On the capacity of spatially correlated MIMO Rayleigh-fading channels

In this paper, we investigate the capacity distribution of spatially correlated, multiple-input-multiple-output (MIMO) channels. In particular, we derive a concise closed-form expression for the characteristic function (c.f.) of MIMO system capacity with arbitrary correlation among the transmitting antennas or among the receiving antennas in frequency-flat Rayleigh-fading environments. Using the exact expression of the c.f., the probability density function (pdf) and the cumulative distribution function (CDF) can be easily obtained, thus enabling the exact evaluation of the outage and mean capacity of spatially correlated MIMO channels. Our results are valid for scenarios with the number of transmitting antennas greater than or equal to that of receiving antennas with arbitrary correlation among them. Moreover, the results are valid for an arbitrary number of transmitting and receiving antennas in uncorrelated MIMO channels. It is shown that the capacity loss is negligible even with a correlation coefficient between two adjacent antennas as large as 0.5 for exponential correlation model. Finally, we derive an exact expression for the mean value of the capacity for arbitrary correlation matrices.     

Performance of dual-diversity predetection EGC in correlated Rayleigh fading with unequal branch SNRs

The bit error probability (BEP) for coherent detection of binary signals with dual-diversity predetection equal gain combining is derived using the Beaulieu (1991) series. In particular, we consider a correlated Rayleigh fading channel with unequal branch signal-to-noise ratios. The BEP expression is in terms of the power correlation coefficient of the branches, is easy to compute, and depicts clearly the effect of correlated fading on the error performance.     

Capacity of MRC on Correlated Rician Fading Channels

A new exact explicit expression is derived for the ergodic capacity of maximal ratio combining (MRC) schemes over arbitrarily correlated Rician fading channels. This is used to study the effects of channel correlation on the ergodic capacity. Numerical results reveal that both the phase and the magnitude of correlation have an impact on the ergodic capacity of Rician fading channels. This is in contrast to correlated Rayleigh fading, where the phase of the correlation has no effect on the ergodic capacity. It is also observed that negatively correlated branches in Rician fading may lead to an increase in ergodic capacity beyond that obtained by uncorrelated branches.     

Effects of correlated shadowing signals on channel reuse in mobileradio systems

The authors present a study to evaluate the cochannel interference probability for the desired and interference signals which are correlated due to shadowing. The effects of correlation on the normalized reuse distance are investigated. A generalized expression for the cochannel interference probability is derived by combining uncorrelated (fast) Rayleigh fading and correlated (slow) log-normal signals. The cochannel interference probability for sectorized cell layouts is compared with the lower bound of cochannel interference probability for omnidirectional antenna systems. It is found that omnidirectional cell layouts cause the highest level of cochannel interference probability. An omnidirectional system requires a higher cluster size than a directional system to maintain acceptable cochannel interference     

波形具有任意相关性时MIMO雷达的检测性能

基于Neyman-Pearson准则,研究了空间分集MIMO(多输入多输出)雷达发射波形相关时的自、互相关旁瓣对MIMO雷达检测性能的影响.首先,分析了波形的相关性,导致了在空间上和时间上的白高斯噪声变为相关色噪声,同时,使得接收的回波信号具有一定的相关性,影响了空间分集的效果;然后,通过理论分析得到了MIMO雷达在波形具有任意相关性时的检测概率和虚警概率的解析表达式.通过数值计算,得到如下结论:与发射正交波形相比,在高信噪比(SNR)工作时,M1MO雷达波形相关时的自、互相关旁瓣使得MIMO雷达的检测性能下降;在低SNR时,波形的相关性能够改善检测性能;波形的低自、互相关旁瓣对MIMO雷达的检测性能影响不大.     

