Laura Cottatellucci

A systematic approach to multistage detectors in multipath fading channels

We consider linear multistage detectors with universal (large system) weighting for synchronous code-division multiple access (CDMA) in multipath fading channels with many users. A convenient choice of the basis of the projection subspace allows a joint projection of all users. Taking advantage of this property, the complexity per bit of multistage detectors with universal weights scales linearly with the number of users on the uplink CDMA channel, while other known multistage detectors with universal weights and different bases of the projection subspace keep the same quadratic complexity order per bit as the linear minimum mean-square error (LMMSE) detector. We focus on the design of two kinds of detectors with linear complexity. The detector of Type I is obtained as an asymptotic approximation of the polynomial expansion detector proposed by Moshavi et al. The detector of Type II has the same performance as the multistage Wiener filter (MSWF) in large systems. Additionally, general performance expressions for large systems, applicable to any multistage detector with the same basis of the projection subspace (e.g., linear parallel interference canceling detectors), are derived. As a by-product, the performance analysis disproves the widespread belief that the MSWF and the polynomial expansion detector are equivalent. We show that, in general, the MSWF outperforms the latter one and they are equivalent only asymptotically in the case of equal received powers.

Asynchronous CDMA Systems With Random Spreading—Part I: Fundamental Limits

Spectral efficiency for asynchronous code division multiple access (CDMA) with random spreading is calculated in the large system limit allowing for arbitrary chip waveforms and frequency-flat fading. Signal-to-interference and noise ratios (SINRs) for suboptimal receivers, such as the linear minimum mean square error (MMSE) detectors, are derived. The approach is general and optionally allows even for statistics obtained by undersampling the received signal. All performance measures are given as a function of the chip waveform and the delay distribution of the users in the large system limit. It turns out that synchronizing users on a chip level impairs performance for all chip waveforms with bandwidth greater than the Nyquist bandwidth, e.g., positive roll-off factors. For example, with the pulse shaping demanded in the UMTS standard, user synchronization reduces spectral efficiency up to 12% at 10 dB normalized signal-to-noise ratio. The benefits of asynchronism stem from the finding that the excess bandwidth of chip waveforms actually spans additional dimensions in signal space, if and only if the users are desynchronized at chip-level. The analysis of linear MMSE detectors shows that the limiting interference effects can be decoupled both in the user domain and in the frequency domain such that the concept of effective interference spectral density arises. This generalizes and refines Tse and Hanlys concept of effective interference. In Part II, the analysis is extended to any linear detector that admits a representation as multistage detector and guidelines for the design of low complexity multistage detectors with universal weights are provided.

The effect of line of sight on the asymptotic capacity of MIMO systems

The asymptotic (in the number of antennas) theoretic mutual information of a MIMO system in the case of Ricean fading is provided. The results are especially useful for understanding the effect of line of sight components on the overall capacity performance.

Asymptotic design and analysis of multistage detectors with unequal powers

In this work we provide equations to precisely calculate the asymptotic weighting of multistage detectors satisfying the individually and jointly LMMSE criteria in the projection subspace for scenarios with unequal powers. Additionally, a general expression of the SINR achievable at the filter output as system size grows large is derived. Such an equation can be applied to any multistage detector. We specialize this result to both the individually and jointly LMMSE multistage detector with asymptotic weighting. We show that the individually LMMSE detector outperforms the other detector in the case of unequal received powers while both the detectors are equivalent in the case of equal received powers.

CDMA Systems With Correlated Spatial Diversity: A Generalized Resource Pooling Result

This correspondence analyzes the behavior of code-division multiple-access (CDMA) systems with correlated spatial diversity. The users transmit to one or more antenna arrays. The centralized receiver employs a linear multiuser detector. We derive the performance of a large system with random spreading sequences and weak assumptions on the flat-fading channel gains-the fading may be correlated and contain line-of-sight components. We show that, as the number of users and the spreading factor grow large with fixed ratio, the performance of the system is fully characterized by a square matrix with size equal to the number of receiving antennas and multiuser efficiencies are not identical for all users. Our general result includes the analysis of CDMA systems with spatial diversity discussed by Hanly and Tse (01) for independent channel gains in case of both micro-diversity and macro-diversity and provides a rigorous proof for the macro-diversity case missing in their work. We also show that to any scenario with correlated Rayleigh fading, there exists a macro-diversity scenario with independent Rayleigh fading which is characterized by the same signal-to-interference-and-noise ratio (SINR). Furthermore, sufficient conditions are given which force the multiuser efficiencies of all users to become identical also in case of statistically dependent channel gains

Asynchronous CDMA Systems With Random Spreading—Part II: Design Criteria

Totally asynchronous code-division multiple-access (CDMA) systems are addressed. In Part I, the fundamental limits of asynchronous CDMA systems are analyzed in terms of spectral efficiency and SINR at the output of the optimum linear detector. The focus of Part II is the design of low-complexity implementations of linear multiuser detectors in systems with many users that admit a multistage representation, e.g., reduced rank multistage Wiener filters, polynomial expansion detectors, weighted linear parallel interference cancellers. The effects of excess bandwidth, chip-pulse shaping, and time delay distribution on CDMA with suboptimum linear receiver structures are investigated. Recursive expressions for universal weight design are given. The performance in terms of SINR is derived in the large-system limit and the performance improvement over synchronous systems is quantified. The considerations distinguish between two ways of forming discrete-time statistics: chip-matched filtering and oversampling.

Asymptotic design and analysis of linear detectors for CDMA systems

The asymptotic performance of the linear MMSE detector for any finite observation window and any symbol impinging the observed signal is derived for asynchronous but chip synchronous CDMA systems with random spreading. Additionally, a multistage detector that does not suffer from windowing effects and performs as well as the correspondent detector in synchronous systems is proposed. In contrast to the synchronous case, considering a sufficient large delay, the proposed multistage detector can even outperform the full rank linear MMSE detector constrained to a finite fixed observation window.

Statistics and Chip Pulse Design for Efficient Multiuser Detection in Asynchronous CDMA

The design and analysis of multistage detectors with universal weights for asynchronous CDMA systems is presented. The use of a front-end that enables joint detection and provides sufficient statistics is proposed. With such a front end the proposed multistage detector has the same complexity order per bit as the matched filter. The proposed approach can also take into account other suboptimum statistics and the non-ideality of the chip pulse waveforms. In such a way, the universal weights can be designed and the performance can be computed for very realistic scenarios.

Asymptotic design and analysis of multistage detectors and multistage channel estimators for multipath fading channels

The impact of channel estimation errors on the performance of the LMMSE multistage detec- tor for large multiuser systems with random spreading sequences is analyzed. The receiver consists of a mul- tistage filter for channel estimation and an LMMSE multistage detector that takes into account the im- perfect knowledge of the channels. The asymptotic performance of the whole receiver is provided. I. ANALYSIS AND RESULTS Let us consider a synchronous CDMA system with spread- ing factor N and K users. We assume multipath fading chan- nel with known channel length L and additive noise. The equivalent baseband signal at the chip matched filter output is given by y(m) = S(m)A(m)b(m) + n(m)