A Laguerre polynomial-based bound on the symbol error probability for adaptive antennas with optimum combining

We derive a simple closed-form upper bound on the symbol error probability for coherent detection of M-ary phase-shift keying using antenna arrays with optimum combining, in the presence of multiple uncorrelated equal-power cochannel interferers and thermal noise in a Rayleigh fading environment. The new bound, based on Laguerre polynomials, is valid for an arbitrary number of antenna elements as well as arbitrary number of interferers, and it is proven to be asymptotically tight. Comparisons with Monte Carlo simulation are also provided, showing that our bound is useful in many cases of interest.     

Error Probability and SINR Analysis of Optimum Combining in Rician Fading

This paper considers the analysis of optimum combining systems in the presence of both co-channel interference and thermal noise. We address the cases where either the desired-user or the interferers undergo Rician fading. Exact expressions are derived for the moment generating function of the SINR which apply for arbitrary numbers of antennas and interferers. Based on these, we obtain expressions for the symbol error probability with M-PSK. For the case where the desireduser undergoes Rician fading, we also derive exact closed-form expressions for the moments of the SINR. We show that these moments are directly related to the corresponding moments of a Rayleigh system via a simple scaling parameter, which is investigated in detail. Numerical results are presented to validate the analysis and to examine the impact of Rician fading on performance.     

Multiuser Diversity for Antenna Optimal Combining in Interference-Limited Systems

This letter explores the benefit of exploiting multiuser diversity for improving the performance of antenna optimum combining in the interference-limited cellular system. The asymptotic achievable rate is derived to assess this improvement as well as to reveal the interaction of multiuser diversity and optimum combining. For the overloaded case where the number of antennas is insufficient to suppress all the impact of interferers, it is shown that multiuser diversity considerably improves the achievable rate. For the underloaded case where the number of interferers is smaller than that of antennas, multiuser diversity can also provide additional rate increments so that it is possible to use a fewer number of antennas for optimum combining without sacrificing the system achievable rate.     

Upper bounds on the bit-error rate of optimum combining in wirelesssystems

This paper presents upper bounds on the bit-error rate (BER) of optimum combining in wireless systems with multiple cochannel interferers in a Rayleigh fading environment. We present closed-form expressions for the upper bound on the bit-error rate with optimum combining, for any number of antennas and interferers, with coherent detection of BPSK and QAM signals, and differential detection of DPSK. We also present bounds on the performance gain of optimum combining over maximal ratio combining. These bounds are asymptotically tight with decreasing BER, and results show that the asymptotic gain is within 2 dB of the gain as determined by computer simulation for a variety of cases at a 10^-3 BER. The closed-form expressions for the bound permit rapid calculation of the improvement with optimum combining for any number of interferers and antennas, as compared with the CPU hours previously required by Monte Carlo simulation. Thus these bounds allow calculation of the performance of optimum combining under a variety of conditions where it was not possible previously, including analysis of the outage probability with shadow fading and the combined effect of adaptive arrays and dynamic channel assignment in mobile radio systems     

Outage probability and spectrum efficiency of cellular mobile radio systems with smart antennas

Relying on the distribution of noncentral multivariate F variates, we investigate the outage probability and spectrum efficiency performance of cellular systems with smart antennas. We consider interference-limited systems in which the number of interferers exceeds or is equal to the number of antenna elements, and we present closed-form expressions when the desired signal is subject to Rician-type fading and interfering signals exhibit Rayleigh-, or, more general Nakagami-type fading. When applicable, these new expressions are compared to those previously reported in the literature dealing with the performance of cellular systems without smart antenna capabilities and the performance of cellular systems with optimum combining when both the desired and interfering signals are subject to Rayleigh-type fading. Corresponding numerical results and plots are also provided and discussed.     

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     

Exact Performance Analysis of Optimum Combining With Multiple Interferers in Flat Rayleigh Fading

This letter provides a comprehensive overview and extension of recent results on outage probabilities and bit-error rates (BER) for optimal combiners in the presence of multiple interferers and additive noise. Desired signal and interferers are subject to flat Rayleigh fading and all channels are independent. In addition to summarizing previous work, this letter also derives the BER for a wider range of modulations than previously considered. We show that previous approximate results on the equal power interferer case where the number of interferers is less than the number of antenna elements can be made exact in a straightforward way. Finally we extend previous work on the single and double interferer case to the general case of arbitrary numbers of interferers.     

