Constantin Siriteanu

Maximal-Ratio Eigen-Combining for Smarter Antenna Arrays

In typical mobile wireless scenarios, signals are received with power azimuth angle spectrum (p.a.s.) of variable azimuth angle spread (AS). Therefore, conventional maximum average signal-to-noise ratio beamforming (BF) or maximal-ratio combining (MRC) may not necessarily be effective in terms of performance or signal processing complexity. A newer, more flexible, approach, called maximal-ratio eigen-combining (MREC) is analyzed and found to generalize BF and MRC. For imperfectly-known channels we study both suboptimal and optimal eigen-/combining. MREC-based analysis is shown to simplify MRC performance investigations for correlated channel gains. For MPSK signals, we present average error probability (AEP) expressions for MREC, BF, and MRC, that are new or generalizations of our previous work. Furthermore, we propose a performance-complexity tradeoff criterion (PCTC) for MREC-receiver adaptation to changing AS. Numerical evaluations for typical urban scenarios with realistic Laplacian p.a.s. of random AS demonstrate that PCTC-based MREC is an interesting alternative to BF and MRC, for smart antenna arrays

MIMO Zero-Forcing Detection Analysis for Correlated and Estimated Rician Fading

Experimental modeling of wireless fading channels performed by the WINNER II project has been shown to fit a Rician rather than Rayleigh distribution, the latter being assumed in many analytical studies of multiple-input-multiple-output (MIMO) communication systems. Unfortunately, a Rician MIMO channel matrix has a nonzero mean (i.e., specular component) that yields, for the matrix product that determines the MIMO performance, a noncentral Wishart distribution that is difficult to analyze. Previously, the noncentral Wishart distribution has been approximated, based on a first-order-moment fit, by a central Wishart distribution and used to derive average error probability (AEP) expressions for zero-forcing (ZF) detection. We first reveal that this approximation and the MIMO performance evaluation tools derived from it may be reliable only for rank-one specular matrices. We then exploit this approximation to derive an AEP expression for a lesser known, yet optimal, MIMO ZF approach that, unlike the conventional approach, accounts for channel estimation accuracy through the channel statistics. After validating this AEP expression for the rank-one case, it is shown that the ZF performance averaged over realistic (i.e., WINNER II) distributions of the Rician K-factor and azimuth spread (AS) can be much worse than that for the average K and AS. Finally, through simulations, it is shown that the optimal detection approach can substantially outperform the conventional approach for ZF for full-rank specular matrices, as well as for minimum mean square error detection for both rank-one and full-rank specular matrices.

Exact MIMO Zero-Forcing Detection Analysis for Transmit-Correlated Rician Fading

We analyze the performance of multiple input/multiple output (MIMO) communications systems employing spatial multiplexing and zero-forcing detection (ZF). The distribution of the ZF signal-to-noise ratio (SNR) is characterized when either the intended stream or interfering streams experience Rician fading, and when the fading may be correlated on the transmit side. Previously, exact ZF analysis based on a well-known SNR expression has been hindered by the noncentrality of the Wishart distribution involved. In addition, approximation with a central-Wishart distribution has not proved consistently accurate. In contrast, the following exact ZF study proceeds from a lesser-known SNR expression that separates the intended and interfering channel-gain vectors. By first conditioning on, and then averaging over the interference, the ZF SNR distribution for Rician-Rayleigh fading is shown to be an infinite linear combination of gamma distributions. On the other hand, for Rayleigh-Rician fading, the ZF SNR is shown to be gamma-distributed. Based on the SNR distribution, we derive new series expressions for the ZF average error probability, outage probability, and ergodic capacity. Numerical results confirm the accuracy of our new expressions, and reveal effects of interference and channel statistics on performance.

FPGA-based communications receivers for smart antenna array embedded systems

Field-programmable gate arrays (FPGAs) are drawing ever increasing interest from designers of embedded wireless communications systems. They outpace digital signal processors (DSPs), through hardware execution of a wide range of parallelizable communications transceiver algorithms, at a fraction of the design and implementation effort and cost required for application-specific integrated circuits (ASICs). In our study, we employ an Altera Stratix FPGA development board, along with the DSP Builder software tool which acts as a high-level interface to the powerful Quartus II environment. We compare single- and multibranch FPGA-based receiver designs in terms of error rate performance and power consumption. We exploit FPGA operational flexibility and algorithm parallelism to design eigenmode-monitoring receivers that can adapt to variations in wireless channel statistics, for high-performing, inexpensive, smart antenna array embedded systems.

Performance and Complexity Analysis of Eigencombining, Statistical Beamforming, and Maximal-Ratio Combining

For receive-side maximal-ratio combining (MRC) and maximum-average-SNR beamforming (BF), the wireless-channel fading correlation impacts the symbol-detection performance-decreasing correlation improves/degrades MRC/BF performance-whereas the numerical complexity of these methods is fixed-high/low for MRC/BF. Matching signal processing complexity to the actual correlation conditions and, thus, to the achievable performance is possible with a superset of MRC and BF known as maximal-ratio eigencombining (MREC). For imperfectly known and correlated fading gains, new closed-form expressions are derived for the probability density function of the MREC-output SNR, as well as for the outage probability (OP) and the average error probability. These new expressions permit seamless evaluation for any correlation value of MREC, MRC, and BF performance measures, such as the amount of fading, the deep-fade probability, diversity and array gains, and the OP. Our results confirm that, in realistic scenarios, adaptive MREC can achieve MRC-like performance for BF-like complexity.

