 MHz, 1200 bits/s) recordings were made of the digital signal and the field strength. These recordings were later analyzed by a computer. Some existing models for digital channels have been tested. Theoretically motivated probability density functions for the fading envelope have also been considered. A new model for the digital channel is proposed. This model is a memoryless binary symmetric channel (BSC) with field strength dependent crossover error probability. This model fits very well to the recorded data.
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paper_title: The land mobile satellite communication channel-recording, statistics, and channel model

paper_content:

The communication channel between the MARECS satellite at 26 degrees W and a cruising van was measured and recorded in European areas exhibiting satellite elevations from 13 to 43 degrees . Different environments and mobile antennas were tested. The results of an extensive statistical evaluation include spectra of the fading amplitude; probability density, and distribution of the received signal power; and the percentage of time for fade and nonfade periods. Based on the physical phenomena of multipath fading and signal shadowing, an analog model of the land mobile satellite channel which can readily be used for software and hardware fading simulation is developed. The most important parameter of this model is the time-share of shadowing. The Rice factor which characterizes the channel during unshadowed periods, can vary from 3.9 to 18.1 dB. Block error probability density, error gap distribution, and block error probability are discussed. >
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paper_title: Statistical Methods in Radio Wave Propaga-tion

paper_content:

A dispenser such as may be needed in conjunction with machines for vending canned food items (e.g., hot cans of soup) to dispense bowls (e.g., paper or plastic bowls) for holding the items. It holds two stacks of bowls, with each bowl in each stack nested in the next bowl below. A stack support is reciprocable between a first position holding up a first of the two stacks at the bottom and clear of the second stack, and a second position holding up the second stack and clear of the first. A first pair of wedging fingers is movable with the stack support for entry between the rim of the bottom bowl of the first stack and the next bowl above when the stack support moves from its first to its second position to wedge the bottom bowl away from the next bowl above and insure its dropping away from the first stack, which is then held up by these first wedging fingers. A second pair of wedging fingers is movable with the stack support for entry between the rim of the bottom bowl of the second stack and the next bowl above when the stack support moves from its second to its first position to wedge this bottom bowl away from the next bowl above and insure its dropping away from the second stack, which is then held up by these second wedging fingers.
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paper_title: The distribution of amplitude scintillation and the conversion of scintillation indices

paper_content:

Abstract The relationship between the most commonly used measures of scintillation depth is deduced assuming that the probability density of amplitude distribution is Nakagami's m -distribution.
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paper_title: Probability functions for the modulus and angle of the normal complex variate

paper_content:

This paper deals mainly with various ‘distribution functions’ and ‘cumulative distribution functions’ pertaining to the modulus and to the angle of the ‘normal’ complex variate, for the case where the mean value of this variate is zero. Also, for auxiliary uses chiefly, the distribution function pertaining to the reciprocal of the modulus is included. For all of these various probability functions the paper derives convenient general formulas, and for four of the functions it supplies comprehensive sets of curves; furthur, it gives a table of computed values of the cumulative distribution function for the modulus, serving to verify the values computed by a different method in an earlier paper by the same author.1
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paper_title: Co-channel interference of microcellular systems on shadowed Nakagami fading channels

paper_content:

The probability of cochannel interference is evaluated for a microcellular environment with log-normal shadowing and Nakagami fading. For the case when the interfering signals have the same shadowing and fading statistics, an exact mathematical expression is presented for the probability of cochannel interference. For the case when the interfering signals have different shadowing and fading statistics, the probability of cochannel interference is evaluated by approximating the individual interfering signals as having a log-normal distribution, and then applying Schwartz and Yeh's method to obtain a purely log-normal distribution for total interference, while maintaining a composite Nakagami log-normal distribution for the desired signal.
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paper_title: Statistical channel impulse response models for factory and open plan building radio communicate system design

paper_content:

Statistical radio channel impulse response models are presented for the analysis and design of wireless factory and open plan office communication systems. The models incorporate first- and second-order statistics to characterize the discrete impulse responses of indoor radio channels for both line-of-sight (LOS) and obstructed (OBS) topographies. The effects of large-scale transmitter-receiver separation distance, small-scale receiver movement, and models for the correlation of multipath component amplitudes over 1 m local areas are developed from 1.3 GHz measurements. SIRCIM, a computer simulator based on the models presented, has recreated multipath power delay profiles and CW fading profiles that are representative of measured data. Large-scale models for path loss are implicitly included in this work. >
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paper_title: Some Tropospheric Scatter Propagation Measurements near the Radio Horizon

paper_content:

Measurements of small variations in 100 mc field intensity within and just beyond the radio horizon are reported. The measured fields are assumed to be the resultant of two field components, one having a constant amplitude and the other being a rapidly-fading scattered component. The fading range of the resultant field intensity over a 10-minute period is used to determine K. Here, K is the ratio in decibels of the root-mean-square amplitude of the scattered component to the amplitude of the constant vector. Curves showing the measured median values of basic transmission loss, fading rate, and K plotted vs hour of the day are included for three of the Cheyenne Mountain transmission paths. Diurnal variation of these quantities is also discussed. The average basic transmission loss of the scattered component, Lba8, can be found if K and the resultant basic transmission loss, Lbm are known. Median values of Lba8 and Lbm are plotted vs the angular path distance, ?. Measurement of the correlation of the resultant field strengths received on two horizontally-spaced antennas within the radio horizon is reported. When the spacing was varied from ? to 20 wavelengths and the correlation compared to other characteristics of the field, the correlation was found to be as much a function of Lba8 and fading rate as it was of antenna spacing.
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paper_title: Statistical analysis and characterization of the indoor propagation channel

paper_content:

This paper presents statistical analysis of data obtained by measuring narrowband path loss at DECT (digital enhanced cordless telecommunications) frequency (1.89 GHz) in an indoor environment. Specific goodness-of-fit tests are applied to the data. The tests assess whether the data generating source belongs to a known family of random variables. Results obtained support that local path-loss distribution can be represented as Weibull or Nakagami in most environments. The close resemblance between such distributions and Rice distribution (with Rayleigh as a special case) confirms that Rice/Rayleigh description of fading can be applied to indoor environments. That similarity leads to a general, simple, approximate expression for the cumulative distribution function of the signal-to-interference ratio. The expression can be used without limitations to the number and the parameters of the Rice interferers.
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paper_title: Microwave Mobile Communications

paper_content:

From the Publisher: ::: IEEE Press is pleased to bring back into print this definitive text and reference covering all aspects of microwave mobile systems design. Encompassing ten years of advanced research in the field, this invaluable resource reviews basic microwave theory, explains how cellular systems work, and presents useful techniques for effective systems development. The return of this classic volume should be welcomed by all those seeking the original authoritative and complete source of information on this emerging technology. An in-depth and practical guide, Microwave Mobile Communications will provide you with a solid understanding of the microwave propagation techniques essential to the design of effective cellular systems.
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paper_title: A Unified Approach to the Probability of Error for Noncoherent and Differentially Coherent Modulations Over Generalized Fading Channels

paper_content:

We present a unified approach to determine the exact bit error rate (BER) of noncoherent and differentially coherent modulations with single and multichannel reception over additive white Gaussian noise and generalized fading channels. The multichannel reception results assume independent fading in the channels and are applicable to systems that employ post-detection equal gain combining. Our approach relies on an alternate form of the Marcum Q-function and leads to expressions of the BER involving a single finite-range integral which can be readily evaluated numerically. Aside from unifying the past results, the new approach also allows for a more general solution to the problem in that it includes many situations that in the past defied a simple solution. The best example of this occurs for multichannel reception where the fading on each channel need not be identically distributed nor even distributed according to the same family of distributions.
---
paper_title: Statistical Methods in Radio Wave Propaga-tion

paper_content:

