Performance analysis of optimum combining with multiple interferersin flat Rayleigh fading

This paper is a performance analysis of optimum combining in the presence of multiple equal power interferers and noise when the number of interferers is less than the number of antenna elements. Desired signal and interferers are subject to flat Rayleigh fading, and the propagation channels are independent. An approximate expression of the probability density function of the output signal-to-interference-plus-noise ratio (SINR) is derived analytically. It is then applied to obtain the cumulative distribution function of the SINR, and the bit-error rate (BER) of some binary modulations, including coherent binary phase-shift keying. In the case of a single interferer, an exact analysis is performed to prove the validity of the approximation. In the case of multiple interferers, the accuracy of the approximation is assessed through simulations. Although limited to equipower interferers, this analysis is a convenient way of assessing the performance of optimum combining in some typical situations and comparing it with that of maximal-ratio combining. The final results are remarkably simple and provide a useful complement to previous analyzes, especially in the region of reasonably high BERs which are of practical interest     

Performance analysis of optimum combining for dual-antenna diversity with multiple interferers in a Rayleigh fading channel

We study the performance analysis of optimum combiner for M-ary phase-shift keying (MPSK) with multiple interferers in a flat Rayleigh fading channel. The first-order approximation is considered for the dual-antenna diversity reception. We derive the analytical solutions for the ordered mean eigenvalues of interference-plus-noise covariance matrix and a simple closed-form expression for the average symbol error rate of MPSK in the case of multiple cochannel interferers.     

Exact closed-form performance analysis of optimum combining with multiple cochannel interferers and Rayleigh fading

A new closed-form expression is derived for the exact bit-error probability (BEP) for optimum combining with binary phase-shift keying. The exact BEP expression is for multiple, equal power, cochannel interferers and multiple reception branches. It is assumed that the aggregate interference and noise is Gaussian and that both the desired signal and interference are subject to Rayleigh fading. The derivation starts by expressing the optimum combining decision statistic as a sum of quadratic forms of Gaussian random variables and it proceeds to average over the fading interference. The new BEP expression has low complexity as it contains only finite sums and products.     

Performance of antenna array systems with optimum combining in aRayleigh fading environment

The effect of cochannel interference on the performance of digital mobile radio systems in a Rayleigh fading environment is studied. The average bit error rate (BER) of an antenna array system with an optimum combining scheme that maximizes the output signal-to-interference-plus-noise ratio (SINR) is analyzed. BER expressions which are easy to evaluate numerically are derived for coherent binary phase shift keying (BPSK) schemes in an environment with cochannel interference and noise     

Performance of antenna array systems with optimum combining in aRayleigh fading environment

The effect of cochannel interference on the performance of digital mobile radio systems in a Rayleigh fading environment is studied. The average bit error rate (BER) of an antenna array system with an optimum combining scheme that maximizes the output signal-to interference-plus-noise ratio is analyzed. BER expressions which are easy to evaluate numerically are derived for coherent binary phase-shift keying schemes in an environment with cochannel interference and noise     

Closed-form expressions of approximate error rates for optimum combining with multiple interferers in a Rayleigh fading channel

This paper presents approximate error rates of M-ary phase shift keying (MPSK) for optimum combining (OC) with multiple cochannel interferers in a flat Rayleigh fading channel. For the first-order approximation, we derive the closed-form expression for ordered mean eigenvalues of the interference-plus-noise covariance matrix, which facilitates performance evaluation for the OC with arbitrary numbers of interferers and antenna elements without Monte Carlo simulation and multiple numerical integrals. We also derive the closed-form expressions for approximate error rates of MPSK for the OC in terms of the average error rate of MPSK for maximal ratio combining (MRC). From the simple evaluation of ordered mean eigenvalues, we show that the first-order approximation gives a simple and accurate way to analyze the performance of the OC.     

Performance analysis of optimum combining in wirelesscommunications with Rayleigh fading and cochannel interference

Optimum combining for space diversity reception is studied in digital cellular mobile radio communication systems with Rayleigh fading and multiple cochannel interferers. This paper considers binary phase-shift keying (BPSK) modulation in a flat Rayleigh-fading environment when the number of interferences L is no less than the number of antenna elements N(L⩾N). The approach of this paper and its main contribution is to carry out the analysis in a multivariate framework. Using this approach and with the assumption of equal-power interferers, it is shown that the probability density function of the maximum signal-to-interference ratio (SIR) at the output of the optimum combiner has a Hotelling T² distribution. Closed form expressions using hypergeometric functions are derived for the outage probability and the average probability of bit error. Theoretical results are demonstrated by Monte Carlo simulations     