Spectral efficiency of dual diversity selection combining schemes under correlated Nakagami-0.5 fading with unequal average received SNR

The spectral efficiency results for different adaptive transmission schemes over correlated diversity branches with unequal average signal to noise ratio (SNR) obtained so far in literature are not applicable for Nakagami-0.5 fading channels. In this paper, we investigate the effect of fade correlation and level of imbalance in the branch average received SNR on the spectral efficiency of Nakagami-0.5 fading channels in conjunction with dual-branch selection combining (SC). This paper derived the expressions for the spectral efficiency over correlated Nakagami-0.5 fading channels with unequal average received SNR. This spectral efficiency is evaluated under different adaptive transmission schemes using dual-branch SC diversity scheme. The corresponding expressions for Nakagami-0.5 fading are considered to be the expressions under worst fading conditions. Finally, numerical results are provided to illustrate the spectral efficiency degradation due to channel correlation and unequal average received SNR between the different combined branches under different adaptive transmission schemes. It has been observed that optimal simultaneous power and rate adaptation (OPRA) scheme provides improved spectral efficiency as compared to truncated channel inversion with fixed rate (TIFR) and optimal rate adaptation with constant transmit power (ORA) schemes under worst case fading scenario. It is very interesting to observe that TIFR scheme is always a better choice over ORA scheme under correlated Nakagami-0.5 fading channels with unequal average received SNR.     

多输入多输出系统信道容量研究

该文研究接收端采用均圆阵天线阵放置空间有限的条件下,存在相关衰落时MIMO系统的信道容量。建立了衰落相关模型,分析了散射角大小及天线数对信道容量的影响,采用随机理论推导了MN的MIMO系统信道容量的闭式解。分析结果表明,MIMO系统信道容量主要由衰落相关矩阵的特征值决定。仿真结果表明,在接收端空间有限的情况下,天线数增大到一定程度时,信道容量达到饱和,再增加天线数,对信道容量的影响很小。     

Bit error probability for MDPSK and NCFSK over arbitrary Ricianfading channels

In this paper, we analyze the bit error probability (BEP) of binary and quaternary differential phase shift keying (2/4 DPSK) and noncoherent frequency shift keying (NCFSK) with postdetection diversity combining in arbitrary Rician fading channels. The model is quite general in that it accommodates fading correlation and noise correlation between different diversity branches as well as between adjacent symbol intervals. We show that the relevant decision statistic can be expressed in a noncentral Gaussian quadratic form, and its moment generating function (MGF) is derived. Using the MGF and the saddle point technique, we give an efficient numerical quadrature scheme to compute the BEP. The most significant contribution of the paper, however, lies in the derivation of a closed-form cumulative distribution function (cdf) for the decision statistic. As a result, a closed-form BEP expression in the form of an infinite series of elementary functions is developed, which is general and unifies previous published BEP results for 2/4 DPSK and NCFSK for multichannel reception in Rician fading. Specialization to some important cases are discussed and, as a byproduct, a new and general finite-series expression for the BEP in arbitrarily correlated Rayleigh fading is obtained. The theory is applied to study 2/4 DPSK and NCFSK performance for independent and correlated Rician fading channels; and some interesting findings are presented     

Performance of QDPSK signals with postdetection equal gaindiversity combining in arbitrarily correlated Nakagami-m fading channels

This letter derives a bit-error probability (BEP) expression for quadrature differential phase-shift keying (QDPSK) signals with post-detection equal gain combining (EGC) in additive white Gaussian noise and slow frequency-nonselective arbitrarily correlated Nakagami-m fading channels. Unlike previous work, the effects of arbitrary values of fading severity parameter m and the arbitrary correlation between the L diversity channels are considered. The derived expression can be easily computed via numerical integration routines, and hence, can be usefully exploited in the performance evaluation of digital mobile radio systems     

Performance analysis of square arranged antenna array with SC and MRC receiver over Nakagami fading channel

In this paper, the performance of using a square array of four antennas for selection combining (SC) and maximal-ratio combining (MRC) of Nakagami correlated signals is investigated. The closed form of average output signal-to-noise ratio and bit error rate (BER) for SC with arbitrary four correlated branches is derived; the expression of BER with MRC is also derived by utilizing the characteristic function method. Two models for the angle of arrival (AOA), i.e., uniform and truncated Gaussian, are considered in the system performance evaluation. The effects of correlation coefficients and fading factor on the system performance are investigated through numerical examples, which show that the uniformly distributed AOA system outperforms the truncated Gaussian-distributed counterpart with small angular spread. The degradation of system performance in the presence of one-antenna failure is also investigated.     

