Optimum transmit-receive beamforming with noisy channel estimates for correlated MIMO Rayleigh channels

In this paper, we design jointly optimum transmitter and receiver beamforming structures in correlated MIMO Rayleigh fading channels with noisy channel estimates, and evaluate their performance through a closed-form expression for the probability of error. At the receiver, an estimate of the channel is obtained based on the transmitted pilot symbols. The knowledge of the estimate is then made available to the transmitter through a feedback channel. It is assumed that spatial correlation exists, either at the transmitter or at the receiver. A new exact closed-form expression for the probability of error is derived and the joint effects of diversity order and channel estimation accuracy on system performance are analyzed.     

Analysis of diffuse optical wireless channels employing spot-diffusing techniques, diversity receivers, and combining schemes

In this letter, the performance of an indoor optical wireless spot-diffusing system using various multibeam transmitter configurations, in association with direction diversity and combining techniques, is assessed and compared under the impact of multipath dispersion and ambient light noise through theoretical analysis and computer simulation. Computer simulation for three different multibeam transmitter configurations and a conventional diffuse transmitter is carried out. Diversity receiver and wide field-of-view (FOV) receiver configurations are evaluated in conjunction with the proposed configurations. For the diversity-detection case, a receiver comprising an array of narrow FOV detectors (three and seven segments) oriented in different directions is used to maximize the collected signals and minimize noise. A novel line-strip multibeam system (LSMS) is investigated with single and diversity receiver configurations, and is compared with other spot-diffusing methods. Combining schemes, including selection combining, maximum ratio combining, and equal gain combining are employed for the presented configurations. Our results indicate that the performance improvement obtained through the use of LSMS with a three-direction diversity receiver is about 20 dB signal-to-noise ratio enhancement over the conventional diffuse system, and 26 dB when combining techniques are used. Root mean square delay-spread performance for the proposed configurations, at different positions on the communication floor, are also evaluated and compared.     

Optimum Receiver for a Realistic Transmit–Receive Diversity System in Correlated Fading

A transmit–receive diversity system in correlated Rayleigh fading in which the receiver estimates the channel through pilot symbols, and feeds this information back to the transmitter through a feedback path, is considered. The imperfect channel state information (CSI) is used by the transmitter to obtain the transmit weight vector for data transmission. The optimum receiver in the maximum-likelihood (ML) sense obtained from the conditional distribution of the received signal vector, conditioned on the imperfect CSI and the transmit weight vector, is derived for the system. For the case of $M$-ary phase-shift keying (MPSK), an analytical expression for the conditional symbol error probability (SEP), conditioned on the channel estimate and the transmit weight vector, is obtained, with the transmit weight vector chosen to minimize this conditional SEP. For the receive-only and transmit-only correlation scenarios with ill-conditioned eigenvalues of the receive and transmit covariance matrices (that is, some of the eigenvalues are very small), we derive expressions for the diversity gain. Numerical results are presented to compare the performance of our receiver with that of a conventional receiver in case of exponentially correlated fading. These results show that the optimum receiver typically has about a 0.5-dB gain over a conventional receiver when the correlation coefficient exceeds 0.5 and the number of receive antennas is much larger than the number of transmit antennas.      

Extended MLSE diversity receiver for the time- andfrequency-selective channel

This paper develops a maximum-likelihood sequence estimation (MLSE) diversity receiver for the time- and frequency-selective channel corrupted by additive Gaussian noise when linear constellations (M-ASK, M-PSK, M-QAM) are employed. The paper extends Ungerboeck's derivation of the extended MLSE receiver for the purely frequency-selective channel to the more general channel. Although the new receiver structure and metric assume ideal channel-state information (CSI), the receiver can be used wherever high-quality CSI is available, such as a comb of pilot tones or time-isolated symbols. The major contributions of this paper are as follows: (1) the derivation of a finite-complexity diversity receiver that is maximum likelihood (ML) for all linear channel models and sources of diversity, as long as ideal CSI is available; (2) a benchmark, in that the new receiver's performance is a lower bound on the performance of practical systems, which either lack ideal CSI or are not ML; (3) insight into matched filtering and ML diversity receiver processing for the time- and frequency-selective channels; and (4) bounds on the new receiver's bit-error rate (BER) for ideal CSI and pilot tone CSI, in a fast Rayleigh-fading channel with multiple independently faded paths. The new receiver can seamlessly tolerate square-root Nyquist pulses without a fading-induced ISI error floor     

Differentially amplitude and phase-encoded QAM for the correlatedRayleigh-fading channel with diversity reception