A dispenser such as may be needed in conjunction with machines for vending canned food items (e.g., hot cans of soup) to dispense bowls (e.g., paper or plastic bowls) for holding the items. It holds two stacks of bowls, with each bowl in each stack nested in the next bowl below. A stack support is reciprocable between a first position holding up a first of the two stacks at the bottom and clear of the second stack, and a second position holding up the second stack and clear of the first. A first pair of wedging fingers is movable with the stack support for entry between the rim of the bottom bowl of the first stack and the next bowl above when the stack support moves from its first to its second position to wedge the bottom bowl away from the next bowl above and insure its dropping away from the first stack, which is then held up by these first wedging fingers. A second pair of wedging fingers is movable with the stack support for entry between the rim of the bottom bowl of the second stack and the next bowl above when the stack support moves from its second to its first position to wedge this bottom bowl away from the next bowl above and insure its dropping away from the second stack, which is then held up by these second wedging fingers.
---
paper_title: Probability functions for the modulus and angle of the normal complex variate

paper_content:

This paper deals mainly with various ‘distribution functions’ and ‘cumulative distribution functions’ pertaining to the modulus and to the angle of the ‘normal’ complex variate, for the case where the mean value of this variate is zero. Also, for auxiliary uses chiefly, the distribution function pertaining to the reciprocal of the modulus is included. For all of these various probability functions the paper derives convenient general formulas, and for four of the functions it supplies comprehensive sets of curves; furthur, it gives a table of computed values of the cumulative distribution function for the modulus, serving to verify the values computed by a different method in an earlier paper by the same author.1
---
paper_title: Co-channel interference of microcellular systems on shadowed Nakagami fading channels

paper_content:

The probability of cochannel interference is evaluated for a microcellular environment with log-normal shadowing and Nakagami fading. For the case when the interfering signals have the same shadowing and fading statistics, an exact mathematical expression is presented for the probability of cochannel interference. For the case when the interfering signals have different shadowing and fading statistics, the probability of cochannel interference is evaluated by approximating the individual interfering signals as having a log-normal distribution, and then applying Schwartz and Yeh's method to obtain a purely log-normal distribution for total interference, while maintaining a composite Nakagami log-normal distribution for the desired signal.
---
paper_title: A Unified Approach to the Performance Analysis of Digital Communication over Generalized Fading Channels

paper_content:

Presented here is a unified approach to evaluating the error-rate performance of digital communication systems operating over a generalized fading channel. What enables the unification is the recognition of the desirable form for alternate representations of the Gaussian and Marcum Q-functions that are characteristic of error-probability expressions for coherent, differentially coherent, and noncoherent forms of detection. It is shown that in the largest majority of cases, these error-rate expressions can be put in the form of a single integral with finite limits and an integrand composed of elementary functions, thus readily enabling numerical evaluation.
---
paper_title: Mobile Communications Design Fundamentals

paper_content:

From the Publisher: ::: The most recent addition to William C. Y. Lee's acclaimed series on mobile and cellular communications, Mobile Communications Design Fundamentals, Second Edition offers designers, researchers, and students an up-to-date, invaluable guide to the theoretical framework of mobile radio communications and how such systems are designed. With an abundance of new material, this Second Edition covers leading-edge Personal Communications Service (PCS), microcell, and CDMA systems, providing all the theoretical and design knowledge and know-how needed to design with both present and future technology. Useful as a professional handbook or as a senior/graduate level text, the book provides complete coverage of the differences between fixed and wireless radio systems, up to and including the new FCC-promoted PCS systems; an authoritative description of the mobile radio environment that gives engineers the necessary technical background to confidently select the appropriate radio technology; definitive, clearly presented design parameters for both the base and mobile units; troubleshooting approaches that help you anticipate the problems associated with each system and solve them when they arise; comprehensive guidelines for how to develop the system design and frequency plan and how to tackle all capacity issues, and new information on CDMA, a hot broadband radio technology...boosting microcell technology capacity with system planning...built in prediction...analyzing digital communication systems...and covering noncellular mobile radio systems, including those for data communication. With more than half of the material in this new edition based on the author's own widely recognized research work, Mobile Communications Design Fundamentals is a book no one interested in the new wave in mobile communications can afford to miss.
---
paper_title: On the Probability of Error for Multichannel Reception of Binary Signals

paper_content:

