Random coding error exponent for dual-hop nakagami-m fading channels with amplify-and-forward relaying

We derive the random coding error exponent for dual-hop transmission over Nakagami-m fading channels with amplify-and-forward relaying. This information-theoretic measure allows us to determine the capacity and cutoff rate as well as to gain valuable insight into the inherent tradeoff between the communication reliability and transmission rate in such channels.     

An improved upper bound on the block coding error exponent for binary-input discrete memoryless channels (Corresp.)

The recent upper bounds on the minimum distance of binary codes given by McEliece, Rodemich, Rumsey, and Welch are shown to result in improved upper bounds on the block coding error exponent for binary-input memoryless channels.     

Approximating the pairwise error probability for fading channels

The computation of the pairwise error probability (PEP) for coded digital communications in the presence of fading is often performed by using the Chernoff upper bound, which is simple to evaluate but rather loose. Exact evaluation of the PEP is possible in principle by computing the residues of a complex function, but this may be complicated in practice. In the Letter the authors derive two approximations to the PEP. The first one, based on saddle-point integration, is simple to compute and generally tighter than the Chernoff bound. The second one, based on Gauss-Chebyshev quadrature rules, is both easy to use and computationally stable, and approximates the true value of PEP within any degree of accuracy     

Adaptive quantization for fading channels with feedback

The effect of the presence of a feedback channel on the transmission of information was first considered by Shannon, who showed that the capacity of a memoryless channel is not increased by the existence of a feedback link even if the feedback link is noiseless. Later it was shown that the information on a feedback channel can be used to improve considerably the performance of channel coding. In this work we study the transmission of an information source through a fading channel with feedback, modeled by a finite-state channel in the Gilbert-Elliot sense. We show that by employing the feedback information in the quantizer design for this finite-state channel, one can achieve lower overall distortion compared to the case where feedback is not available. The feedback channel is used to estimate the channel state using a hidden Markov model, and a quantizer matched to the channel state is chosen based on this information.     

Coded differential space-time modulation for flat fading channels

In this paper, powerful coding techniques for differential space-time modulation (DSTM) over Rayleigh flat fading channels and noncoherent detection without channel state information at the receiver are investigated. In particular, multilevel coding, bit-interleaved coded modulation, and so-called hybrid coded modulation (HCM) are devised and compared. For improved noncoherent reception multiple-symbol differential detection (MSDD) is adapted to DSTM. In order to reduce the computational effort required for MSDD, a low-complexity version of MSDD is applied. Evaluating the ergodic channel capacity for the different schemes as appropriate performance measure, HCM with simplified MSDD is shown to offer a favorable tradeoff between complexity and achievable power efficiency. Simulation results employing turbo codes in properly designed HCM schemes confirm the predictions from information theory.     

ARQ error control for fading mobile radio channels

In this paper, we study the correlation properties of the fading mobile radio channel. Based on these studies, we model the channel as a one-step Markov process whose transition probabilities are a function of the channel characteristics. Then we present the throughput performance of the Go-Back-N and selective-repeat automatic repeat request (ARQ) protocols with timer control, using the Markov model for both forward and feedback channels. This approximation is found to be very good, as confirmed by simulation results     

Multiuser detection in flat fading non-Gaussian channels

This paper deals with the problem of multiuser detection in direct-sequence code-division multiple-access (CDMA) fading channels with impulsive noise. This issue arises in practical situations because in many realistic wireless channels, the ambient channel noise is impulsive, resulting from various natural and man-made impulsive sources. An M-estimator-based structure for noncoherent demodulation of differentially phase-shift keyed (DPSK) signals transmitted simultaneously via a CDMA flat-fading channel and embedded in impulsive noise, is proposed and analyzed. Analytical and numerical results show that, in highly impulsive noise, the performance gain afforded by the proposed multiuser detector can be substantial when compared to the linear decorrelating detector for DPSK, with little attendant increase in algorithmic complexity.     

Recursive receivers for diversity channels with correlated flat fading

This paper addresses the design and performance of time-recursive receivers for diversity based communication systems with flat Rayleigh or Ricean fading. The paper introduces a general state-space model for such systems, where there is temporal correlation in the channel gain. Such an approach encompasses a wide range of diversity systems such as spatial diversity, frequency diversity, and code diversity systems which are used in practice. The paper describes a number of noncoherent receiver structures derived from both sequence and a posteriori probability-based cost functions and compares their performance using an orthogonal frequency-division multiplex example. In this example, the paper shows how a standard physical delay-Doppler scattering channel model can be approximated by the proposed state-space model. The simulations show that significant performance gains can be made by exploiting temporal, as well as diversity channel correlations. The paper argues that such time-recursive receivers offer some advantages over block processing schemes such as computational and memory requirement reductions and the easier incorporation of adaptivity in the receiver structures.     