This paper studies the differentially amplitude and phase-encoded (DAPE) quadrature amplitude modulation (QAM) transmission over correlated Rayleigh channels with diversity reception. Operating over two successive received symbols, the optimum and an asymptotic maximum-likelihood (AML) differentially coherent receiver are developed and compared with a conventional switched diversity combining (SDC) grid receiver. It is shown that the AML and SDC grid receivers are much simpler in complexity than the optimum receiver in that no channel side information is required in their realization. An exact expression of the bit-error probability (BEP) is obtained for the SDC grid receiver. Based on a union bound argument, a BEP upper bound for the AML receiver is also derived and verified by simulation. Numerical results on 16- and 64-point constellations show that the AML receiver exhibits an almost optimum performance and the SDC grid receiver with a small level of diversity is nearly optimum. It is also shown by simulation that the conventional equal-gain diversity receiver is almost optimal for demodulating a 16-point DAPE QAM signal     

信道相关对空间分集接收信号闪烁的影响

为了探究信道相关性对无线光通信中空间分集接收信号闪烁的影响,给采用空间分集接收技术的通信端的各子孔径大小与分布设计提供参考,理论推导了弱起伏条件下空间分集接收信道相关系数的表达式,给出了信道相关系数与分集接收信号闪烁的关系;数值研究了水平湍流均匀路径与整层大气湍流非均匀下行传输路径下的信道相关系数。结果表明,对于平面波,湍流非均匀路径下孔径接收时信道间存在明显的负相关特性。对于球面波,湍流非均匀路径下孔径接收时的信道相关性与湍流均匀路径情况类似,负相关特性都不明显。     

Spatial diversity in radars-models and detection performance

Inspired by recent advances in multiple-input multiple-output (MIMO) communications, this proposal introduces the statistical MIMO radar concept. To the authors' knowledge, this is the first time that the statistical MIMO is being proposed for radar. The fundamental difference between statistical MIMO and other radar array systems is that the latter seek to maximize the coherent processing gain, while statistical MIMO radar capitalizes on the diversity of target scattering to improve radar performance. Coherent processing is made possible by highly correlated signals at the receiver array, whereas in statistical MIMO radar, the signals received by the array elements are uncorrelated. Radar targets generally consist of many small elemental scatterers that are fused by the radar waveform and the processing at the receiver, to result in echoes with fluctuating amplitude and phase. It is well known that in conventional radar, slow fluctuations of the target radar cross section (RCS) result in target fades that degrade radar performance. By spacing the antenna elements at the transmitter and at the receiver such that the target angular spread is manifested, the MIMO radar can exploit the spatial diversity of target scatterers opening the way to a variety of new techniques that can improve radar performance. This paper focuses on the application of the target spatial diversity to improve detection performance. The optimal detector in the Neyman-Pearson sense is developed and analyzed for the statistical MIMO radar. It is shown that the optimal detector consists of noncoherent processing of the receiver sensors' outputs and that for cases of practical interest, detection performance is superior to that obtained through coherent processing. An optimal detector invariant to the signal and noise levels is also developed and analyzed. In this case as well, statistical MIMO radar provides great improvements over other types of array radars.     

Fast adaptive equalization/diversity combining for time-varyingdispersive channels

We examine adaptive equalization and diversity combining methods for fast Rayleigh-fading frequency selective channels. We assume a block adaptive receiver in which the receiver coefficients are obtained from feedforward channel estimation. For the feedforward channel estimation, we propose a novel reduced dimension channel estimation procedure, where the number of unknown parameters are reduced using a priori information of the transmit shaping filter's impulse response. Fewer unknown parameters require a shorter training sequence. We obtain least-squares, maximum-likelihood, and maximum a posteriori (MAP) estimators for the reduced dimension channel estimation problem. For symbol detection, we propose the use of a matched filtered diversity combining decision feedback equalizer (DFE) instead of a straightforward diversity combining DFE. The matched filter form has lower computational complexity and provides a well-conditioned matrix inversion. To cope with fast time-varying channels, we introduce a new DFE coefficient computation algorithm which is obtained by incorporating the channel variation during the decision delay into the minimum mean square error (MMSE) criterion. We refer to this as the non-Toeplitz DFE (NT-DFE). We also show the feasibility of a suboptimal receiver which has a lower complexity than a recursive least squares adaptation, with performance close to the optimal NT-DFE     

A new base station receiver for increasing diversity order in a CDMA cellular system

A new base station receiver is proposed and analyzed for a code-division multiple-access (CDMA) cellular system. The proposed receiver can achieve remarkable diversity gain by increasing diversity order with reasonable cost and complexity. From the numerical results, it is confirmed that the proposed receiver structure can be a practical solution for enhancing reverse-link capacity and improving performance in CDMA cellular system operations. The result in the letter can find its applications to legacy IS-95/cdma2000 1x base stations with simple modifications.     

