On Optimum Power Allocation for the V-BLAST

A unified analytical framework for optimum power allocation in the unordered V-BLAST algorithm and its comparative performance analysis are presented. Compact closed-form approximations for the optimum power allocation are derived, based on average total and block error rates. The choice of the criterion has little impact on the power allocation and, overall, the optimum strategy is to allocate more power to lower step transmitters and less to higher ones. High-SNR approximations for optimized average block and total error rates are given. The SNR gain of optimization is rigorously defined and studied using analytical tools, including lower and upper bounds, high and low SNR approximations. The gain is upper bounded by the number of transmitters, for any modulation format and type of fading channel. While the average optimization is less complex than the instantaneous one, its performance is almost as good at high SNR. A measure of robustness of the optimized algorithm is introduced and evaluated. The optimized algorithm is shown to be robust to perturbations in individual and total transmit powers. Based on the algorithm robustness, a pre-set power allocation is suggested as a low-complexity alternative to the other optimization strategies, which exhibits only a minor loss in performance over the practical SNR range.Comment: Accepted by IEEE Transactions on Communications, Apr. 200

Optimum Power and Rate Allocation for Coded V-BLAST: Average Optimization

An analytical framework for performance analysis and optimization of coded V-BLAST is developed. Average power and/or rate allocations to minimize the outage probability as well as their robustness and dual problems are investigated. Compact, closed-form expressions for the optimum allocations and corresponding system performance are given. The uniform power allocation is shown to be near optimum in the low outage regime in combination with the optimum rate allocation. The average rate allocation provides the largest performance improvement (extra diversity gain), and the average power allocation offers a modest SNR gain limited by the number of transmit antennas but does not increase the diversity gain. The dual problems are shown to have the same solutions as the primal ones. All these allocation strategies are shown to be robust. The reported results also apply to coded multiuser detection and channel equalization systems relying on successive interference cancellation

On Optimization of the V-BLAST Algorithm

Optimum power allocation for the V-BLAST algorithm, which is based on various criteria (average and instantaneous block and total error rates (BLER and TBER)), is considered. Closed-form expressions are derived for high-SNR case in a Rayleigh fading channel. It is demonstrated that, in that case, the optimization "on average" is almost identical to the instantaneous one (while the former requires only the feedback "on average", the latter requires instantaneous feedback and hence is of higher complexity). The BLER and TBER optimization criteria result in the same performance. Power optimization (of un-ordered BLAST) and optimal ordering result in the same performance improvement at high SNR

Transmit Power Allocation for the V-BLAST Algorithm

Optimum power allocation for the V-BLAST algorithm, which is based on various criteria (average and instantaneous block and total error rates (BLER and TBER)), is considered. Closed-form solutions are derived for high-SNR case in a Rayleigh fading channel. They are shown to be robust to small variations in allocated power and average SNR. It is demonstrated that the optimization "on average" is only slightly worse than the instantaneous one, albeit the latter requires an instantaneous feedback and hence is of higher complexity. The generic upper-bound for the SNR gain of any power allocation technique is derived. The BLER and TBER optimization criteria result in the same performance. Power optimization (of unordered BLAST) and optimal ordering result in almost the same performance improvement at high SNR

Error Rates of the Maximum-Likelihood Detector for Arbitrary Constellations: Convex/Concave Behavior and Applications

Motivated by a recent surge of interest in convex optimization techniques, convexity/concavity properties of error rates of the maximum likelihood detector operating in the AWGN channel are studied and extended to frequency-flat slow-fading channels. Generic conditions are identified under which the symbol error rate (SER) is convex/concave for arbitrary multi-dimensional constellations. In particular, the SER is convex in SNR for any one- and two-dimensional constellation, and also in higher dimensions at high SNR. Pairwise error probability and bit error rate are shown to be convex at high SNR, for arbitrary constellations and bit mapping. Universal bounds for the SER 1st and 2nd derivatives are obtained, which hold for arbitrary constellations and are tight for some of them. Applications of the results are discussed, which include optimum power allocation in spatial multiplexing systems, optimum power/time sharing to decrease or increase (jamming problem) error rate, an implication for fading channels ("fading is never good in low dimensions") and optimization of a unitary-precoded OFDM system. For example, the error rate bounds of a unitary-precoded OFDM system with QPSK modulation, which reveal the best and worst precoding, are extended to arbitrary constellations, which may also include coding. The reported results also apply to the interference channel under Gaussian approximation, to the bit error rate when it can be expressed or approximated as a non-negative linear combination of individual symbol error rates, and to coded systems.Comment: accepted by IEEE IT Transaction

