Philippe Rostaing

Optimal minimum distance-based precoder for MIMO spatial multiplexing systems

We describe a new precoder based on optimization of the minimum Euclidean distance d/sub min/ between signal points at the receiver side and for use in multiple-input multiple-output (MIMO) spatial multiplexing systems. Assuming that channel state information (CSI) can be made available at the transmitter, the three steps ( noise whitening, channel diagonalization and dimension reduction), which are currently used in investigations on MIMO systems, are performed. Thanks to this representation, an optimal d/sub min/ precoder is derived in the case of two different transmitted data streams. For quadrature phase-shift keying (QPSK) modulation, a numerical approach shows that the precoder design depends on the channel characteristics. Comparisons with maximum signal-to-noise ratio (SNR) strategy and other precoders based on criteria, such as water-filling (WF), minimum mean square error (MMSE), and maximization of the minimum singular value of the global channel matrix, are performed to illustrate the significant bit-error-rate (BER) improvement of the proposed precoder.

Extension of the MIMO Precoder Based on the Minimum Euclidean Distance: A Cross-Form Matrix

Under full channel state information at the transmitter side (Tx-CSI), MIMO precoders can be designed by the optimization of many pertinent criteria, like, for example, the maximizing post-processing signal-to-noise ratio (max-SNR or beamforming solution), or the minimizing weighted mean square error between transmit and receive vector-symbols (W-MMSE solution). These solutions decouple the MIMO channel into b parallel independent datastreams. This diagonal structure reduces the complexity of the maximum likelihood (ML) decisions but the diversity order of these schemes is limited. Recently, we proposed a precoder, max-dmjn solution, which optimizes the exact expression of the minimum Euclidean distance and leads to a non diagonal structure allowing to achieve maximum diversity order. However, the result is available only for two transmit datastreams (6 = 2) and BPSK and QPSK modulations. In this paper, we propose a heuristic method to deal with the case b > 2, which provides a suboptimal, but good solution to this general problem. The new precoder, Equal-dm;n (E-dmin), is based on a non diagonal cross-form structure. It significantly enhances the transmit diversity in the eigen-subchannels. We demonstrate that the achieved diversity order is greater than that of precoders with diagonal structure for the same number of datastreams despite a tradeoff between rate and diversity. This design can also ensure quality of service (QoS) by using an adapted power allocation strategy. Performance comparisons show the BER improvement for MIMO and MIMO-OFDM systems.

Minimum BER diagonal precoder for MIMO digital transmissions

We propose a minimum bit error rate (MBER) diagonal precoder for multi-input multi-output (MIMO) transmission systems. This work is based on previous results obtained by Sampath et al. (IEEE ISPACS, Honolulu, Hawaii, 2000, p. 823) in which the global transmission system (precoder and equalizer) is optimized with the minimum mean square error (MMSE) criterion. This process leads to an interesting diagonality property which decouples the MIMO channel into parallel and independent data streams and allows to perform an easy maximum likelihood (ML) detection. This system is then optimized using a new diagonal precoder that minimizes the BER. Our work is motivated by the fact that, from a practical point of view, people are likely to prefer a system that minimizes the BER rather than the mean square error. The performance improvement is illustrated via Monte Carlo simulations using a quadratic amplitude modulation (QAM).

Asymptotic performance analysis of cyclic detectors

The paper deals with the analytical evaluation of the asymptotic detection and false-alarm probabilities of multicycle and single-cycle detectors operating in additive white Gaussian noise with unknown and nonrandom spectral level, which are based on the cyclostationarity properties of the signal to be intercepted. The receiver operating characteristics are derived by using the asymptotic complex normality and the covariance expression of the sample average estimator of the cyclic covariance in an observed discrete-time series. A numerical example for interception of a binary phase-shift keying signal is considered.

Performance analysis of a statistical test for presence of cyclostationarity in a noisy observation

The purpose of this paper is to evaluate theoretically in terms of receiver operating characteristics (ROC) the performance of a statistical test (based on the second order statistic) for the presence of cyclostationarity in a noisy observation. In order to obtain false alarm and detection probabilities, we consider the following specific situation: we choose a cycle frequency contained in a binary-phase-shift-keyed (BPSK) signal of interest (SOI) (BPSK signal is considered for its increasing attention in digital communications) and we test the presence of cyclostationarity of the SOI in a noisy observation. Two examples are considered, the SOI is buried either in a stationary Gaussian noise or in an another BPSK signal.