An adaptive multiantenna transceiver for slowly flat fading channels

The paper proposes an adaptive multiantenna transceiver for narrowband reception. Blind channel tracking algorithms are developed to track the eigen directions of the channel directly instead of the channel itself. Two algorithms are proposed to track the column space of the channel at the receiver, based on the received data. One of the algorithms is free of any division operation, which is more favorable in practice. For the row space of the channel, two approaches are proposed as well. The first approach requires periodic feedback of the demodulated signal from the receiver back to the transmitter where it can make use of its knowledge on the prior transmitted symbols to estimate the row space. In the second approach, the estimation is done at the receiver based on the detected symbols, and the estimated row space is sent back to the transmitter. Adaptive resource allocation is also incorporated into the design.     

Estimation of continuous flat fading MIMO channels

Multiple-input-multiple-output (MIMO) systems can provide high data rate wireless services in a rich scattering environment. We study one of the proposals for MIMO systems, the Bell Labs Layered Space-Time (BLAST) architecture. Channel estimation using training sequences is required for coherent detection in BLAST. We apply the maximum-likelihood channel estimator and the optimal training sequences for block flat fading channels to continuous flat fading channels and analyze the estimation error. The optimal training length and training interval that maximize the throughput for a given target bit error-rate are found by computer simulations as functions of the Doppler frequency and the number of antennas.     

Hidden Markov modeling of flat fading channels

Hidden Markov models (HMMs) are a powerful tool for modeling stochastic random processes. They are general enough to model with high accuracy a large variety of processes and are relatively simple allowing us to compute analytically many important parameters of the process which are very difficult to calculate for other models (such as complex Gaussian processes). Another advantage of using HMMs is the existence of powerful algorithms for fitting them to experimental data and approximating other processes. In this paper, we demonstrate that communication channel fading can be accurately modeled by HMMs, and we find closed-form solutions for the probability distribution of fade duration and the number of level crossings     

On the mutual information of memoryless channels

Letx_1, cdots ,x_nandy_1, cdots, y_nbe input and output sequences of a channel. In the case of memoryless input sources, the following inequality on mutual information is well known: begin{equation} I((x_1, cdots ,x_n),(y_1, cdots ,y_n)) geq sum I(x_i, y_i). end{equation} It is straightforward to show that the inequality sign is reversed if the channel instead of the input source is memoryless. In this paper we establish these inequalities when the input and output are functions instead of sequences.     

On the error probability of linearly modulated signals on Rayleighfrequency-flat fading channels

Consideration is given to optimal detection of linearly modulated signals subject to multiplicative Rayleigh-distributed distortion and additive white Gaussian noise. For coherent detection, regenerated amplitude and phase references are employed at the receiver to compensate for amplitude and phase deviations from the correct values. A system model is formulated under the assumption of perfect symbol timing and in the absence of intersymbol interference, producing a final additive noise term, applied just before the detection, which contains the effects of the original additive and multiplicative distortions and of the errors in the phase and amplitude references. By determining the probability density function of this final noise term for arbitrary types of linear modulation, it is possible to perform exact calculations of error probabilities     

Reed-Solomon error control coding for Rayleigh fading channels withfeedback

The use of nonbinary block error control codes over Rayleigh fading channels with feedback is examined. It is assumed that the fading is slow with respect to the rate of symbol transmission. Expressions are derived for the probabilities of channel symbol error and erasure, which are in turn used to develop expressions for code symbol error and erasure. Two erasure generation mechanisms are considered, one based on the existence of channel amplitude side information, the other not. This analytical framework is used to evaluate the performance of the Reed-Solomon/hybrid-ARQ protocol (RS/HARQ) over fading channels with feedback. The RS/HARQ system uses erasure decoding in a hybrid-ARQ protocol to provide excellent reliability performance at the expense of a reduction in throughput. The RS/HARQ protocol allows for the variation of the erasure threshold and the effective diameter of the decoding operation     

Communication over fading dispersive channels with feedback

An intermittent on-off noiseless feedback scheme for binary communication over the slow- and fast-fading Rayleigh channels is proposed and analyzed. At high energy-to-noise ratios, doubling the number of feedback iterations yields a 3-dB power saving for the slowly fading channel. Power savings ranging from 1 dB for one feedback iteration to 9 dB for 16 iterations are typical for the fast-fading model. Also for the fast-fading model, by picking the optimum number of forward transmissions for each value of energy-to-noise ratio, the best achievable performance requires approximately 7.5 dB more energy than the minimum predicted by the rate-distortion bound. Also presented is a feedback communication system for wide-sense stationary, uncorrelated-scatterer, fading, and dispersive forward and feedback channels. The model used for both forward and feedback channels is Kennedy's. Upper and lower bounds on the error probability for block orthogonalM-ary communication are presented for this system.     