Outage analysis of selection diversity over Rayleigh fading channels with multiple co-channel interferers

In this paper an approach to the performance analysis of signal-to-interference (SIR) based selection combining (SC) operating over the Rayleigh fading channels experiencing an arbitrary number of multiple, Rayleigh co-channel interferers is presented. We have presented a general analysis of multibranch SC where each branch experiences an arbitrary number of multiple equal power co-channel interferers. Useful closed form expressions are derived for the probability density function (PDF) and cumulative distribution function (CDF) at the output of the combiner. Also an outage analysis is performed in order to show the effects of the number of multiple interferers, diversity order and input SIR unbalance to the system performances.     

Performance analysis of coded modulation with generalized selection combining in Rayleigh fading

We consider coded modulation with generalized selection combining (GSC) for bandwidth-efficient-coded modulation over Rayleigh fading channels. Our results show that reception diversity with generalized selection combining can conveniently trade off system complexity versus performance. We provide a number of new results by calculating the cutoff rate, and by deriving analytical upper bounds on symbol-interleaved trellis-coded modulation (TCM) and bit-interleaved-coded modulation (BICM) with GSC. All are verified by simulation. We show that our new bounds on TCM with GSC, which includes maximum ratio combining and selection combining as special cases, are tighter than the previously derived bounds. A new asymptotic analysis on the pairwise error probability, which can be used as a guideline for designing coded modulation over GSC channels, is also given. Finally, we show that BICM with iterative decoding (BICM-ID) can achieve significant coding gain over conventional coded modulation in a multiple-receiving-antenna channel.     

Performance analysis of TCM with generalized selection combining on Rayleigh fading channels

We derive the computational cutoff rate, R/sub 0/, for coherent trellis-coded modulation (TCM) schemes on independent identically distributed (i.i.d.) Rayleigh fading channels with (K, L) generalized selection combining (GSC) diversity, which combines the K paths with the largest instantaneous signal-to-noise ratios (SNR) among the L available diversity paths. The cutoff rate is shown to be a simple function of the moment generating function (MGF) of the SNR at the output of the (K, L) GSC receiver. We also derive the union bound on the bit error probability of TCM schemes with (K, L) GSC in the form of a simple, finite integral. The effectiveness of this bound is verified through simulations.     

Performance of an array receiver with a Kalman channel predictorfor fast Rayleigh flat fading environments

We develop an approach for using an antenna array for tracking fast Rayleigh flat fading channels and suppressing cochannel interference. The fast flat fading process is assumed to be a general autoregressive (AR) process in order to characterize temporal variation of channels and evaluate its effect on the receiver structure and performance. The optimal array receiver structure that minimizes the probability of error for BPSK signals is derived, which includes a Kalman filter to predict the fading channels. A simple integral expression for the probability of error is also derived for the optimal receiver. In particular, we analyze the case with identical shaping filters. An irreducible probability of error is shown to exist due to the prediction error of multiple channels. Another interesting observation from the study is that the diversity gain with m antenna elements in the presence of k interferences is usually greater than (m-k), even in the presence of channel prediction error. Simulations are carried out to verify the theoretical analysis     

Performance analysis of equalized OFDM systems in Rayleigh fading

Channel estimation is usually needed to compensate for the amplitude and phase distortions associated with a received orthogonal frequency-division multiplexing (OFDM) waveform. This paper presents a systematic approach for analyzing the bit-error probability (BEP) of equalized OFDM signals in Rayleigh fading. Closed-form expressions for BEP performance of various signal constellations [phase-shift keying (PSK), differential phase-shift keying (DPSK), quaternary phase-shift keying (QPSK)] are provided for receivers that use a linear pilot-assisted channel estimate. We also derive the optimal linear channel estimates that yield the minimum BEP and show that some previous known results are special cases of our general formulae. The results obtained here can be applied to evaluate the performance of equalized single-carrier narrowband systems as well.     

Ergodic capacity of switch-and-examine combining under flat Rayleigh fading channels

Switch-and-examine combining (SEC) is an interesting diversity technique that is simpler than selection combining (SC), whereas its performances is similar in terms of bit error rate (BER) and diversity order. As ergodic capacity is also a key performance index in modern wireless systems, this article analyzes the ergodic capacity of the SEC system. The numerical results show that the ergodic capacity of SEC with optimal threshold is similar to that of SC for arbitrary number of diversity branches.     