Symbol Error Rates of Maximum-Likelihood Detector: Convex/Concave Behavior and Applications

Convexity/concavity properties of symbol error rates (SER) of the maximum likelihood detector operating in the AWGN channel (non-fading and fading) are studied. Generic conditions are identified under which the SER is a convex/concave function of the SNR. Universal bounds for the SER 1st and 2nd derivatives are obtained, which hold for arbitrary constellations and are tight for some of them. Applications of the results are discussed, which include optimum power allocation in spatial multiplexing systems, optimum power/time sharing to decrease or increase (jamming problem) error rate, and implication for fading channels.Comment: To appear in 2007 IEEE International Symposium on Information Theory (ISIT 2007), Nice, June 200

Approximate minimum BER power allocation for MIMO-THP system

This paper proposes a transmit power allocation (TPA) scheme based on multiple-input multiple-output (MIMO) Tomlinson-Harashima precoding (THP) structure, where a TPA matrix is introduced to the conventional MIMO-THP. We analyze the influence of the introduced TPA matrix on the performance of MIMO-THP. The proposed TPA scheme invokes the minimum average uncoded bit-error rate (BER) criterion subjected to a sum-power constraint. During the derivation, we consider the effects of precoding loss factor on the TPA scheme and obtain a closed-form expression of the TPA. Compared to existing TPA methods for MIMO-THP systems, the proposed scheme reduces processing complexity and improves the BER performance

High-Rate Space-Time Coded Large MIMO Systems: Low-Complexity Detection and Channel Estimation

In this paper, we present a low-complexity algorithm for detection in high-rate, non-orthogonal space-time block coded (STBC) large-MIMO systems that achieve high spectral efficiencies of the order of tens of bps/Hz. We also present a training-based iterative detection/channel estimation scheme for such large STBC MIMO systems. Our simulation results show that excellent bit error rate and nearness-to-capacity performance are achieved by the proposed multistage likelihood ascent search (M-LAS) detector in conjunction with the proposed iterative detection/channel estimation scheme at low complexities. The fact that we could show such good results for large STBCs like 16x16 and 32x32 STBCs from Cyclic Division Algebras (CDA) operating at spectral efficiencies in excess of 20 bps/Hz (even after accounting for the overheads meant for pilot based training for channel estimation and turbo coding) establishes the effectiveness of the proposed detector and channel estimator. We decode perfect codes of large dimensions using the proposed detector. With the feasibility of such a low-complexity detection/channel estimation scheme, large-MIMO systems with tens of antennas operating at several tens of bps/Hz spectral efficiencies can become practical, enabling interesting high data rate wireless applications.Comment: v3: Performance/complexity comparison of the proposed scheme with other large-MIMO architectures/detectors has been added (Sec. IV-D). The paper has been accepted for publication in IEEE Journal of Selected Topics in Signal Processing (JSTSP): Spl. Iss. on Managing Complexity in Multiuser MIMO Systems. v2: Section V on Channel Estimation is update

How much training is needed in multiple-antenna wireless links?

Multiple-antenna wireless communication links promise very high data rates with low error probabilities, especially when the wireless channel response is known at the receiver. In practice, knowledge of the channel is often obtained by sending known training symbols to the receiver. We show how training affects the capacity of a fading channel-too little training and the channel is improperly learned, too much training and there is no time left for data transmission before the channel changes. We compute a lower bound on the capacity of a channel that is learned by training, and maximize the bound as a function of the received signal-to-noise ratio (SNR), fading coherence time, and number of transmitter antennas. When the training and data powers are allowed to vary, we show that the optimal number of training symbols is equal to the number of transmit antennas-this number is also the smallest training interval length that guarantees meaningful estimates of the channel matrix. When the training and data powers are instead required to be equal, the optimal number of symbols may be larger than the number of antennas. We show that training-based schemes can be optimal at high SNR, but suboptimal at low SNR