Capacity of memoryless channels and block-fading channels with designable cardinality-constrained channel state feedback

A coding theorem is proved for memoryless channels when the channel state feedback of finite cardinality can be designed. Channel state information is estimated at the receiver and a function of the estimated channel state is causally fed back to the transmitter. The feedback link is assumed to be noiseless with a finite feedback alphabet, or equivalently, finite feedback rate. It is shown that the capacity can be achieved with a memoryless deterministic feedback and with a memoryless device which select transmitted symbols from a codeword of expanded alphabet according to current feedback. To characterize the capacity, we investigate the optimization of transmission and channel state feedback strategies. The optimization is performed for both channel capacity and error exponents. We show that the design of the optimal feedback scheme is identical to the design of scalar quantizer with modified distortion measures. We illustrate the optimization using Rayleigh block-fading channels. It is shown that the optimal transmission strategy has a general form of temporal water-filling in important cases. Furthermore, while feedback enhances the forward channel capacity more effectively in low-signal-to noise ratio (SNR) region compared with that of high-SNR region, the enhancement in error exponent is significant in both high- and low-SNR regions. This indicates that significant gain due to finite-rate channel state feedback is expected in practical systems in both SNR regions.     

On the error probability of binary and M-ary signals in Nakagami-m fading channels

In this letter, we present new closed-form formulas for the exact average symbol-error rate (SER) of binary and M-ary signals over Nakagami-m fading channels with arbitrary fading index m. Using the well-known moment generating function-based analysis approach, we express the average SER in terms of the higher transcendental functions such as the Gauss hypergeometric function, Appell hypergeometric function, or Lauricella function. The results are generally applicable to arbitrary real-valued m. Furthermore, with the aid of reduction formulas of hypergeometric functions, we show previously published results for Rayleigh fading (m=1) as special cases of our expressions.     

On coding for block fading channels

This work considers the achievable performance for coded systems adapted to a multipath block-fading channel model. This is a particularly useful model for analyzing mobile-radio systems which employ techniques such as slow frequency-hopping under stringent time-delay or bandwidth constraints for slowly time-varying channels. In such systems, coded information is transmitted over a small number of fading channels in order to achieve diversity. Bounds on the achievable performance due to coding are derived using information-theoretic techniques. It is shown that high diversity can be achieved using relatively simple codes as long as very high spectral efficiency is not required. Examples of simple block codes and carefully chosen trellis codes are given which yield, in some cases, performances approaching the information-theoretic bounds     

A general method for calculating error probabilities over fading channels

Signal fading is a ubiquitous problem in mobile and wireless communications. In digital systems, fading results in bit errors, and evaluating the average error rate under fairly general fading models and multichannel reception is often required. Predominantly to date, most researchers perform the averaging using the probability density function method or the moment generating function (MGF) method. This paper presents a third method, called the characteristic function (CHF) method, for calculating the average error rates and outage performance of a broad class of coherent, differentially coherent, and noncoherent communication systems, with or without diversity reception, in a myriad of fading environments. Unlike the MGF technique, the proposed CHF method (based on Parseval's theorem) enables us to unify the average error-rate analysis of different modulation formats and all commonly used predetection diversity techniques (i.e., maximal-ratio combining, equal-gain combining, selection diversity, and switched diversity) within a single common framework. The CHF method also lends itself to the averaging of the conditional error probability involving the complementary incomplete Gamma function and the confluent hypergeometric function over fading amplitudes, which heretofore resisted to a simple form. As an aside, we show some previous results as special cases of our unified framework.     

Approximate average bit error probability for DQPSK over fading channels

The bit error probability (BEP) of DQPSK with Gray coding over an AWGN channel can be computed simply, although it is hard to integrate and derive the average BEP for fading channels. Presented are novel approximations of the average BEP of DQPSK with Gray coding over fading channels. Numerical results show that the novel formulations are quite accurate.