射频接收机非线性对分集与复用影响分析

分别从分单输入单输出系统(single-input single-output, SISO)与多输入多输出系统(multiple-input multiple-output, MIMO)研究了多天线系统中射频接收机非线性对通信系统性能的影响规律,发现原有对非线性分集与复用折中的定义不再适用于考虑射频接收机非线性情况,并给出了适用于考虑射频接收机非线性情况的新定义. 通过复合信道建模推导了非理想情况下分集增益的定义和中断概率表达式,仿真了考虑射频接收机非线性时多天线系统分集增益与复用增益关系曲线,得出了考虑分集与复用折中时目标速率的增长规律. 理论和仿真表明,传统的分集增益和复用增益的定义并不适用于考虑接收机非线性的实际情况,SISO系统中射频接收机非线性对分集与复用的折中影响与理想情况一样,MIMO系统中需要对原有的分集增益和复用增益进行修正才能得到分集与复用的最优折中.     

A differential detection scheme for transmit diversity

We present a transmission scheme for exploiting diversity given by two transmit antennas when neither the transmitter nor the receiver has access to channel state information. The new detection scheme can use equal energy constellations and encoding is simple. At the receiver, decoding is achieved with low decoding complexity. The transmission provides full spatial diversity and requires no channel state side information at the receiver. The scheme can be considered as the extension of differential detection schemes to two transmit antennas     

多天线无线数据通信系统中多用户分集的研究

研究当接收天线不少于发送天线时多输入多输出(MIMO)系统的多用户分集能力。首先从理论上分析了发送天线个数等于1和2时最大似然接收和迫零接收系统的平均吞吐量和调度增益,以及仿真分析了发送天线个数大于2时系统性能。理论分析和仿真表明：在多用户的MIMO系统中,接收的平均信噪比、用户个数、收发天线个数、接收机的结构等对于多用户分集有很大的影响。当发送天线个数为1时,接收天线较少(1,2,3)和平均信噪比为．10dB时调度增益很大,但调度增益随着天线个数和发送功率增大急剧下降。和最大似然接收相比,迫零接收具有更大的多用户分集增益,因此迫零接收机的吞吐量可以很容易超过最大似然接收机。     

Generalized performance analysis of a delay diversity receiver in asynchronous CDMA channels

In this letter, the performance for the delay diversity receiver is analyzed in asynchronous code division multiple access (CDMA) channels. The outage probability and the bit error probability of the delay diversity receiver are accurately derived and compared with those of the conventional diversity receiver. From the analytical and numerical results, it is confirmed that the delay diversity receiver achieves a remarkable diversity gain with reasonable cost and complexity in asynchronous CDMA channels. Specifically, for roughly the same hardware complexity, the delay diversity receiver achieves nearly twice the diversity order of the conventional receiver.     

Probability of Error Analyses of a BFSK Frequency-Hopping System with Diversity Under Partial-Band Jamming Interference--Part III: Performance of a Square-Law Self-Normalizing Soft Decision Receiver

Linear and nonlinear diversity combining receivers for multihops-per-bit FH/BFSK waveforms in the partial-band noise jamming environment were studied in Parts I and II. It was shown that nonlinear combining receivers (Part II) can achieve a diversity gain for error rate improvement, while the linear combining receiver (Part I) cannot. The two types of nonlinear combining receivers treated in Part II required knowledge of system operational parameters for their optimum performance, such as measured noise power and the signal energy level at the receiver. In this paper, a self-normalizlng nonlinear combining receiver is shown to achieve a diversity gain without knowledge of signal or jamming levels, unlike the nonlinear schemes studied previously. The worst-case error probability performance of the self-normalizing receiver is obtained with and without system thermal noise. The numerical results are compared to those for the receivers studied earlier.     

Postdetection diversity receiver for DAPSK signals on the Rayleigh and Rician-fading channel

In this paper, the optimum decision boundaries for (N, M) differential amplitude phase-shift keying on the Rayleigh-fading channel are analyzed. A postdetection maximal ratio combining (MRC) and weighted maximal ratio combining (WMRC) diversity receivers are proposed. In the Rayleigh-fading channel, assuming a high signal-to-noise ratio and a small normalized Doppler frequency, the analytical optimum decision boundaries are obtained. In addition, it is shown that an outer optimum decision boundary is the inverse of the inner optimum decision boundary. In the proposed MRC receiver, the decision at each branch is made based on the minimum distance criterion. The performance of the MRC receiver is analyzed, in terms of the union bound for bit error probability. The proposed WMRC receiver assigns weighting factors to the decision variable at each branch, based on the optimum decision boundaries. The performance of the WMRC is investigated through computer simulation and compared with those of MRC and equal gain combining (EGC). From the results, the performances of MRC and WMRC are found to be better than those of the EGC receiver on both the Rayleigh- and Rician-fading channels. It is also found that the performance improvement of WMRC over MRC is more pronounced as the number of diversity branches increases     

