Optimal training for MIMO frequency-selective fading channels

High data rates give rise to frequency-selective propagation effects. Space-time multiplexing and/or coding offer attractive means of combating fading and boosting capacity of multi-antenna communications. As the number of antennas increases, channel estimation becomes challenging because the number of unknowns increases, and the power is split at the transmitter. Optimal training sequences have been designed for flat-fading multi-antenna systems or for frequency-selective single transmit antenna systems. We design a low-complexity optimal training scheme for block transmissions over frequency-selective channels with multiple antennas. The optimality in designing our training schemes consists of maximizing a lower bound on the ergodic (average) capacity that is shown to be equivalent to minimizing the mean square error of the linear channel estimator. Simulation results confirm our theoretical analysis that applies to both single- and multicarrier transmissions.     

An iterative particle filter signal detector for MIMO fast fading channels

For flat fast fading Multiple-Input Multiple-Output （MIMO） channels, this paper presents a sampling based channel estimation and an iterative Particle Filter （PF） signal detection scheme. The channel estimation is comprised of two parts： the adaptive iterative update on the channel distribution mean and a regular update on the ＂adaptability＂ via pilot. In the detection procedure, the PF is employed to produce the optimal decision given the known received signal and the sequence of the channel samples, where an asymptotic optimal importance density is constructed, and in terms of the asymptotic update order, the Parallel Importance Update （PIU） and the Serial Importance Update （SIU） scheme are performed respectively. The simulation results show that for the given fading channel, if an appropriate pilot mode is selected, the proposed scheme is more robust than the conventional Kalman filter based superimposed detection scheme.     

BER performance of linear STBC from orthogonal designs over MIMO correlated Nakagami-m fading channels

This paper presents the evaluation of the average bit error rate (BER) performance of linear space-time block codes (STBC) from orthogonal designs over correlated identically distributed Nakagami-m fading channels. Starting from the moment-generating function (MGF) of the multipath component signals at the antenna array elements, analytical expressions of the BER performance for both integral and nonintegral Nakagami-m fading parameters are derived. Closed-form expressions of the spatial cross-correlation function for mobile nonfrequency selective Nakagami-m fading multiple-input-multiple-output (MIMO) channels are obtained, which are valid for small angle-of-arrival (AOA) spread. In this expressions, various parameters of interest, such as the mean AOA of the signal, AOA spread, and array configurations, are all taken into account. The effects of antenna array configuration and the operating environment (mean AOA, AOA spread, Nakagami fading parameter) on the BER performance of the system are illustrated by several numerical examples.     

On coding for block fading channels

This work considers the achievable performance for coded systems adapted to a multipath block-fading channel model. This is a particularly useful model for analyzing mobile-radio systems which employ techniques such as slow frequency-hopping under stringent time-delay or bandwidth constraints for slowly time-varying channels. In such systems, coded information is transmitted over a small number of fading channels in order to achieve diversity. Bounds on the achievable performance due to coding are derived using information-theoretic techniques. It is shown that high diversity can be achieved using relatively simple codes as long as very high spectral efficiency is not required. Examples of simple block codes and carefully chosen trellis codes are given which yield, in some cases, performances approaching the information-theoretic bounds     

Maximum-SNR spatial-temporal formatting designs for MIMO channels

We consider a communication scenario involving an m /spl times/ n multiple input multiple output (MIMO) flat fading channel whose input is a symbol stream multiplied prior to transmission by an n /spl times/ n spatial-temporal formatting matrix X and whose output is fed into an m /spl times/ n linear combiner Z. We show how to choose the matrices X and Z to maximize the signal-to-noise ratio (SNR) of the linear combiner output data that are used for detection, under the total power constraint (TPC), the elemental power constraint (EPC), or the total and elemental power constraint (TEPC). The TEPC design (considered here for the first time) is shown to include the TPC and EPC designs (previously considered by the authors) as special cases and, hence, to provide a theoretically and practically interesting unifying framework. We make use of this framework to discuss various tradeoffs of the three space-time formatting designs considered, such as transmission rate and requirements for channel state information at the transmission side. Additionally, we show that the EPC design, which is the only one of the aforementioned designs that does not require channel information at the transmission side, is also the maximum SNR design in the worst channel case under a TPC.     

Estimation of continuous flat fading MIMO channels

Multiple-input-multiple-output (MIMO) systems can provide high data rate wireless services in a rich scattering environment. We study one of the proposals for MIMO systems, the Bell Labs Layered Space-Time (BLAST) architecture. Channel estimation using training sequences is required for coherent detection in BLAST. We apply the maximum-likelihood channel estimator and the optimal training sequences for block flat fading channels to continuous flat fading channels and analyze the estimation error. The optimal training length and training interval that maximize the throughput for a given target bit error-rate are found by computer simulations as functions of the Doppler frequency and the number of antennas.     

