Comments on "MRC performance for M-ary modulation in arbitrarily correlated Nakagami fading channels"

Using the results in the article by Win et al. (see ibid., vol.4, no.10, p.301-3, Oct. 2000) regarding the maximal ratio combiner for correlated Nakagami-m fading channels, we provide a simple analytic proof, applicable to a general class of modulation schemes, that uncorrelated branches result in a lower symbol error probability than do correlated branches.     

Exact performance analysis of M-ary QAM with MRC diversity in Rician fading channels

The exact expression of symbol error rate (SER) is derived for coherent square M-ary quadrature amplitude modulation (M-QAM) using Lth order maximal-ratio combining (MRC) diversity in Rician fading channels with an arbitrary fading parameter. The accuracy of the SER estimates evaluated by this expression is verified through comparison with the results evaluated by numerical integration.     

A decomposition technique for efficient generation of correlatedNakagami fading channels

Correlated Nakagami m-fading is commonly encountered in wireless communications. Its generation in a laboratory environment is therefore of theoretical and practical importance. However, no generic technique for this purpose is available in the literature. Correlated Rayleigh fading is easy to simulate since it has a simple relationship with a complex Gaussian process. Unfortunately, this is not the case for Nakagami fading. The difficulty lies in that the fading parameter can be a real number and there is no general theory linking a Nakagami vector to a finite set of correlated Gaussian vectors. In this paper, by introducing a direct-sum decomposition principle and determining the statistical mapping between the correlated Nakagami process and a set of Gaussian vectors for its generation, a simple general procedure is derived for the generation of correlated Nakagami channels with arbitrary parameters. A key parameter in the statistical mapping can be determined by using an iterative method. The validity of the new technique is examined through the generation of a correlated Nakagami sequence, as encountered in U.S. digital cellular, and a multibranch vector channel as encountered in diversity reception     

Optimum selection combining for M-ary signals in frequency-nonselective fading channels

We present the optimum selection-combining (SC) rule for M-ary signals based on the log-likelihood ratio (LLR) in frequency-nonselective, independent and nonidentically distributed fading channels. The motivation for using the LLR in selecting the diversity branch is that it provides the reliability information of the maximum a posteriori probability decision which minimizes the probability of symbol error. We present coherent and noncoherent optimum SC rules with and without fading information that minimize the probability of symbol error. It is shown that the optimum SC rule provides a significant power gain over the conventional signal-to-noise ratio-based SC rule, and the power gain increases with an increasing number of available diversity branches and decreasing alphabet size. We also present suboptimum SC rules that require less computation, but provide a power gain close to that provided by the optimum SC rule.     

Concatenated coding performance for FSK modulation ontime-correlated Rician fading channels

We present an analytical method for evaluating the performance of noninterleaved concatenated codes over channels modeled as a nonfrequency selective correlated Rician fading channel with a known power spectral density. The main idea is to model the communication system from the modulator input to the demodulator output as a finite state channel (FSC) model, and apply powerful enumeration techniques to such a discrete channel in order to gain useful information on the system performance. The concatenated scheme makes use of two codes; Reed-Solomon codes are employed for the outer code, and binary block codes are used as the inner code. Next, the method is extended to study the effect on the performance when an interleaving with finite depth is incorporated into the communication system. A comparison between symbol and bit interleaving is made. Finally, we study the potential gain produced when channel information is passed on to the outer decoder in the form of an erasure symbol. In all cases, analytical expressions for the probability of the number of error symbols produced by the FSC model were obtained in terms of a coefficient in a formal power series. This is an interesting alternative approach with respect to computer simulations     

Adaptive coded modulation for fading channels

We apply coset codes to adaptive modulation in fading channels. Adaptive modulation is a powerful technique to improve the energy efficiency and increase the data rate over a fading channel. Coset codes are a natural choice to use with adaptive modulation since the channel coding and modulation designs are separable. Therefore, trellis and lattice codes designed for additive white Gaussian noise (AWGN) channels can be superimposed on adaptive modulation for fading channels, with the same approximate coding gains. We first describe the methodology for combining coset codes with a general class of adaptive modulation techniques. We then apply this methodology to a spectrally efficient adaptive M-ary quadrature amplitude modulation (MQAM) to obtain trellis-coded adaptive MQAM. We present analytical and simulation results for this design which show an effective coding gain of 3 dB relative to uncoded adaptive MQAM for a simple four-state trellis code, and an effective 3.6-dB coding gain for an eight-state trellis code. More complex trellis codes are shown to achieve higher gains. We also compare the performance of trellis-coded adaptive MQAM to that of coded modulation with built-in time diversity and fixed-rate modulation. The adaptive method exhibits a power savings of up to 20 dB     