Quadratic forms in complex Gaussian matrices and performance analysis of MIMO systems with cochannel interference

This paper establishes an analytical framework for the performance analysis of multiple-input/multiple output (MIMO) systems subject to cochannel interference and operating over fading channels. First, we present some new statistical results dealing with the distribution of the largest eigenvalue of certain quadratic forms in complex Gaussian matrices and establish the connection between these results and the performance analysis of MIMO systems subject to cochannel interference. We consider interference limited systems in which the number of cochannel interferers exceeds or is equal to the number of receiving antenna elements. We then derive new "closed-form" expressions of the probability density function of the outage signal-to-interference ratio and the system outage probability for MIMO systems in Rician-Rayleigh (i.e., the desired user is subject to Rician fading while cochannel interferers are subject to Rayleigh fading) and Rayleigh-Rayleigh fading environments. When applicable, these expressions are compared to special cases previously reported in the literature dealing with the performance of single-input/multiple-output (SIMO) systems. As a double check, these analytical results and assumptions are validated by Monte Carlo simulations and as an illustration of the mathematical formalism some numerical examples for particular cases of interests are plotted and discussed. These results show that under the same the scattering and interfering conditions and given a fixed number of total antenna elements and cochannel interferers: 1) SIMO systems will always outperform multiple-input/single-output systems and 2) it is preferable to distribute the number of antenna elements evenly between the transmitter and the receiver for an optimum performance.     

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 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 probability of cellular radio systems using maximal ratiocombining in the presence of multiple interferers

In mobile radio systems, antenna diversity is used to combat fading and reduce the impact of cochannel interference. We derived a new expression for probability density functions of the signal-to-interference-plus-noise ratio and apply it to analyze the outage probability (OTP) for a maximal ratio combining diversity system when multiple cochannel interferers are present. Numerical results showing the impact of the number of antenna elements, the number of cochannel interferers, and signal-to-noise ratio on the OTP are presented. Simulation results validating the analytical results are also presented     

Optimum combining in digital mobile radio with cochannel interference

This paper studies optimum signal combining for space diversity reception in cellular mobile radio systems. With optimum combining, the signals received by the antennas are weighted and combined to maximize the output signal-to-interference-plus-noise ratio. Thus, with cochannel interference, space diversity is used not only to combat Rayleigh fading of the desired signal (as with maximal ratio combining) but also to reduce the power of interfering signals at the receiver. We use analytical and computer simulation techniques to determine the performance of optimum combining when the received desired and interfering signals are subject to Rayleigh fading. Results show that optimum combining is significantly better than maximal ratio combining even when the number of interferers is greater than the number of antennas. Results for typical cellular mobile radio systems show that optimum combining increases the output signal-to-interference ratio at the receiver by several decibels. Thus, systems can require fewer base station antennas and/or achieve increased channel capacity through greater frequency reuse. We also describe techniques for implementing optimum combining with least mean square (LMS) adaptive arrays.     

Optimum Combining in Digital Mobile Radio with Cochannel Interference

This paper studies optimum signal combining for space diversity reception in cellular mobile radio systems. With optimum combining, the signals received by the antennas are weighted and combined to maximize the output signal-to-interference-plus-noise ratio. Thus, with cochannel interference, space diversity is used not only to combat Rayleigh fading of the desired signal (as with maximal ratio combining) but also to reduce the power of interfering signals at the receiver. We use analytical and computer simulation techniques to determine the performance of optimum combining when the received desired and interfering signals are subject to Rayleigh fading. Results show that optimum combining is significantly better than maximal ratio combining even when the number of interferers is greater than the number of antennas. Results for typical cellular mobile radio systems show that optimum combining increases the output signalto-interference ratio at the receiver by several decibels. Thus, systems can require fewer base station antennas and/or achieve increased channel capacity through greater frequency reuse. We also describe techniques for implementing optimum combining with least mean square (LMS) adaptive arrays.     

Explicit Analytical Expressions for Outage and Error Rate of Diversity Cellular Systems in the Presence of Multiple Interferers and Correlated Rayleigh Fading

The outage probability of maximal ratio combining diversity with an arbitrary number of antennas in the presence of an arbitrary number of cochannel interferers and thermal noise is derived when the branch gains of the desired user signal and interfering signals experience Rayleigh fading and have the same correlation matrix. Two special cases, when the correlation matrix is equicorrelated and when the correlation matrix has different eigenvalues, are considered for both the equal-power cochannel interference case and the unequal-power cochannel interference case. Further, the average bit-error rate of a coherent binary phase-shift keying (BPSK)-modulated cellular system using maximal ratio combining diversity in cochannel interference and correlated Rayleigh fading is derived. The effects of the average signal-to-noise ratio (SNR) and the average signal-power-to-interference-power ratio on the system performance are examined.     