Outage probability analysis for microcell mobile radio systems with cochannel interferers in Rician/Rayleigh fading environment

A microcell mobile radio system where the desired signal within a cell experiences Rician fading while interfering signals from cochannel cells experience Rayleigh fading is studied. This model is named a Rician/Rayleigh fading environment. Expressions of outage probabilities are presented for the mobile radio system in the Rician/Rayleigh fading environment.<>     

Performance analysis of coherent TCM systems with diversityreception in slow Rayleigh fading

Coherent trellis-coded modulation (TCM) systems employing diversity combining are analyzed. Three different kinds of combining are considered: maximal ratio, equal gain, and selection combining (SC). First, the cutoff rate parameter is derived for equal gain combining (EGG) and SC assuming transmission over a fully interleaved channel with flat slow Rayleigh fading, which permits comparison with previously derived results for maximal ratio combining (MRC). Then, tight upper bounds on the pairwise error probabilities are derived for all three combining techniques. These upper bounds are expressed in product form to permit bounding of the bit error rate (BER) via the transfer function approach. In each case, it is assumed that the diversity branches are independent and that the channel state information (CSI) can be recovered perfectly. Also included is an analysis of MRC when the diversity branches are correlated-the cutoff rate and a tight upper bound on the pairwise error probability are derived. It is shown that with double diversity a branch correlation coefficient as high as 0.5 results in only slight performance degradation     

Outage probability for optimum combining of arbitrarily faded signals in the presence of correlated Rayleigh interferers

Exact outage-probability analysis for optimum combining of arbitrarily faded signals in the presence of correlated Rayleigh-faded interferers is not available in the literature. In this paper, we show that the conditional probability density of the reciprocal of the instantaneous signal-to-interference ratio (SIR), given the signal vector, can be represented as the higher order derivative of a simple exponential function in signal power whereby generic formulas for the outage probability and probability density function related to SIR can be determined. The new formulas take simple closed form in terms of the characteristic function of the signal vector. They are, therefore, widely applicable, leading to various results for correlated Rayleigh-, Rician-, and Nakagami-faded signals. Numerical examples are also presented for illustration.     

Performance analysis of the closed-loop transmit antenna diversitysystem over Rayleigh fading channels

As a diversity technique, transmit antenna diversity (TAD) recently has been considered for third-generation (3G) code-division multiple-access systems. There are two different types of TAD techniques: closed loop and open loop. In this correspondence, the performance of the closed-loop TAD system equipped with multiple transmit and receive antennas is analyzed using bounds of the pairwise error probability (PEP) under a flat fading channel environment. In addition, the cutoff rate from the Chernoff bound has been considered to understand the overall performance, which may include channel coding     

Rayleigh衰落信道下多载波DS-CDMA系统性能分析

本文基于多载波传输技术，提出了一种多载波码分多址模型。并在Rayleigh衰落信道下对其误码性能进行了分析。分析及仿真结果表明，系统具有降低多址干扰的能力，同传统的单载波直接序列码分多址系统相比，能支持更大的用户容量。本系统能满足第三代移动通信系统对高速数据传输的要求。     

Analysis of asynchronous FFH-MA systems with a hard-limited combining in Rayleigh fading

The bit error rate (BER) performance of the asynchronous fast frequency hopping multiple access (AFFH-MA) system with multiple hops per symbol is investigated considering the noncoherent M-ary frequency shift keying (MFSK) modulation and hard-limited linear combiner in Rayleigh fading. We present a method for the accurate evaluation of the BER of the AFFH-MA system, and verify the analytic works by Monte Carlo simulations.     

A novel adaptive beamforming algorithm for antenna array CDMA systems with strong interferers

Blind beamforming based on the maximum signal-to-noise ratio (MSNR) can improve the performance of an array system only when the processing gain of the given code-division multiple-access (CDMA) system is high enough such that the desired signal can become dominant after despreading (see Choi, S. and Shim, D., IEEE Trans. Veh. Technol., vol.49, p.1793-1806, 2000; Choi, S. and Yun, D., IEEE Trans. Antennas Propagat., vol.45, p.1393-1404, 1997). We consider a maximum signal-to-interference-plus-noise ratio (MSINR) beamforming. The MSINR performance criterion is chosen to deal with strong interferers effectively. It is shown that blind MSINR beamforming is possible by directly utilizing the input and output signals of correlators of the CDMA systems. In addition, we propose an adaptive beamforming algorithm at a lower computational complexity - about O(7.5N) - where N is the number of antenna elements of the array system. Simulation results are presented in various signal environments to show the performance of the proposed adaptive algorithm.