分集技术及Pake接收机误码率的仿真

Rake接收技术是CDMA蜂窝移动通信系统中的关键技术之一。分集的基本思想是将接收到的多径信号分离成不相关的多路信号,把这些多径信号的能量按一定的规则合并,使接收到的有用信号能量最大化,进而提高接收信号信噪比达到抗衰落的目的。文中以异步DS-CDMA系统为例,论述了分集技术并对Rake接收机的误码率进行了分析与仿真。     

Optimal diversity combining based on linear estimation of rician fading channels

Optimal receiver diversity combining employing linear channel estimation is examined. Based on the statistical properties of least-squares (LS) and minimum mean square error (MMSE) channel estimation, an optimal diversity receiver for wireless systems employing practical linear channel estimation on Rician fading channels is proposed. The new receiver structure includes the conventional maximal ratio combining receiver as a special case. Exact analytical expressions for the symbol error rates (SERs) of LS and MMSE channel estimation aided optimal diversity combining are derived. It is shown that, if an optimal detector is used, an MPSK wireless system with MMSE channel estimation has the same SER when the MMSE channel estimation is replaced by LS estimation. This is an interesting counterexample to the common perception that channel estimation with smaller mean square error leads to smaller SER. Extensive simulation results validate the theoretical results.     

Performance evaluation of 2.5 Gbit/s and 5 Gbit/s optical wireless systems employing a two dimensional adaptive beam clustering method and imaging diversity detection

Previous indoor mobile optical wireless systems operated typically at 30 Mbit/s to 100 Mbit/s and here we report on systems that operate at 2.5 Gbit/s and 5 Gbit/s. We are able to achieve these improvements through the introduction of three new approaches: transmit beam power adaptation, a two dimensional beam clustering method (2DBCM), and diversity imaging. Through channel and noise modeling we evaluated the performance of our systems. The performance of a novel optical wireless (OW) configuration that employs a two dimensional adaptive beam clustering method (2DABCM) in conjunction with imaging diversity receivers is evaluated under multipath dispersion and background noise (BN) impairments. The new proposed system (2DABCM transmitter with imaging diversity receiver) can help reduce the effect of intersymbol interference and improve the signal-to-noise ratio (SNR) even at high bit rate. At a bit rate of 30 Mbit/s, previous work has shown that imaging conventional diffuse systems (CDS) with maximal ratio combining (MRC) offer 22 dB better SNR than the non-imaging CDS. Our results indicate that the 2DABCM system with an imaging diversity receiver provides an SNR improvement of 45 dB over the imaging CDS with MRC when both operate at 30 Mbit/s. In the CDS system, an increase in bandwidth from 38 MHz (non-imaging CDS) to 200 MHz approximately, is achieved when an imaging receiver is implemented. Furthermore, the three new methods introduced increase the bandwidth from 38 MHz to 5.56 GHz. At the least successful receiver locations, our 2.5 Gbit/s and 5 Gbit/s imaging 2DABCM systems with MRC offer significant SNR improvements, almost 26 dB and 19 dB respectively over the non-imaging CDS that operates at 30 Mbit/s.     

Probability-of-error bounds for binary transmission on the slowly fading Rician channel

Chernoff bounds and tilted distribution arguments are applied to obtain error probability bounds for binary signaling on the slowly-fading Rician channel with L diversity. For the maximum likelihood receiver, the CB-optimum [optimum in the sense of minimizing the Chernoff (upper) bound on error probability] signal correlation is determined and plotted; it is found that antipodal signals should be used ifa > b^{2}(1 + b), where a is the signal-to-noise ratio of the specular components andbis that of the fading components. The CB-optimum number of diversity paths is then obtained. Ifa/b > 0.2, antipodal signaling with unlimited diversity is CB-optimum; whereas, ifa/b < 0.2, orthogonal signaling with properly chosen diversity is very nearly CB-optimum. If restricted to orthogonal signaling, unlimited diversity is CB-optimum whenevera/b > 1.0. Similar results are obtained for the generally nonoptimum square-law-combining receiver. In this case, orthogonal signaling with finite diversity is always CB-optimum.     

Pre-DFT combining space diversity assisted COFDM

A new pre-discrete Fourier transformation (DFT) combining diversity receiver is proposed for coded orthogonal frequency-division multiplexing systems and investigated in a frequency-selective fading channel. Although the post-DFT combining space diversity receiver is optimum in terms of maximizing the signal-to-noise ratio (SNR) after combining, it requires an increased number of DFT processors, which increases the computational complexity. Since the proposed pre-DFT combining receiver requires only one DFT processor, while achieving space diversity gain, the proposed scheme can drastically reduce the computational complexity. This paper derives the optimum diversity weights for the proposed receiver analytically, in order to maximize the SNR after combining. Computer simulation results show that the proposed scheme can reduce the computational complexity by tolerating a slight performance degradation