Performance analysis of orthogonal space-time block codes in spatially correlated MIMO Nakagami fading channels

Orthogonal space-time block coding (STBC) is an open-loop transmit diversity scheme that decouples the multiple-input multiple-output (MIMO) channel, thereby reducing the space-time decoding into a scalar detection process. This characteristic of STBC makes it a powerful tool, achieving full diversity over MIMO fading channels, and requiring little computational cost for both the encoding and decoding processes. In this paper, we exploit the single-input single-output equivalency of STBC in order to analyze its performance over nonselective Nakagami fading channels in the presence of spatial fading correlation. More specifically, we derive exact closed-form expressions for the outage probability and ergodic capacity of STBC, when the latter is employed over spatially correlated MIMO Nakagami fading channels. Moreover, we derive the exact symbol error probability of coherent M-PSK and M-QAM, when these modulation schemes are used along with STBC over such fading channels. The derived formulae are then used to assess the robustness of STBC to spatial correlation by considering general MIMO correlation models and analyzing their effects on the outage probability, ergodic capacity, and symbol error probability achieved by STBC.     

CRC-aided turbo equalization for MIMO frequency selective fading channels

This paper presents a CRC （Cyclic Redundancy Check）-aided turbo equalization approach to reduce the computational complexity. In this approach, CRC code bits are padded to the end of each transmit block, and a cyclic redundancy check is performed after decoding each block at the receiver en.d. If the check sum is zero, which means the receive block is correct, the corresponding LLRs （Log Likelihood Ratios） of this block are set high reliable values, and all the computations corresponding to this block can be cancelled for the subsequent outer iterations. With a lower computational complexity the proposed approach can achieve the same as or even better performance than the conventional non-CRC method.     

Correlated jamming on MIMO Gaussian fading channels

We consider a zero-sum mutual information game on multiple-input multiple-output (MIMO) Gaussian Rayleigh-fading channels. The players are an encoder-decoder pair as the maximizer, and a jammer as the minimizer, of the mutual information between the input and the output of the channel. There are total power constraints on both the jammer and the encoder. Also, the jammer has access to the encoder output. We find the unique saddle point of this game, and prove the somewhat surprising result that the knowledge of the channel input is useless to the jammer.     

Interference cancellation schemes for MIMO MC-CDM in fading channels

A novel interference cancellation (IC) scheme for MIMO MC-CDM systems is proposed. It is shown that the existing IC schemes are suboptimum and their performance can be improved by utilising some special properties of the residual interference after interference cancellation.     

Space-time-Doppler block coding for correlated time-selective fading channels

Coping with time-selective fading channels is challenging but also rewarding, especially with multiantenna systems, where joint space-Doppler diversity and coding gains can be collected to enhance performance of wireless mobile links. These gains have not been quantified, and space-time coded systems maximizing joint space-Doppler benefits have not been designed. Based on a parsimonious basis expansion model for the underlying time-selective (and possibly correlated) channels, we quantify these gains in closed form. Furthermore, we develop space-time-Doppler coded systems that guarantee the maximum possible space-Doppler diversity, along with the largest coding gains within all linearly coded systems. Our three novel designs exploit knowledge of the maximum Doppler spread, and each offers a uniquely desirable tradeoff, including high spectral efficiency, low decoding complexity, and high performance. Our analytical results are confirmed by simulations and reveal the relative of merits of our three designs in comparison with an existing approach.     

Bandwidth efficient block codes for Rayleigh fading channels

It is shown that the effective code length (ECL) of a short ECL block modulation code (BCM) is the dominant factor in its performance over a Rayleigh fading channel. To demonstrate this, three new BCM codes are presented as examples. Their performances are evaluated and compared on both Gaussian and fading channels.<>     

Decision-directed estimation of MIMO time-varying Rayleigh fading channels

This paper presents a decision-directed (DD) maximum a posteriori probability (MAP) channel-estimation scheme for multiple-input multiple-output (MIMO) time-varying fading channels. With the estimate of the channel matrix for the current symbol interval, a zero-forcing (ZF) receiver is applied to detect the spatially multiplexed data on a symbol-by-symbol basis. Symbol decisions are then fed to the channel predictor for estimation of channel coefficients in future symbol intervals. Simulated error performance of a ZF receiver with the DD MAP and perfect channel estimates is provided and compared.     

Differential space-time modulation with eigen-beamforming for correlated MIMO fading channels

In this paper, joint differential space-time modulation (DSTM) and eigen-beamforming for correlated multiple-input multiple-output (MIMO) fading channels. While DSTM does not require knowledge of each channel realization, the channel's spatial correlation can be easily estimated without training at the receiver and exploited by the transmitter to enhance the error probability performance. A transmission scheme is developed here that combines beamforming with differential multiantenna modulation based on orthogonal space-time block coding. Error probability is analyzed for both spatially correlated and independent Rayleigh fading channels. Based on the error probability analysis, power loading coefficients are derived to improve performance. The analytical and simulation results presented here corroborate that the proposed scheme can achieve considerable performance gain in correlated channels relative to DSTM without beamforming.     

