On optimum combining of M-PSK signals with unequal-power interferers and noise

In this letter, we derive a closed-form symbol-error probability expression for adaptive antenna array with optimum (or, equivalently, linear minimum mean-square error) combining. We consider coherent detection of M-ary phase-shift keying signals in the presence of unequal-power interferers and thermal noise. The analysis is based on our new results on the eigenvalues distribution of central Wishart matrices with correlation.     

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.     

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.     

Outage probability of mimo optimum combining in presence of unbalanced co-channel interferers and noise

This paper studies the performance of multiple-input-multiple-output (MIMO) systems with optimum combining in the presence of both co-channel interference (CCI) and noise. We assume that both desired and CCI users are subject to Rayleigh fading and allow the number of CCI users to be arbitrary and their short-term average powers to be non-identical. Given these assumptions, we derive exact results on the cumulative distribution function (CDF) of the output signal-to-interference-plus-noise ratio (SINR), or equivalently, the outage probability of this MIMO optimum combining scheme. Finally, we present and discuss some numerical examples to validate our analytical expressions and to show the effect of CCI on the performance of MIMO optimum combining systems     

Bit-error probability for optimum combining of binary signals in the presence of interference and noise

We derive an exact bit-error probability (BEP) expression for coherent detection of binary signals with optimum combining in wireless systems in the presence of multiple cochannel interferers and thermal noise. A flat Rayleigh fading environment with space diversity, uncorrelated equal-power interferers, and additive white Gaussian noise is considered. The approach is to use the chain rule of conditional expectation together with the joint probability density function (pdf) of the eigenvalues of the interference correlation matrix. This joint pdf is related to the Vandermonde determinant. Let N/sub A/ denote the number of antennas and N/sub I/ the number of interferers. We consider both the cases of an overloaded system, in which N/sub I//spl ges/N/sub A/, and an underloaded system, in which N/sub I/相似文献   

Performance analysis of maximal ratio combining in the presence ofmultiple equal-power cochannel interferers in a Nakagami fading channel

The effect of cochannel interference on the performance of digital mobile radio systems in a Nakagami (1960) fading channel is studied. The performance of maximal ratio combining (MRC) diversity is analyzed in the presence of multiple equal-power cochannel interferers and additive white Gaussian noise. Closed-form expressions are derived for the average probability of error as well as outage probability of both coherent and noncoherent (differentially coherent) binary frequency-shift keying and binary phase-shift keying schemes in an environment with cochannel interference and noise. The results are expressed in terms of the confluent hypergeometric function of the second kind, a function that can be easily evaluated numerically. The analysis assumes an arbitrary number of independent and identically distributed Nakagami interferers     

Performance of generalized selection combining for mobile radiocommunications with mixed cochannel interferers

The performance of generalized selection combining (GSC) space diversity for mobile radio systems in the presence of multiple cochannel interferers is studied. Two cochannel interference models are considered: (1) L cochannel interferers consisting of L-N Nakagami-m (1960) interferers and N Rayleigh interferers and (2) L cochannel interferers in which each interferer follows Nakagami-m distribution for a fraction of time and Rayleigh distribution for the remaining of time. The fading parameters of the Nakagami-m interferers are limited to integer values only. The desired signal is assumed to be Rayleigh faded. Also, all the desired signals and the cochannel interferers received on each branch are independent of each other. Closed-form expressions are derived for the probability density functions (PDFs) of the instantaneous signal-to-interference power ratio (SIR) at the output of the GSC for the two cochannel interference models. Using these SIR PDFs, closed-form expression for evaluating the outage probability and the average bit error probability (BEP) are subsequently derived. A differential phase-shift keying scheme is considered in the derivation. Numerical results showing the influences of various system parameters on the outage probability and the average BEP are then presented     

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.     

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 antenna array systems with multiple interferers in flat Rayleigh fading

In this letter, we examine the statistical distribution of the signal-to-interference-plus-noise ratio (SINR) of the optimum combining (OC) technique in receive-antenna diversity systems. We decompose the SINR into two components by projection onto the interference subspace for systems with more antennas than interferers. For the case when the number of interferers is larger than the number of antennas, upper and lower bounds on performance are provided.     