In this paper a derivation of the probability of error which arises in 1) adaptive multichannel reception of binary signals and 2) multichannel communication with binary signaling over channels that are characterized by both a specular (nonfading or constant) component and a Rayleigh fading component is presented.
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paper_title: Unified error analysis of DQPSK in fading channels

paper_content:

A general result is derived for the bit error rate (BER) of differential quadrature phase shift keying (DQPSK) for reception in slow fading and additive white Gaussian noise (AWGN). Fading models include Rayleigh, Rician, Nakagami and shadowed Rician, which describe a wide range of fading conditions encountered in mobile communications. Easily computable, the result is potentially useful in evaluating the BER of such systems.
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paper_title: Finite-state Markov channel-a useful model for radio communication channels

paper_content:

The authors first study the behavior of a finite-state channel where a binary symmetric channel is associated with each state and Markov transitions between states are assumed. Such a channel is referred to as a finite-state Markov channel (FSMC). By partitioning the range of the received signal-to-noise ratio into a finite number of intervals, FSMC models can be constructed for Rayleigh fading channels. A theoretical approach is conducted to show the usefulness of FSMCs compared to that of two-state Gilbert-Elliott channels. The crossover probabilities of the binary symmetric channels associated with its states are calculated. The authors use the second-order statistics of the received SNR to approximate the Markov transition probabilities. The validity and accuracy of the model are confirmed by the state equilibrium equations and computer simulation. >
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paper_title: Digital Communications: Fundamentals and Applications

paper_content:

For courses in Digital Communications. Exceptionally accessible, this book presents the often "difficult" concepts of digital communications in an easy-to- understand manner-without diluting the mathematical precision. Using a student-friendly approach, it develops the important techniques in the context of a unified structure (in block diagram form)-providing organization and structure to a field that has, and continues, to grow rapidly, and ensuring that students gain an awareness of the "big picture" even while delving into the details (the most up-to-date modulation, coding, and signal processing techniques that have become the basic tools of our modern era). It traces signals and key processing steps from the information source through the transmitter, channel, receiver, and ultimately to the information sink.
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paper_title: Analysis of DPSK with equal gain combining in Nakagami fading channels

paper_content:

A new closed form for the bit error rate of a binary non-coherent DPSK receiver with equal gain combining diversity over frequency non-selective m-distributed Nakagami fading channels is presented. The analysis is shown to be efficient and accurate in the simulation.
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paper_title: Bit error rate of DQPSK signals in slow Nakagami fading

paper_content:

A new expression for the bit error rate of DQPSK signals operating in slow Nakagami fading and additive white Gaussian noise is derived. The proposed formula can be easily computed numerically, and, hence, can be usefully exploited in the performance evaluation of digital mobile radio systems.
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paper_title: BER performance of DQPSK in slow Rician fading

paper_content:

A new expression involving an infinte series of finite integral terms is derived for the bit error rate (BER) of DQPSK in slow Rician fading channels. The formula reduces to a new closed form BER expression for DQPSK in Rayleigh fading channels when the K factor (ratio of LOS to multipath power) equals zero.
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paper_title: Reception Through Nakagami Fading Multipath Channels with Random Delays

paper_content:

The Nakagami fading distribution is shown to fit empirical results more generally than other distributions. A statistical model for a noisy, Nakagami fading multipath channel is given, following Turin's delay-line model. Optimal receivers are derived for two states of knowledge of the channel-known path delays and random path delays. Upper bounds on the probability of error are computed, for binary, equal-energy, equiprobable signals, which are uniformly orthogonal and have equal, triangular, autocorrelation moduli. Results are graphically displayed and show the dependence of error probability on number of paths, amount of fading and spread of path delays.
---
paper_title: A Unified Approach to the Performance Analysis of Digital Communication over Generalized Fading Channels

paper_content:

Presented here is a unified approach to evaluating the error-rate performance of digital communication systems operating over a generalized fading channel. What enables the unification is the recognition of the desirable form for alternate representations of the Gaussian and Marcum Q-functions that are characteristic of error-probability expressions for coherent, differentially coherent, and noncoherent forms of detection. It is shown that in the largest majority of cases, these error-rate expressions can be put in the form of a single integral with finite limits and an integrand composed of elementary functions, thus readily enabling numerical evaluation.
---
paper_title: A trace-based approach for modeling wireless channel behavior

paper_content:

The loss behavior of wireless networks has become the focus of many recent research efforts. Although it is generally agreed that wireless communications experience higher error rates than wireline, the nature of these lossy links is not fully understood. This paper describes an effort to characterize the loss behavior of the AT&T WaveLAN, a popular in-building wireless interface. Using a trace-based approach, packet loss information is recorded, analyzed, and validated. Our results indicate that WaveLAN experiences an average packet error rate of 2 to 3 percent. Further analysis reveals that these errors are not independent, making it hard to model them with a simple two-state Markov chain. We derive another model based on the distributions of the error and error-free length of the packet streams. For validation, we modulate both the error models and the traces in a simulator. Trace-driven simulations yield an average TCP throughput of about 5 percent less than simulations using our best error model.
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paper_title: A Markov-based channel model algorithm for wireless networks

paper_content:

Techniques for modeling and simulating channel conditions play an essential role in understanding network protocol and application behavior. In [11], we demonstrated that inaccurate modeling using a traditional analytical model yielded significant errors in error control protocol parameters choices. In this paper, we demonstrate that time-varying effects on wireless channels result in wireless traces which exhibit non-stationary behavior over small window sizes. We then present an algorithm that divides traces into stationary components in order to provide analytical channel models that, relative to traditional approaches, more accurately represent characteristics such as burstiness, statistical distribution of errors, and packet loss processes. Our algorithm also generates artificial traces with the same statistical characteristics as actual collected network traces. For validation, we develop a channel model for the circuit-switched data service in GSM and show that it: (1) more closely approximates GSM channel characteristics than a traditional Gilbert model and (2) generates artificial traces that closely match collected traces' statistics. Using these traces in a simulator environment enables future protocol and application testing under different controlled and repeatable conditions.
---
paper_title: Microwave Mobile Communications

paper_content:

From the Publisher: ::: IEEE Press is pleased to bring back into print this definitive text and reference covering all aspects of microwave mobile systems design. Encompassing ten years of advanced research in the field, this invaluable resource reviews basic microwave theory, explains how cellular systems work, and presents useful techniques for effective systems development. The return of this classic volume should be welcomed by all those seeking the original authoritative and complete source of information on this emerging technology. An in-depth and practical guide, Microwave Mobile Communications will provide you with a solid understanding of the microwave propagation techniques essential to the design of effective cellular systems.
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Title: Error modeling schemes for fading channels in wireless communications: A survey

Section 1: Introduction
Description 1: Provide the introduction and motivation for surveying error modeling methods for fading channels in wireless communications.

Section 2: Multipath Fading
Description 2: Describe multipath fading, including the types and models of fading channels, and the main mechanisms impacting radio propagation.

Section 3: Large-Scale Fading and Small-Scale Fading
Description 3: Detail the differences between large-scale fading and small-scale fading, and their impacts on received signal strength.

Section 4: Different Types of Fading-Channel Models
Description 4: Present the various types of fading channels typical in communication environments, and the mathematical models used to describe them.

Section 5: Error Models of Fading Channels
Description 5: Discuss the characterization of packet loss behavior in fading channels, and classify the error models into analytical and empirical distribution-based models.

Section 6: Analytical Models
Description 6: Explain the analytical error modeling methods, including physical-layer oriented and higher-layer oriented modeling, with a focus on BER and block error calculations.

Section 7: Empirical Distribution-Based Models
Description 7: Outline the empirical distribution-based modeling methods, including the phases of development and the advantages of using empirical data for more accurate models.

Section 8: Summary
Description 8: Provide a summary of the surveyed wireless error modeling methods, including the classification of models and the importance of reproducible modeling for realistic channel parameters.