Bounds and approximations for optimum combining of signals in the presence of multiple cochannel interferers and thermal noise

We derive an upper bound and investigate some approximations on the symbol error probability (SEP) for coherent detection of M-ary phase-shift keying, using an array of antennas with optimum combining in wireless systems in the presence of multiple uncorrelated equal-power cochannel interferers and thermal noise in a Rayleigh fading environment. Our results are general and valid for an arbitrary number of antenna elements as well as an arbitrary number of interferers. In particular, the exact SEP is derived for an arbitrary number of antennas and interferers; the computational complexity of the exact solution depends on the minimum number of antennas and interferers. Moreover, closed-form approximations are provided for the cases of dual optimum combining with an arbitrary number of interferers, and of two interferers with an arbitrary number of antenna elements. We show that our bounds and approximations are close to Monte Carlo simulation results for all cases considered in this paper.     

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     

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.     

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 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.     

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   

Diversity combining for coherent and differential M-PSK in fading and class-A impulsive noise

In this paper, optimum and suboptimum diversity combining schemes for coherent and differential M-ary phase-shift keying (M-PSK) transmission impaired by general Ricean fading and impulsive Class-A noise are derived and analyzed. The proposed suboptimum coherent combining (SCC) and suboptimum noncoherent combining (SNC) schemes yield similar performance as the corresponding optimum combining schemes but require a lower computational complexity. In addition, the novel SCC and SNC strategies achieve large performance gains over conventional maximum ratio combining (MRC) and equal gain combining (EGC), respectively. For MRC and EGC, respectively, we also provide a performance analysis for coherent and differential M-PSK transmissions over general Ricean fading channels with Class-A noise. Furthermore, tight performance upper bounds for the proposed optimum and suboptimum combining schemes are derived.     

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.     

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.     

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.     

Outage performance for maximal ratio combiner in the presence of unequal-power co-channel interferers

Outage probability for maximal ratio combining (MRC) is usually tackled in the framework of Rayleigh or Nakagami faded co-channel interferers with equal power, which allows for the treatment of the total interference power as a single gamma distributed variable to simplify the analysis. The more general case with unequal-power co-channel interferers is formulated and solved differently in this paper ending up with simple closed-form solutions for Rician/Rayleigh and Nakagami/Rayleigh channel models.     

On optimum combining at the mobile

Optimum combining for diversity antennas at the mobile is discussed. Effectively, the aim is to add the wanted signal vectors in a maximum ratio sense, while interferers are weighted so that their resultant is in a permanent deep fade. Even if there are not enough degrees of freedom available to accomplish this fully, an optimum solution can still be found. Many interpretations from conventional array technology do not apply to the mobile communications case and the mechanism of optimum combining for array branch signals rather than discrete spatial signals is reviewed. Physical interpretation of the formulation is emphasized throughout. Problems with the adaptive algorithm and its implementation are also identified. Sample matrix inversion is shown to be a likely algorithm to apply in vehicular mobile communications receivers. A worst case example gives an idea of the required computation rates     

Approximately optimum detection of deterministic signals inGaussian and compound Poisson noise

An approximate but explicit likelihood ratio is derived for detecting deterministic signals in Gaussian and compound Poisson noise. The approximation in the derivation is based on the assumption that the localized noise elements rarely overlap each other. The derived log-likelihood ratio consists of two distinct parts. One is the conventional correlation detector for detecting deterministic signals in Gaussian noise. The other is a nonlinear processor which compensates for the degradation of the correlation detector caused by the localized noise, and is activated only by the presence of the localized noise. As such, it involves covariance operators of both the Gaussian and the localized noise, and is obtained by using the simultaneous diagonalization and orthogonalization of quadratic forms in function space involving eigenfunctions of certain composite operators     

Locally optimum rank detection of correlated random signals inadditive noise

Nonparametric detection of a zero-mean random signal in additive noise is considered. The locally optimum detector based on signs and ranks of observations is derived, for good weak-signal detection performance under any specified noise probability density function. This detector is shown to have interesting similarities to the locally optimum detector for random signals. It may also be viewed as a generalization of the locally optimum rank detector for known signals. Examples of the test statistic of the detector are given for some specific noise probability density functions. Asymptotic and finite sample-size performance of the locally optimum rank detector is also considered     

Analysis of LDPC with optimum combining

Low density parity check (LDPC) codes have shown exceptionally good performance for single antenna systems over a wide class of channels. LDPC when implemented with a single input multiple output system with maximum ratio combining is optimum from the standpoint of maximising signal-to-noise ratio at combiner output without the presence of interferer. Optimum combining outperforms maximal ratio combining (MRC) in the presence of interferer(s). In this article, the performance of the LDPC codes with multiple receiver antennas with optimum combining in the presence of single interferer is investigated. The simulation results showed that LDPC codes of irregular construction are able to give high coding and diversity gain with optimum combining. The proposed LDPC optimum combined (LDPC–OC) system in Rayleigh fading channel in the presence of a single interferer improves the signal to interferer plus noise ratio by 2.62 dB with four receiver antennas and by 1.98 dB when the number of receiver antennas is three.     

A multi-band low noise amplifier with strong immunity to interferers

A multi-band low noise amplifier (LNA) is designed to operate over a wide range of frequencies (with center frequencies at 1.2, 1.7 and 2.2 GHz respectively) using an area efficient switchable \(\pi\) network. The LNA can be tuned to different gain and linearity combinations for different band settings. Depending upon the location of the interferers, a specific band can be selected to provide optimum gain and the best signal-to-intermodulation ratio. This is accomplished by the use of an on-chip built-in-self-test circuit. The maximum power gain of the amplifier is 19 dB with a return loss better than 10 dB for 7 mW of power consumption. The noise figure is 3.2 dB at 1 GHz and its third-order intercept point (\(IIP_3\)) ranges from ?15 to 0 dBm. Implemented in a 0.13 \(\upmu\)m CMOS technology, the LNA occupies an active area of about 0.29 mm\(^2\). This design can be used for cognitive radio and other wideband applications, which require a dynamic configuration of the signal-to-intermodulation ratio, when sufficient information about the power and the location of the interferers is not available.     

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     

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.     

On optimum detection of linearly filtered CPM signals

A novel structure of the MLSE receiver for linearly filtered CPM (continuous phase modulation) signals is derived. It is shown that the correlator bank required in the works of Svensson (1987) can equivalently be replaced by a reduced correlator bank, preceded by a linear filter with impulse response h*(-t) [channel matched filter]. The reduced correlator bank only incorporates characteristics of the CPM signals and is independent of the channel impulse response. This implies that the complexity of the modified correlator bank depends only linearly on the channel filter impulse response length. The proposed receiver structure permits considerable complexity reduction when compared to the currently known solution