MIMO Zero-Forcing Detection Performance for Correlated and Estimated Rician Fading with Lognormal Azimuth Spread and K-Factor

For multiple-input multiple-output (MIMO) wireless communications systems, we propose a new zero-forcing (ZF) detection approach that explicitly accounts for instantaneous channel state information (ICSI) estimation error and spatial correlation. For this ZF approach, we derive an average error probability (AEP) expression for transmit-correlated Rician fading. Our AEP derivation exploits the effective signal-to-noise ratio that results by compounding ICSI estimation error and receiver noise. The derived AEP expression is then applied to evaluate MIMO ZF performance in Rayleigh and Rician fading for samples from recently-measured lognormal azimuth spread (AS) and Rician K-factor distributions, for pilot-based ICSI estimation. Numerical results depict the dependence of the AEP averaged over the AS and K distributions on fading type, rank of the deterministic component of the channel matrix, and AS-K correlation, for realistic scenarios.

Smart antenna arrays for correlated and imperfectly-estimated Rayleigh fading channels

Eigenbeamforming, herein referred to as maximal-ratio eigen-combining (MREC), was recently proposed as an alternative to maximum average signal-to-noise ratio beamforming (Max-ASNR BF) and maximal-ratio combining (MRC) in antenna array systems. An analysis of MREC is undertaken and an average error probability (AEP) expression is obtained for BPSK modulation and Rayleigh fading when the channel gains may be imperfectly-known and partially correlated. The analysis is further specialized to pilot-symbol-aided channel estimation, to allow an analytical performance assessment of smart antenna arrays (SAAs) employing MREC in realistic scenarios with angle-of-arrival (AOA) dispersion. Numerical results show that MREC may significantly outperform Max-ASNR BF and MRC in imperfect conditions.

Exact

We study zero-forcing (ZF) detection for multiple input/multiple output (MIMO) spatial multiplexing under transmit-correlated Rician fading for an NR× NT channel matrix with rank-1 line-of-sight component. By using matrix transformations and multivariate statistics, our exact analysis yields the signal-to-noise ratio moment generating function (M.G.F.) as an infinite series of gamma distribution M.G.F.s and analogous series for ZF performance measures, e.g., outage probability and ergodic capacity. However, their numerical convergence is inherently problematic with increasing Rician K-factor, NR, and NT. We circumvent this limitation as follows. First, we derive differential equations satisfied by the performance measures with a novel automated approach employing a computer-algebra tool that implements Gröbner basis computation and creative telescoping. These differential equations are then solved with the holonomic gradient method (HGM) from initial conditions computed with the infinite series. We demonstrate that HGM yields more reliable performance evaluation than by infinite series alone and more expeditious than by simulation, for realistic values of K, and even for NR and NT relevant to large MIMO systems. We envision extending the proposed approaches for exact analysis and reliable evaluation to more general Rician fading and other transceiver methods.

{\sf ZF}

For multiple-input/multiple-output (MIMO) wireless communications systems employing spatial multiplexing transmission we evaluate the convergence performance of genetic algorithm (GA)-based detection against the maximum-likelihood (ML) approach. We consider transmit-correlated Rayleigh and Rician fading with Laplacian power azimuth spectrum. The values of the azimuth spread (AS) and Rician K-factor are selected according to the measurement-based WINNER II channel models, for several relevant scenario types. We consider the effect on GA convergence speed and population size requirements of the following: number of antennas, modulation constellation size, scenario (i.e., AS and K values), and rank of the deterministic component of the channel matrix. We find that the GA population size needs to be carefully adjusted to the antenna geometry and modulation constellation in order to maintain fast convergence. On the other hand, changes in the channel fading type and geometry do not appear to affect GA convergence. GA is shown to achieve ML-like performance, possibly for lower complexity, i.e., more efficient hardware and power usage.

Analysis and Computer-Algebra-Aided Evaluation in Rank-1 LoS Rician Fading

The performance of multiple-input/multiple-output (MIMO) communications systems employing spatial multiplexing and zero-forcing detection (ZF) has yet to be analyzed for several cases of practically-relevant Rician fading. For the special case of Rician-Rayleigh fading, we have recently derived a set of expressions for important MIMO ZF performance measures. They were obtained from the moment generating function of the signal-to-noise ratio (SNR) expressed in terms of the confluent hypergeometric function, i.e., an infinite-series. Herein, the prove the convergence of the ensuing infinite-series expressions obtained for the SNR probability density function, as well as for the ZF outage probability, average error probability, and ergodic capacity. For the ergodic-capacity infinite-series, we describe a computation method and discuss its numerical instability issues.