Error probability for coherent and differential PSK over arbitraryRician fading channels with multiple cochannel interferers

This paper discusses the performance of communication systems using binary coherent and differential phase-shift keyed (PSK) modulation, in correlated Rician fading channels with diversity reception. The presence of multiple Rician-faded cochannel users, which may have arbitrary and nonidentical parameters, is modeled exactly. Exact bit error probability (BEP) expressions are derived via the moment generating functions (MGFs) of the relevant decision statistics, which are obtained through coherent detection with maximum ratio combining for coherent PSK modulation, and differential detection with equal gain combining (EGC) for differential modulation. Evaluating the exact expressions requires a complexity that is exponential in the number of interferers. To avoid this potentially time-consuming operation, we derive two low-complexity approximate methods each for coherent and differential modulation formats, which are more accurate than the traditional Gaussian approximation approach. Two new and interesting results of this analysis are: (1) unlike in the case of Rayleigh fading channels, increasing correlation between diversity branches may lead to better performance in Rician fading channels and (2) the phase distribution of the line-of-sight or static fading components of the desired user has a significant influence on the BEP performance in correlated diversity channels     

Exact bit-error probability for optimum combining with a Rayleighfading Gaussian cochannel interferer

We derive expressions for the exact bit-error probability (BEP) for the detection of coherent binary phase-shift keying signals of the optimum combiner employing space diversity when both the desired signal and a Gaussian cochannel interferer are subject to flat Rayleigh fading. Two different methods are employed to reach two different, but numerically identical, expressions. With the direct method, the conditional BEP is averaged over the fading of both signal and interference, With the moment generating function based method, expressions are derived from an alternative representation of the Gaussian Q-function     

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     

On the average outage rate and average outage duration of wireless communication systems with multiple cochannel interferers

This paper studies the average outage rate [or average level crossing rate (LCR)] and average outage duration (AOD) of wireless communication systems subject to cochannel interference. In particular, it presents closed-form expressions for the LCR and AOD when a minimum desired signal power requirement is specified for satisfactory reception. The results are quite general and account for systems operating over independent identically distributed Rician and/or Nakagami fading environments. When applicable, these new expressions are compared to those previously reported in the literature dealing with the LCR and AOD of 1) interference-limited systems when both the desired and interfering signals are subject to Rayleigh type of fading and 2) power-limited systems operating over Rician or Nakagami fading channels. Corresponding numerical examples that illustrate applications of the results are also provided and discussed. These results show that specifying a certain minimum desired signal power requirement induces a floor on the AOD. They also show that the AOD is essentially affected by the the maximum Doppler frequencies (or equivalently the speed) of the desired users.     

Rank-order statistics for optimum detection of binary signals in the presence of white noise and dc drift (Corresp.)

The well-known technique of detecting binary pulses in white noise and unknown dc drift by means of a high-pass filter followed by a bit-by-bit detector is not theoretically optimum. The optimum procedure is shown to require a rank-ordering operation on the received data.     

A series technique for the optimum detection of stochastic signals in noise

A procedure for the optimum detection of stochastic signals in noise is discussed. The optimum test function is expanded in a point-wise convergent series for which a bound on the convergence properties can be obtained. Knowledge of this bound permits the substitution of a truncated version of the series for the optimum test function. This leads to a test procedure that uses a variable number of terms of the series for each decision and also gives the same decision as the optimum detector. For detection of stochastic signals in Gaussian noise, an expansion is obtained in terms of the eigenfunctions associated with the Gaussian probability density function, which leads to optimum decisions with a moderate number of terms of the series. It is also well suited for adaptive detection in which the distribution function of the stochastic signal is unknown--the coefficients of the expansion factor into two terms, one dependent only on the noise distribution and the other dependent on the distribution of the stochastic signal. Computer results for Gaussian noise are given. For this case, the test procedure can be viewed as a sequence of linear, quadratic, etc., detectors that, when a basic inequality is met, terminates with an optimum decision.     

Performance analysis of maximum ratio combining with imperfect channel estimation in the presence of cochannel interferences

In this paper, we analyze the performance of maximum ratio combining (MRC) systems with imperfect channel estimation in the presence of cochannel interference (CCI) with an arbitrary power interference-to-noise ratio (INR). The maximum combining weights are the imperfect estimates of the desired user's fading channel coefficients and are assumed to be complex Gaussian distributed. The quantified measure for estimation error is the correlation coefficient between the true fading channel coefficients and their estimates. Exact closedform expressions are derived for the probability density function (pdf) of the signal-to-interference-plus-noise ratio (SINR), as well as performance metrics including outage probability and the average symbol error probability (ASEP) for some modulation formats. Simulation results demonstrate the accuracy of our theoretic analysis.     

Outage probability of MRC with unequal-power cochannel interferers in correlated Rayleigh fading

Under the assumption that the branch gains of the desired user signal and interfering signals experience Rayleigh fading and have the same correlation matrix, the outage probability of maximal ratio combining (MRC) in the presence of unequal-power cochannel interference (CCI) is derived for the two cases that the correlation matrix is equi-correlated and that the correlation matrix has different eigenvalues.