Performance of M-ary PSK signals in slow Rayleigh fading channels

The error rate performance of M-ary coherent phase shift keyed signals and M-ary differential phase shift keyed signals in slow Rayleigh fading channels is analysed. Closed-form expressions for the symbol error rate are presented. The coherent PSK signals are 3 dB stronger than the differential PSK signals at high SNR for given M in a Rayleigh fading environment.<>     

Pilot-symbol aided coherent M-ary PSK in frequency-selective fastRayleigh fading channels

Pilot-symbol aided coherent M-ary PSK modems in digital cellular mobile radio systems are analyzed theoretically. The error-floors caused by the Doppler spread in a fast fading channel are removed in both flat and selective fading channels. However, the error-floors caused by the delay spread are lower-bounded by those that exist in the ideal coherent detection. The systems are modeled as frequency-selective fast Rayleigh fading channels, corrupted by co-channel interference (CCI) and additive white Gaussian noise (AWGN). In the proposed scheme, pilot symbols are inserted periodically to monitor the channel characteristics. The fading processes experienced by the pilot symbols are used to estimate those suffered by the data symbols using interpolation or filtering. The estimated fade characteristics are used to compensate the random phase variation caused by the Doppler spread, so that the signals can be demodulated coherently. The theoretical performances of the fade compensated coherent modems are evaluated. The results show that the fade compensated coherent demodulation with the least redundancy achieves the same performance as the ideal differential detection in a fading channel. The performance approaches that of the ideal coherent demodulation as more redundancy is allowed. The pilot-symbol-insertion (PSI) scheme is also applicable to M-ary QAM modems and Rician channels. The residual frequency offset can also be compensated by the PSI technique     

Error performance of MPSK trellis-coded modulation overnonindependent Rician fading channels

This paper presents new upper bounds on the pairwise error probability (PEP) of trellis-coded modulation (TCM) schemes over nonindependent Rician fading channels. Cases considered are coherent and pilot-tone-aided detection and differential detection of trellis-coded multilevel phase-shift keying (TC-MPSK) systems. The average bit-error probability P_b can be approximated by truncating the union bound. This method does not necessarily lead to an upper bound on P_b, and, hence, the approximation must be used with simulation results. In addition, for Rayleigh fading channels with an exponential autocovariance function, bounds resembling those for memoryless channels have been derived. The bounds are substantially more accurate than Chernoff bounds and hence allow for accurate estimation of system performance when the assumption of ideal interleaving is relaxed     

Another look at the performance of MRC schemes in Nakagami-m fading channels with arbitrary parameters

In this letter, we take a close look at the performance of maximal ratio combining (MRC) schemes operating in a flat-Nakagami-m fading environment with arbitrary fading parameters. We derive an expression for the probability density function (pdf) of the output signal-to-noise ratio (SNR) by expressing the moment generating function of the output SNR in the form of multiple Barnes-type contour integrals. By evaluating the inverse transform and converting the multiple contour integrals into infinite series, we are able to derive an expression for the pdf of the output SNR when the Nakagami fading parameters along the diversity branches take on real and arbitrary values. Consequently, the average bit-error rate can now be expressed in terms of Lauricella's multivariate hypergeometric function, which can be easily evaluated numerically. Special cases of the main results reduce to known results in the literature. The results, which apply to independent as well as correlated diversity branches, will be useful for predicting the system performances when the Nakagami fading parameters are real and arbitrary.     

A performance analysis of trellis-coded modulation schemes overRician fading channels

This paper presents a saddle point approximation (SAP) method to compute the pairwise error probability (PEP) of trellis-coded modulation (TCM) schemes over Rician fading channels. The approximation is applicable under several conditions, such as finite and ideal interleaving, ideal coherent and pilot-tone aided detection, and differential detection. The accuracy of this approximation is demonstrated by comparison to the results of numerical integration. When ideal interleaving is assumed, an asymptotic approximation for the PEP of ideal coherent, pilot-tone aided or differentially detected TCM is derived. This asymptotic approximation of the PEP is in a product form and much tighter than the ordinary Chernoff bound on the PEP. Also, based on the SAP, the effect of finite interleaving depth on the error performance of TCM schemes over Rician and shadowed Rician channels is studied     

M-ary symbol error outage over Nakagami-m fading channels in shadowing environments

This letter addresses the problem of finding a tractable expression for the symbol error outage (SEO) in flat Nakagami-m fading and shadowing channels. We deal with M-ary phase shift keying (M-PSK) and quadrature amplitude modulation (M-QAM) which extends our previous results on BPSK signaling. We propose a new tight approximation of the symbol error probability (SEP) holding for M-PSK and M-QAM signals which is accurate over all signal to noise ratios (SNRs) of interest. We derive a new generic expression for the inverse SEP which facilitates the derivation of a tight approximation of the SEO in a lognormal shadowing environment.     

