Bounds on the Sum Capacity of Synchronous Binary CDMA Channels

In this paper, we obtain a family of lower bounds for the sum capacity of Code Division Multiple Access (CDMA) channels assuming binary inputs and binary signature codes in the presence of additive noise with an arbitrary distribution. The envelope of this family gives a relatively tight lower bound in terms of the number of users, spreading gain and the noise distribution. The derivation methods for the noiseless and the noisy channels are different but when the noise variance goes to zero, the noisy channel bound approaches the noiseless case. The behavior of the lower bound shows that for small noise power, the number of users can be much more than the spreading gain without any significant loss of information (overloaded CDMA). A conjectured upper bound is also derived under the usual assumption that the users send out equally likely binary bits in the presence of additive noise with an arbitrary distribution. As the noise level increases, and/or, the ratio of the number of users and the spreading gain increases, the conjectured upper bound approaches the lower bound. We have also derived asymptotic limits of our bounds that can be compared to a formula that Tanaka obtained using techniques from statistical physics; his bound is close to that of our conjectured upper bound for large scale systems.Comment: to be published in IEEE Transactions on Information Theor

Large-System Analysis of Multiuser Detection with an Unknown Number of Users: A High-SNR Approach

We analyze multiuser detection under the assumption that the number of users accessing the channel is unknown by the receiver. In this environment, users' activity must be estimated along with any other parameters such as data, power, and location. Our main goal is to determine the performance loss caused by the need for estimating the identities of active users, which are not known a priori. To prevent a loss of optimality, we assume that identities and data are estimated jointly, rather than in two separate steps. We examine the performance of multiuser detectors when the number of potential users is large. Statistical-physics methodologies are used to determine the macroscopic performance of the detector in terms of its multiuser efficiency. Special attention is paid to the fixed-point equation whose solution yields the multiuser efficiency of the optimal (maximum a posteriori) detector in the large signal-to-noise ratio regime. Our analysis yields closed-form approximate bounds to the minimum mean-squared error in this regime. These illustrate the set of solutions of the fixed-point equation, and their relationship with the maximum system load. Next, we study the maximum load that the detector can support for a given quality of service (specified by error probability).Comment: to appear in IEEE Transactions on Information Theor

Spectral Efficiency of Random Time-Hopping CDMA

Traditionally paired with impulsive communications, Time-Hopping CDMA (TH-CDMA) is a multiple access technique that separates users in time by coding their transmissions into pulses occupying a subset of $N_\mathsf{s}$ chips out of the total $N$ included in a symbol period, in contrast with traditional Direct-Sequence CDMA (DS-CDMA) where $N_\mathsf{s}=N$. This work analyzes TH-CDMA with random spreading, by determining whether peculiar theoretical limits are identifiable, with both optimal and sub-optimal receiver structures, in particular in the archetypal case of sparse spreading, that is, $N_\mathsf{s}=1$. Results indicate that TH-CDMA has a fundamentally different behavior than DS-CDMA, where the crucial role played by energy concentration, typical of time-hopping, directly relates with its intrinsic "uneven" use of degrees of freedom.Comment: 26 pages, 13 figure