Performance analysis of maximal ratio transmission with receiver antenna selection over correlated Nakagami-m fading channels

In this paper, we develop a framework to analyze the performance analysis of multi-antenna system that employ maximal-ratio transmission with receive antenna selection (MRT/RAS) over correlated Nakagami-m fading channels. We derive the probability density function (pdf) of the post processing signal-to-noise ratio at the output of the decoder, when spatial fading correlation is assumed. Utilizing the pdf, a closed-form analytical expression is derived in terms of channel capacity, outage probability and symbol error rate (SER) of M-ary modulation schemes. It can be observed that the performance loss in terms of capacity and SER is negligible when the separation between adjacent antennas is as large as 0.5 for exponential correlation model. Numerical outcomes considering the spatial correlation represent the performance characteristics and analyze their impacts on channel capacity, outage probability and SER of MRT/RAS system.

     

Neyman-pearson detection of gauss-Markov signals in noise: closed-form error exponentand properties

The performance of Neyman-Pearson detection of correlated random signals using noisy observations is considered. Using the large deviations principle, the performance is analyzed via the error exponent for the miss probability with a fixed false-alarm probability. Using the state-space structure of the signal and observation model, a closed-form expression for the error exponent is derived using the innovations approach, and the connection between the asymptotic behavior of the optimal detector and that of the Kalman filter is established. The properties of the error exponent are investigated for the scalar case. It is shown that the error exponent has distinct characteristics with respect to correlation strength: for signal-to-noise ratio (SNR) /spl ges/1, the error exponent is monotonically decreasing as the correlation becomes strong whereas for SNR<1 there is an optimal correlation that maximizes the error exponent for a given SNR.     

Ergodic capacity formula of MIMO-OFDM systems under correlated frequency selective Rayleigh fading channels

An explicit formula for the ergodic capacity of Orthogonal Frequency Division Multiplexing (OFDM)-based Multiple-Input Multiple-Output (MIMO) systems under correlated frequency selective Rayleigh channels is derived,by simplifying the channel response matrix in frequency domain into the so-called Kronecker model composed of three kinds of correlations,i.e.multipath tap gain correlation and spatial fading correlations at both transmitter and receiver.The derived formula is very simple and convenient for one to estimate the effects of all three kinds of correlations on MIMO-OFDM capacity.If taps are independent,there is a very simple expression for the ergodic capacity.In case of tap correlation,the capacity formula could be further given in an integral expression.The validity of the new formula is verified and the effects of correlations,delay spread as well as the number of subcarriers on the ergodic capacity are evaluated via Monte Carlo simulations.     

Space–Time Power Schedule for Distributed MIMO Links Without Instantaneous Channel State Information at the Transmitting Nodes

A space-time optimal power schedule for multiple distributed multiple-input multiple-output (MIMO) links without the knowledge of the instantaneous channel state information (CSI) at the transmitting nodes is proposed. A readily computable expression for the ergodic sum capacity of the MIMO links is derived. Based on this expression, which is a non-convex function of power allocation vectors, a projected gradient algorithm is developed to optimize the power allocation. For a symmetric set of MIMO links with independent identically distributed channels, it is observed that the space-time optimal power schedule reduces to a uniform isotropic power schedule when nominal interference is low, or to an orthogonal isotropic power schedule when nominal interference is high. Furthermore, the transition region between the latter two schedules is seen to be very sharp in terms of nominal interference-to-noise ratio (INR). For MIMO links with correlated channels, the corresponding space-time optimal power schedule is developed based on the knowledge of the channel correlation matrices. It is shown that the channel correlation has a great impact on the ergodic capacity and the optimality of different power scheduling approaches.     

