Performance of space-time codes for a large number of antennas

We study the asymptotic behavior of space-time codes when the number of transmit and receive antennas grows to infinity. Specifically, we determine the behavior of pairwise error probabilities with maximum-likelihood (ML) decoding and with three types of receiver interfaces: the ML interface, the linear zero-forcing (ZF) interface, and the linear minimum-mean-square-error (MMSE) interface. Two situations are studied: when the number of receiving antennas grows to infinity while the number of transmitting antennas is finite, and when both numbers grow to infinity but their ratio remains constant. We show that with ML or linear interfaces the asymptotic performance of space-time codes is determined by the Euclidean distances between codewords. Moreover, with the two linear interfaces examined here the number r of receive antennas must be much larger than the number t of transmit antennas to avoid a sizeable loss of performance; on the other hand, when r ≫ t, the performance of these linear interfaces comes close to that of ML. The dependence of error probabilities on Euclidean distance is valid for intermediate signal-to-noise ratios (SNRs) even when the number of antennas is small. Simulations validate our theoretical findings, and show how asymptotic results may be substantially valid even in a nonasymptotic regime: thus, even for few antennas, off-the-shelf codes may outperform space-time codes designed ad hoc     

Linear receivers for the multiple-input multiple-output multiple-access channel

We consider a multiuser multiple-input multiple-output (MIMO) communication system using code-division multiple access (CDMA) and multiuser detection to discriminate the different users. Our focus is on the CDMA uplink of a frequency-nonselective Rayleigh fading channel. We study two types of receivers: joint receivers, which address simultaneously both spatial and multiple-access interference; and separate receivers, addressing the two types of interference individually. This approach allows assessing the benefits of adding MIMO processing capabilities to existing multiuser single-input single-output systems. For both receiver types, we analyze solutions based on linear (matched filter, decorrelator, minimum mean-square error) and maximum-likelihood receivers. For all the receivers considered, we provide closed-form expressions (as expectations of given functions) of the resulting pairwise error probabilities. Performance results are obtained in terms of frame-error rate versus E/sub b//N/sub 0/, following two different approaches. An analytic approach using large-system asymptotic methods, whereby the system parameters (number of users and antennas, spreading gain) are assumed to grow to infinity with finite limiting ratios. A computer-simulation approach is used to illustrate the differences between asymptotic and simulation results.     

Exact pairwise error probability of space-time codes

We describe a simple technique for the numerical calculation, within any desired degree of accuracy, of the pairwise error probability (PEP) of space-time codes over fading channels. This method applies also to the calculation of E[Q(√ξ)] for any nonnegative random variable ξ whose moment-generating function Φ_ξ(s)=E[exp(-sξ)] is known. Its application to the multiple antenna independent Rayleigh-fading channel and to the Rayleigh block fading channel is discussed, and illustrated by two simple examples     

Optimum Receiver Design for Correlated Rician Fading MIMO Channels with Pilot-Aided Detection

Two structures based on pilot symbol-aided channel receiver estimation are considered for the separately-correlated Rician fading MIMO channel. Mismatched receiver, which A decodes the received signal by first using maximum-likelihood (ML) or mean- minimum error square (MMSE) estimation of the MIMO channel matrix, and then by assuming that the estimate is exact. An optimum receiver, which does not estimate explicitly the matrix but jointly channel processes the received pilot and samples assuming known channel distribution.     

Optimal energy transfer in band-limited communication channels

Maximization of the energy transfer ratio for time-limited signals over linear channels is considered. The case of linear channels with rational transfer function is addressed and a general procedure for the analytic solution of the maximization problem is outlined. The maximum energy transfer ratio over a fixed time interval is evaluated in some cases of interest. Two performance metrics-the energy transfer ratio and the energy intersymbol interference (ISI) ratio-are evaluated for optimal signals and compared to those of commonly used rectangular and sinusoidal pulses in order to determine the achievable gain     

Chemical stability of zirconia-stabilized alumina fibers during pressure infiltration by aluminum

Metal matrix composites composed of high-purity aluminum and Du Pont PRD-166 continuous zirconia-stabilized polycrystalline alumina fibers are fabricated by liquid metal infiltration using three different casting procedures. The microstructure of the composites is analyzed using optical and electron microscopy, including analytical electron microscopy. It is found that discrete faceted particles of ZrAl₃ form at the interface and grow into the matrix of samples processed above the melting point of the matrix for 13 minutes or more. The formation of this compound is in agreement with thermodynamic stability calculations. It is also found that there is a reaction between solid aluminum and the fibers at 913 K, yielding a reaction product which has the same morphology as that observed with molten aluminum. When the fibers are infiltrated with an initial preform temperature below the metal melting point and a solidifination time below 1 minute, no reaction products were visible in the composite using the scanning electron microscope (SEM). This leads to the conclusion that aluminum matrix composites can be cast with no apparent interfacial reaction product using these fibers provided that adequate processing parameters are chosen.     

Asymptotic Mutual Information Statistics of Separately Correlated Rician Fading MIMO Channels

The asymptotic probability distribution of the mutual information of a separately correlated Rician fading multiple-input multiple-output (MIMO) channel is addressed. The mean and variance of the mutual information are derived when the number of transmit and receive antennas grows asymptotically large while their ratio approaches a finite constant. This derivation is based on the replica method, widely used in theoretical physics and, more recently, in the analysis of communication systems (code-division multiple access (CDMA) and MIMO). Though the replica method allows to analyze complex systems in a comparatively simple way, some authors pointed out that its assumptions are not always rigorous. It is shown that the mutual information converges asymptotically to a Gaussian distribution under mild technical conditions, which are tantamount to assuming that the spatial correlation structure has no asymptotically dominant eigenmodes. The accuracy of the asymptotic approach is assessed by numerical results. It is shown that the approximation is very accurate in a wide range of system settings, even when the number of transmit and receive antennas is as small as a few units.     

Performance of component interleaved signal sets for fadingchannels

The authors calculate the exact (pairwise) error probability for an arbitrary component-interleaved 2-D constellation over the Rayleigh fading channel. Using this result, they improve the accuracy of the performance analysis at high error rates. For illustration, this is applied to signal sets derived from 4-PSK and 16-QAM over the Rayleigh fading channel     

Co-Channel Interference in Cellular Mobile Radio Systems with Coded PSK and Diversity

In this paper, the performance of coding and diversity in narrowband wireless cellular systems affected by fading, shadowing and co-channel interference is analyzed. We consider low-order diversity, that can be practically realized for both coherent and differential phase shift keying. We assume that the shadowing random processes affecting all transmitted signals do not vary appreciably over the transmission duration. Fading, on the contrary, is assumed to vary more rapidly. Our main focus here is on outage probability. After choosing a performance indicator, its expectation is taken with respect to fading and co-channel interference, conditionally on shadowing. Hence, the resulting average performance indicator is a random variable. The probability that this random variable exceeds a specified threshold defines the outage probability. We consider as performance indicators (i) the channel cut-off rate R₀ and (ii) the bit error rate P_b of an actual coded scheme. As we are interested in interference-limited, rather than power-limited systems, we evaluate both R₀ and P_b for very high signal-to-noise ratios. Results are parameterized by the frequency reuse factor and the diversity order.