Performance of DS-CDMA receivers with MRC in nakagami-m fading channels with arbitrary fading parameters

The receivers that combine spatial antenna diversity with temporal multipath diversity are known as two-dimensional (2-D) RAKE receivers. In this paper, we consider the outage probability and the bit error rate performance of a coherent binary phase shift keying 2-D RAKE receiver in the context of an asynchronous direct sequence (DS)-code division multiple access (CDMA) system operating in a Nakagami-m fading channel with real and arbitrary fading parameters. The closed-form expressions derived for the two wireless performance measures are easily evaluated numerically and enable the link designer to examine the effects of system parameters, such as the number of receive antennas, RAKE fingers per antenna, and asynchronous CDMA users in the cell, as well as channel conditions, such as the amount of fading in the combined paths and the multipath intensity profile of the channel on the link performance. In addition, the diversity loss due to correlated fading among the spatially separated RAKE fingers is quantified.     

MRC performance for binary signals in Nakagami fading with generalbranch correlation

Exact expressions are derived for the performance of predetection maximal ratio combiner diversity reception with L correlated branches in Nakagami fading. Bit error rates are evaluated for both coherent and noncoherent binary phase-shift-keying and frequency-shift-keying signals, starting from the L-variate moment generating function of the random input power vector. The new formulation presented for the bit error rate, in which the covariance matrix of the fading at the L branches explicitly appears, allows arbitrary branch correlation to be taken into account for any diversity order in the case of identical fading severity on the branches. Results are presented for evaluation of the outage probability, for integer values of fading severity, as well as for the effect of the presence of unbalanced channels with arbitrary correlation     

Expression for evaluating performance of BPSK with MRC in Nakagami fading

A strikingly simple and fast to compute expression is derived for the performance of binary phase shift keying (BPSK) with maximal ratio combining (MRC) diversity in a Nakagami (1960) fading channel. The expression is valid for all Nakagami-m parameters. Furthermore, no concession is made as far as the accuracy of the results is concerned.     

Performance limits for filtered multitone modulation in fading channels

In this paper, we investigate the best attainable performance for filtered multitone modulation (FMT) in time-variant frequency-selective fading channels when optimal maximum-likelihood (ML) detection is deployed. FMT generalizes the popular orthogonal frequency division multiplexing (OFDM) scheme through the deployment of subchannel shaping filters. The performance limits are derived by extending to this multichannel context the matched filter bounding technique. We first conduct an exact calculation for the average and the distribution of the matched filter error rate bound. Then, we follow a numerical procedure that overcomes the problems of accuracy and ill conditioning in the implementation of the exact method. This study allows for an analytical treatment of the diversity effect on performance as a function of the time/frequency selectivity of the channel. It is found that FMT is a diversity transform that is capable of yielding coding gains and time/frequency diversity gains as a function of the subcarrier spacing and the subchannel filter shape.     

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.     

Analysis of the error performance of adaptive array antennas for CDMA with noncoherent M-ary orthogonal modulation in Nakagami fading

This letter presents an analytical model for evaluating the bit error rate (BER) of a direct sequence code division multiple access (DS-CDMA) system, with M-ary orthogonal modulation and noncoherent detection, employing an array antenna operating in a Nakagami fading environment. An expression of the signal to interference plus noise ratio (SINR) at the output of the receiver is derived, which allows the BER to be evaluated using a closed form expression. The analytical model is validated by comparing the obtained results with simulation results.     

Performance analysis of dual MRC receiver in correlated hoyt fading channels

Performance of a dual maximal ratio combining receiver has been analyzed in correlated Hoyt fading channels. Analytical expressions for the probability density function of the receiver output signal-to-noise ratio (SNR), average SNR, outage probability and average bit error rate performance for binary, coherent and non-coherent modulations have been presented. Numerical results show that for coherent phase shit-keying and differential phase shift-keying modulations, to achieve an ABER of 10^?7, the required excess SNR is relatively small for correlation coefficient (?) less than 0.5 than it is for ? ≫ 0.5.