标准球形译码算法在发射相关MIMO信道下的平均复杂度分析

球形译码算法作为实现MIMO系统最大似然检测的一种有效方法,受到广泛重视.目前,几乎所有对球形译码算法的研究,均是基于假设信道衰落系数完全统计独立并且同分布,而在实际环境下,天线之间通常存在相关性,这样会使球形译码算法的复杂度发生变化.本文针对标准的球形译码算法,对其在发射相关MIMO信道下的复杂度进行了数学分析,推导了平均复杂度的数学表达式,并利用计算机仿真,比较了在不同的信噪比和不同的发射天线数下,发射相关性强弱对算法复杂度的影响.     

Outage probability of SC receiver over exponentially correlated K fading channels

A mathematical expression for the outage probability of a selection combining diversity receiver with an arbitrary number of input branches is presented for exponentially correlated K fading channels. Numerical and simulation results are plotted and the effect of correlation, number of diversity branches and fading parameter on the outage performance of the receiver is studied. Results suggest that a correlation coefficient less than 0.5 may be used in practice.     

An exact error floor for downlink MC-CDMA in correlated Rayleighfading channels

Downlink multicarrier code-division multiple access (MC-CDMA) with maximal ratio combining (MRC) in correlated Rayleigh fading channels is considered. An exact error floor in a closed-form expression is provided based on the characteristic function (CF) and residue calculation method. Numerical results show that orthogonal spreading sequences (Walsh and orthogonal Gold sequences) perform better than nonorthogonal sequences (Gold sequences) and Walsh codes have the best performance. In addition, downlink MC-CDMA is found to benefit from the correlation between subcarriers     

Effect of joint spatial correlation on the diversity performance of space?time block codes

We characterize the effect of joint spatial correlation on the diversity performance of multiple-input multiple-output (MIMO) systems. The joint spatial correlation is structured by the coupling matrix whose elements determine the average power coupling between the transmit and receive eigenmodes. We first derive the closed-form expression for the exact symbol error probability (SEP) of orthogonal space?time block codes over jointly correlated MIMO Rayleigh-fading channels. We then show that the achievable diversity order is equal to the number of nonzero elements of the power coupling matrix and establish the Schur monotonicity theorems on the SEP and the effective fading figure as a functional of elements of the power coupling matrix. Diversity, orthogonal space?time block code (OSTBC), Schur monotonicity, spatial correlation, symbol error probability (SEP).     

Capacity Per Unit Energy of Fading Channels With a Peak Constraint

A discrete-time single-user scalar channel with temporally correlated Rayleigh fading is analyzed. There is no side information at the transmitter or the receiver. A simple expression is given for the capacity per unit energy, in the presence of a peak constraint. The simple formula of VerdÚ for capacity per unit cost is adapted to a channel with memory, and is used in the proof. In addition to bounding the capacity of a channel with correlated fading, the result gives some insight into the relationship between the correlation in the fading process and the channel capacity. The results are extended to a channel with side information, showing that the capacity per unit energy is one nat per joule, independently of the peak power constraint. A continuous-time version of the model is also considered. The capacity per unit energy subject to a peak constraint (but no bandwidth constraint) is given by an expression similar to that for discrete time, and is evaluated for Gauss–Markov and Clarke fading channels.     

相关局部判决下基于N-P准则的分布式检测融合算法

研究了在相关局部判决条件下的基于N-P准则的分布式检测融合算法，给出了利用相关系数来表示的最优融合规则的表达式，解决了相关系数的求解问题，并在实验仿真的基础上，给出了部分有益的结论。