Statistical comparison between max-dmin, max-SNR and MMSE precoders

In this study, we considered a MIMO system with available channel state information at the transmitter side and compared three known precoders based on different and pertinent criteria: the post processing signal-to-noise ratio (max-SNR), the mean square error between transmitted and received symbols (MMSE) and the minimum distance of the received constellation (max-dmin). We demonstrate that, alike the max-SNR and contrarily to the MMSE, the max-dmin gives the maximum diversity order for a Rayleigh channel. An upper- bound of the MMSE diversity order is given. On the other hand, dmin of the three precoders will be statistically studied as a function of the number of antennas. In addition, BER simulations showed that the best precoder is the max-dmin.

Limited Feedback Unitary Matrix applied to MIMO dmin-based Precoder

In spatial multiplexing systems, transmission reliability is enhanced by the full channel state information (CSI) used to design optimum linear precoders, but in practice a full CSI is often unrealistic. Indeed, a higher number of transmitters and/or receivers elevates the coefficient numbers of the estimated channel, and the precision on coefficients depends on the rate of the feedback stream. An interesting alternative is to return a limited amount of information to the transmitter; this led us to design a dmin precoder based on the use of i) a finite codebook known by the receiver and the transmitter and ii) feedback of only one quantized real-valued parameter. The selection criteria employed to find the optimal precoding matrix are presented. Then, the performances about BER are compared under different criteria and amounts of feedback and confronted to Alamouti code.

Theoretical Results about MIMO Minimal Distance Precoder and Performances Comparison

This study deals with two linear precoders: the maximization of the minimum Euclidean distance between received symbol-vectors, called here max-dmin, and the maximization of the post-processing signal-to-noise ratio termed max-SNR or beamforming. Both have been designed for reliable MIMO transmissions operating over uncorrelated Rayleigh fading channels. Here, we will explain why performances in terms of bit error rates show a significant enhancement of the max-dmin over the max-SNR whenever the number of antennas is increased. Then, from theoretical developments, we will demonstrate that, like the max-SNR precoder, the max-dmin precoder achieves the maximum diversity order, which is warrant of reliable transmissions. The current theoretical knowledge will be applied to the case-study of a system with two transmit- or two receive-antennas to calculate the probability density functions of two channel parameters directly linked to precoder performances for uncorrelated Rayleigh fading channels. At last, this calculation will allow us to quickly get the BER of the max-dmin precoder further to the derivation of a tight semi-theoretical approximation.

Multiple-Votes Parallel Symbol-Flipping Decoding Algorithm for Non-Binary LDPC Codes

A novel decoding algorithm for non-binary low density parity check (NB-LDPC) codes is proposed. The algorithm builds on the recently designed parallel symbol-flipping decoding (PSFD) algorithm and combines a technique of error estimation and a method of multiple voting levels from each unsatisfied check-sum to the corresponding variable nodes. Simulations results, performed on a number of NB-LDPC codes of various lengths and column weights constructed using several methods, show that the new algorithm not only avoids using code-dependent voting threshold but also improves the error rate performance of the PSFD algorithm, particularly for low column weight parity-check matrices.

Digital transmission combining BLAST and OFDM concepts: experimentation on the UHF COST 207 channel

Previous papers have shown that multipath wireless channels are capable of enormous capacities, provided that the multipath scattering is sufficiently rich and is properly exploited. A layered space-time architecture, known as BLAST, has been proposed. A basic hypothesis made by the BLAST algorithm is that the symbol period is large compared to the maximum echo delay (hence, the data rate cannot be too high). In this paper, we use an approach that combines BLAST and OFDM. Its interest is to suppress the data rate constraint. First, the symbols are packed into matrices; then matrix manipulations prior to BLAST transmission provide a transmission system which is theoretically equivalent to many independent BLAST channels. Results obtained with the UHF COST 207 channel corresponding to GSM transmission in an urban area are provided and discussed.