Lower capacity bound for MIMO correlated fading channels with keyhole

It is well known that the existence of spatial fading correlation and keyhole effects severely reduces the capacity of multiple-input and multiple-output (MIMO) channels. In this letter, for correlated Rayleigh frequency-flat fading channels with keyholes, a tight lower capacity bound is given in a closed form. For the uncorrelated case, the lower bound can be proved to be tight asymptotically. The tightness of this bound for both correlated and uncorrelated channels is demonstrated by numerical examples.     

用于快时变MIMO衰落信道的一种差分空时调制技术

针对快时变多输入多输出(MIMO)平坦衰落信道,利用时变信道的基扩展模型(BEM),提出了一种差分空时调制方案。差分编码按块进行,发射信号矩阵为对角酉矩阵。通过设计发射端的交织及接收端的解交织,判决反馈差分检测不需要信道状态信息。理论分析和仿真表明,该方案能同时实现最大的天线分集和信道时变性所提供的Doppler分集。     

Receive antenna selection for MIMO systems over correlated fading channels

In this letter, we propose a novel receive antenna selection algorithm based on cross entropy optimization to maximize the capacity over spatially correlated channels in multiple-input multiple-output (MIMO) wireless systems. The performance of the proposed algorithm is investigated and compared with the existing schemes. Simulation results show that our low complexity algorithm can achieve near-optimal results that converge to within 99% of the optimal results obtained by exhaustive search. In addition, the proposed algorithm achieves near-optimal results irrespective of the mutual relationship between the number of transmit and receive antennas, the statistical properties of the channel and the operating signal-to-noise ratio.     

Performance of cross-layer design for orthogonal space-time block coded MIMO systems with imperfect CSI in Ricean fading channels

A cross-layer design (CLD) scheme for orthogonal space-time block coded MIMO systems with imperfect channel state information is presented by combining adaptive modulation and automatic repeat request, and the corresponding system performance is investigated over Ricean fading channel. The fading gain value is partitioned into a number of regions by which the modulation is adapted in terms of the region the fading gain falls in. The fading gain switching thresholds subject to a target packet error rate (PER) constraint are derived. According to these results, and using the generalized Marcum Q-function, we derive the theoretical formulae of average PER and spectrum efficiency (SE) of the system with CLD for both perfect and imperfect estimation in detail. As a result, closed-form expressions for average PER and SE are obtained. These expressions include some existing expressions in Rayleigh channel as special cases. With these expressions, the system performance in Ricean channel with perfect and imperfect estimation information can be evaluated effectively. Computer simulation for average PER and SE show that the theoretical analysis and simulation are consistent. The results show that the system performance will be effectively improved as Ricean factor increases, but it will be degraded as estimation errors increases.     

General random coding bounds: AWGN channels to MIMO fading channels

Random coding bounds are obtained for multiple-input multiple-output (MIMO) fading channels. To derive the result in a compact and easy-to-evaluate form, a series of combinatorial codeword enumeration problems are solved for input-constrained MIMO fading channels. The bounds obtained in this paper are shown useful as performance prediction measures for MIMO systems which employ turbo-like block codes as the outer code to derive the space-time inner code. The error exponents for MIMO channels are also derived from the bounds, and then compared with the classical Gallager error exponents as well as the channel capacities. The random coding bounds associated with the maximum likelihood receiver exhibit good match with the extensive system simulation results obtained with a turbo-iterative receiver.     

A pre-BLAST-DFE technique for the downlink of frequency-selective fading MIMO channels

In this paper, we propose a pre-Bell Laboratories layered space-time (BLAST)-decision-feedback equalization technique for the downlink of frequency-selective fading multiple-input multiple-output (MIMO) channels to combat multiple-access interference (MAI) and intersymbol interference (ISI). In our technique, we perform MIMO pre-equalization and prelayered space-time processing at the transmitter or base station, with a simplified receiver at the mobile station that requires only limited signal processing. An important application is in the downlink, so that a simplified mobile station can be constructed. An expression for the signal-to-noise ratio (SNR) and error probability based on the Gaussian approximation of the output noise term is derived. Performance is investigated by analysis and simulation results. In particular, it is demonstrated that the diversity order of this technique is higher than that of the MIMO orthogonal frequency-division multiplexing (OFDM) with vertical (V)-BLAST and MIMO OFDM with linear transmit preprocessing. It is also noticed that this technique performs better at high SNR values.