Giorgio Taricco

Bit-interleaved coded modulation

Zehavi (1992) showed that the performance of coded modulation over a Rayleigh fading channel can be improved by bit-wise interleaving the encoder output and by using an appropriate soft-decision metric as an input to a Viterbi decoder. The goal of this paper is to present in a comprehensive fashion the theory underlying bit-interleaved coded modulation, to provide tools for evaluating its performance, and to give guidelines for its design.

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 /spl Gt/ 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.

Impact of diversity reception on fading channels with coded modulation. I. Coherent detection

We address the problem of designing and analyzing the performance of a coded modulation scheme for the fading channel when space diversity is used. Under fairly general conditions, a channel affected by fading can be turned into an additive white Gaussian noise (AWGN) channel by increasing the number of diversity branches. Consequently, it can be expected (and is indeed verified by our analyses and simulations) that a coded modulation scheme designed to be optimal for the AWGN channel also will perform asymptotically well on a fading channel with diversity. This paper presents bounds on the bit-error probability of a system with coded modulation and diversity for space- and time-correlated Rician flat fading. Specifically, we derive a new method which allows evaluation of the pairwise error probability extremely easily, as well as accurately and computationally fast. The accuracy achieved improves considerably on the widely used, but rather loose Chernoff bound. Starting from this analysis, we study the asymptotic behavior of the fading channel with diversity as the number of diversity branches increases, and we address the effects of diversity on coded modulation performance and design criteria, including the effect on interleaver depth (which affects the total delay of the system).

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.

Impact of diversity reception on fading channels with coded modulation. II. Differential block detection

For pt. I see ibid., vol.45, no.6, p.563-572, 1997. We study coded modulation with block differential detection in an arbitrarily correlated Rician fading channel with space diversity. Coded differential q-PSK is included in our analysis as a special case. A metric is chosen that is optimum for perfect interleaving, slow fading, and independent diversity branches. For slow fading, we compare the the cutoff rates of the channels resulting from different choices of block length N and diversity index M. Specifically, we show that block detection with diversity may or may not generate a better coding channel than usual differential detection, according to the code selected and the combination of values of M and N. In particular, for low-diversity orders (M=1,2) and for low-to-medium code rates, differential detection is still an optimal or near-optimal solution, while for high-diversity orders (M/spl ges/2) and medium-to-high code rates (up to uncoded modulation) block detection with N>2 can provide a significant gain. An error floor always exists when fading is fast. It decreases exponentially with the product of code diversity and space diversity, so that the latter emerges as a very effective technique for lowering the error floor of a system affected by fast fading. Performance examples based on actual coding schemes are also shown.

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.

Coding and modulation under power constraints

An issue arising at the physical layer in digital wireless transmission is the choice of the coding/modulation scheme taking into account the availability of a limited energy source. This article is devoted to a description of the rationales behind this choice. As the latter depends on the channel model, we examine four of these, namely, the Gaussian channel, the independent-fading channel, the block-fading channel, and a channel where the transmission quality is limited by interference rather than by noise. Code selection and power-allocation strategies are discussed.

On the Ergodic Capacity of Correlated Rician Fading MIMO Channels With Interference

An asymptotic approach to derive the ergodic capacity achieving covariance matrix for a multiple-input multiple-output (MIMO) channel is presented. The method is applicable to MIMO channels affected by separately correlated Rician fading and co-channel interference. It is assumed that the number of transmit, receive and interfering antennas grows asymptotically while their ratios, as well as the SNR and the SIR, approach finite constants. Nevertheless, it is shown that the asymptotic results represent an accurate approximation in the case of a finitely many antennas and can be used to derive the ergodic channel capacity. This is accomplished by using an iterative power allocation algorithm based on a water-filling approach. The convergence of a similar algorithm (nicknamed frozen water-filling) was conjectured in a work by Dumont Here, we show that, in the Rayleigh case, the frozen water-filling algorithm may not converge while, in those cases, our proposed algorithm converges. Finally, numerical results are included in order to assess the accuracy of the asymptotic method proposed, which is compared to equivalent results obtained via Monte-Carlo simulations.

Doubly-iterative decoding of space-time turbo codes with a large number of antennas

We examine the performance of a reduced-complexity doubly iterative decoder for space-time turbo codes on a quasi-static fading channel. The decoder works by using preliminary soft values of the coded symbols, obtained after a limited number of turbo iterations, to reduce the spatial interference from the received signal. Then, new turbo iterations are performed to improve on the quality of the soft values, and so on. Using a number of approximations, we obtain a receiver interface that achieves a good tradeoff between performance and complexity, and allows the use of turbo space-time codes for a large number of transmit and receive antennas.

Recent results on coding for multiple-antenna transmission systems

We describe recent results on multiple-antenna transmission systems. These are known to offer a potential performance, in terms of bit/s/Hz, that cannot be obtained otherwise with present-day technology. We summarize recent results showing the theoretical performance limits of these systems under the assumptions that the channel gains are known to the receiver, to the transmitter and to the receiver, or to neither. The design of coding schemes that approach these limits is also addressed.