Ateet Kapur

On the Limitation of Linear MMSE Detection

This correspondence highlights the performance limitation of linear minimum mean-squared error (mmse) detection in underdetermined vector Gaussian channels (as in overloaded code-division multiple-access (CDMA) systems) where the number of symbols (users) exceeds the signal space dimension (spread factor). It is shown that for such a simple receiver it is not possible to construct signal sets (or spreading codes) to even satisfy the basic requirement that every users symbol error probability decays exponentially as noise power vanishes. This result holds for arbitrary received energies, modulation schemes, and any strictly underdetermined system with a finite signal space dimension and a finite number of users

Noncoherent MMSE multiuser receivers and their blind adaptive implementations

Three noncoherent minimum mean-squared error (NMSE)-based multiuser receivers are proposed for multipulse modulation. These receivers have a common MMSE prefilter and are followed by one of three phase-independent decision rules. The simplest decision rule selects the maximum magnitude of the MMSE filter outputs, and the other two account for the second-order statistics of the residual multiple-access interference that remains after MMSE filtering. Blind adaptive algorithms are then proposed for the three noncoherent MMSE receivers. The common adaptive algorithm for the MMSE prefilter, which is based on the stochastic approximation method, is shown to converge in the mean-squared error sense to the nonblind NMSE prefilter. Our convergence analysis yields new insight into the tradeoff between the rate of convergence and the residual mean-squared error. The noncoherent blind receivers obtained here do not require the knowledge of the received signals of any of the interfering users, and are hence well-suited for distributed implementation in cellular wireless networks or in communication systems that must operate in noncooperative environments.

Improved signal design for bandwidth efficient multiple access

The problem of optimizing signals for the Gaussian multiple access channel under a quality of service (QoS) constraint is addressed. In particular, the bandwidth efficient multiple access (BEMA) approach (Varanasi, M.K. and Guess, T., IEEE Trans. Commun., vol.49,no.5, p.844-54, 2001) is considered, wherein signals are designed at the base station and fed back to, and for use by, uplink transmitters, in order to minimize a strict bandwidth while ensuring that each user meets a rate-specified QoS constraint. A new recursive, greedy algorithm for signal design is proposed that exactly meets the QoS requirements. Preliminary analysis and numerical examples suggest it is optimal.

Signal design for bandwidth efficient multiple access with guaranteed bit error rate

The problem of signal design for bandwidth efficient multiple access is addressed under quality of service (QoS) constraints specified by (possibly different) BER. Indeed, BER more accurately measures the performance than the signal-to-interference ratio (SIR) for uncoded communication. Furthermore, we argue that the asymptotic effective energy (AEE) faithfully characterizes BER, and we translate the BER-specified QoS into AEE-specified ones. We then propose a recursive, greedy algorithm for joint signal design to minimize the system bandwidth while ensuring that each user achieves its desired AEE (and hence BER). This algorithm successfully converts excess power into bandwidth savings under reliability constraints, and significantly improves spectral efficiency over full-rank (e.g. orthogonal) signaling and SIR-based approaches.

On maximizing symmetric capacity via signal design in cdma systems

The maximization through signal design of the symmetric capacity of CDMA systems with optimal and mini- mum mean-square error decision feedback (MMSE-DF) decod- ing is considered. In particular, lower bounds on maximum sym- metric capacity (and the signal set that achieves them) are derived for the two decoders. A common sufficient condition is obtained for both decoders under which the signal design is optimal in that the lower bounds coincide with an upper bound on the maximum

Signal Design for Bandwidth Efficient Multiple Access under Asymptotic Effective Energy Constraints

The problem of signal design for bandwidth-efficient multiple access (BEMA) over additive white Gaussian noise (AWGN) channels is addressed under quality of service (QoS) requirements specified by asymptotic effective energies (AEEs). The AEE characterizes the bit error rate (BER) in the low-noise regime, but in contrast to BER, it is tractable and amenable to analysis and signal design. We adopt the BEMA strategy of bandwidth conservation where users are detected successively using minimum mean-squared error decision feedback (MMSE-DF) detection and where signals are designed in a greedy fashion for one user at a time, in the reverse order in which the users are detected. The signal design method proposed here is based on an exact characterization of how a signal update for one user affects the issue of preserving bandwidth with the addition of signals for subsequent users. A geometric insight in the construction of good signal sets and significant improvements in bandwidth over full-rank or orthogonal signaling are obtained. The main result of this paper can hence be seen as providing a tight upper bound on the minimum signature sequence dimension or rank (and hence bandwidth) needed to satisfy individual, possibly distinct user QoS constraints specified in terms of the AEE measure.