MIMO capacity through correlated channels in the presence of correlated interferers and noise: a (not so) large N analysis

The use of multiple-antenna arrays in both transmission and reception promises huge increases in the throughput of wireless communication systems. It is therefore important to analyze the capacities of such systems in realistic situations, which may include spatially correlated channels and correlated noise, as well as correlated interferers with known channel at the receiver. Here, we present an approach that provides analytic expressions for the statistics, i.e., the moments of the distribution, of the mutual information of multiple-antenna systems with arbitrary correlations, interferers, and noise. We assume that the channels of the signal and the interference are Gaussian with arbitrary covariance. Although this method is valid formally for large antenna numbers, it produces extremely accurate results even for arrays with as few as two or three antennas. We also develop a method to analytically optimize over the input signal covariance, which enables us to calculate analytic capacities when the transmitter has knowledge of the statistics of the channel (i.e., the channel covariance). In many cases of interest, this capacity is very close to the full closed-loop capacity, in which the transmitter has instantaneous channel knowledge. We apply this analytic approach to a number of examples and we compare our results with simulations to establish the validity of this approach. This method provides a simple tool to analyze the statistics of throughput for arrays of any size. The emphasis of this paper is on elucidating the novel mathematical methods used.     

A low-complexity combined antenna array and interferencecancellation DS-CDMA receiver in multipath fading channels

A simple direct sequence-code division multiple access receiver that combines adaptive beamforming with parallel interference cancellation in a multipath fading channel is proposed and analyzed. A fast adaptation, conjugate gradient algorithm is used to find the optimum beamformer weights. By beamforming, the desired user's signal is enhanced and the cochannel interference from other directions is reduced. For in-beam multiple access interference reduction, a parallel interference canceller is used in each RAKE finger. In the demodulation process, we propose a new demodulation method in which the incoming signal is correlated with the effecting spreading code rather than the physical spreading code called the effective matched filter. A new combining method called equivalent maximal ratio combining is also proposed and analyzed. The average uncoded bit error rate as a function of the average antenna signal-to-noise ratio and the number of receiving antennas is examined in a frequency selective Rayleigh fading channel for all proposed receiver structures. Both simulation and analysis show an increase in system capacity as a function of the number of antennas and the number of interferers canceled per finger     

Performance Analysis of OSTBC Transmission in Amplify-and-Forward Cooperative Relay Networks

A performance analysis is presented for amplify-and-forward (AF) cooperative relay networks employing transmit antenna diversity with orthogonal space-time block codes (OSTBCs), where multiple antennas are equipped at the transmitter. We develop a symbol-error-rate (SER) and outage performance analysis for OSTBC transmissions with and without cooperative diversity over flat Rayleigh fading channels. We first derive exact probability density functions (pdf's) and cumulative distribution functions (cdf's) for the system SNR without direct transmission with an arbitrary number of transmit antennas and then present the exact closed-form SER and outage probability expressions. Next, we derive the moment-generating function (MGF) for the overall system SNR with direct transmission and present the exact SER and outage probability with joint transmit antenna diversity and cooperative diversity. The theoretical analysis is validated by simulations, which indicate an exact match between them. The results also show how the transmit antenna diversity and the cooperative diversity affect the overall system performance.      

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     

Performance Analysis of Quantized Beamforming MIMO Systems

Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using single-stream transmit beamforming and receive combining. A MIMO beamforming system with feedback using a codebook based quantization of the beamforming vector allows practical implementation of such a strategy in a single-user scenario. The performance of this system in uncorrelated Rayleigh flat fading channels is studied from the point-of-view of signal-to-noise ratio (SNR) and outage probability. In this paper, lower bounds are derived on the expected SNR loss and the outage probability of systems that have a single receive antenna or two transmit antennas. For arbitrary transmit and receive antennas, approximations for the SNR loss and outage are derived. In particular, the SNR loss in a quantized MIMO beamforming system is characterized as a function of the number of quantization bits and the number of transmit and receive antennas. The analytical expressions are proved to be tight with asymptotically large feedback rate. Simulations show that the bounds and approximations are tight even at low feedback rates, thereby providing a benchmark for feedback system design