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.

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 user's 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

This correspondence characterizes the performance limitation of the well-acclaimed generalized Welch-bound equality (WBE) signals under linear minimum mean-squared error (MMSE) detection. It is analytically proven, and experimentally verified, that when users in an overloaded but finite-size code-division multiple-access (CDMA) system are allocated such signals, the error rate of at least one user "floors" (i.e., it cannot be driven to zero even in the absence of additive noise), independently of the symbol energies. If, in addition, all users are received with equal energy, then the error rate of every user "floors".

The max-min fairness idea is applied to optimize the CDMA capacity region. For any given signal set, a fair rate-allocation algorithm is specified. The notion of fair capacity is introduced and a signal design algorithm is proposed that produces signal sets with near-maximum fair capacity under (a) optimum decoding and (b) suboptimal decoding based on MMSE filtering and successive decoding, when there is sufficient bandwidth.

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.

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.

Multiuser detection for overloaded code-division multiple-access (CDMA) systems, in which the number of users is larger than the dimension of the signal space, is of particular interest when bandwidth is at a premium. In this paper, certain fundamental questions are answered regarding the asymptotic forms and performance of suboptimum multiuser detectors for cases where the desired and/or interfering signal subspaces are of reduced rank and/or have a nontrivial intersection. In the process, two new suboptimum detectors are proposed that are especially well suited to overloaded systems, namely, the group pseudo-decorrelator and the group minimum mean-squared error (MMSE) detector. The former is seen to be the correct extension of the group decorrelator in the sense that it is the limiting form (in the low-noise regime) of the group MMSE detector. Pseudo-decorrelation is also used as a feedforward filter in a new decision feedback scheme. For the particular case of real-valued modulation, it is shown that the proposals of the so-called "improved" linear (also known as "linear-conjugate" or "widely linear") detectors were more simply derived earlier using the idea of minimal sufficiency, which we also apply to the new detectors of this paper.

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.