Fast Decoder for Overloaded Uniquely Decodable Synchronous CDMA

We consider the problem of designing a fast decoder for antipodal uniquely decodable (errorless) code sets for overloaded synchronous code-division multiple access (CDMA) systems where the number of signals K_{max}^a is the largest known for the given code length L. The proposed decoder is designed in a such a way that the users can uniquely recover the information bits with a very simple decoder, which uses only a few comparisons. Compared to maximum-likelihood (ML) decoder, which has a high computational complexity for even moderate code length, the proposed decoder has a much lower computational complexity. Simulation results in terms of bit error rate (BER) demonstrate that the performance of the proposed decoder only has a 1-2 dB degradation at BER of 10^{-3} when compared to ML

Finite-step algorithms for constructing optimal CDMA signature sequences

A description of optimal sequences for direct-spread code-division multiple access (DS-CDMA) is a byproduct of recent characterizations of the sum capacity. This paper restates the sequence design problem as an inverse singular value problem and shows that the problem can be solved with finite-step algorithms from matrix theory. It proposes a new one-sided algorithm that is numerically stable and faster than previous methods

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 under-sampling 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 the users are de-synchronized on the 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 the effective interference spectral density arises. This generalizes and refines Tse and Hanly's 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

Construction of equiangular signatures for synchronous CDMA systems

Welch bound equality (WBE) signature sequences maximize the uplink sum capacity in direct-spread synchronous code division multiple access (CDMA) systems. WBE sequences have a nice interference invariance property that typically holds only when the system is fully loaded, and, to maintain this property, the signature set must be redesigned and reassigned as the number of active users changes. An additional equiangular constraint on the signature set, however, maintains interference invariance. Finding such signatures requires equiangular side constraints to be imposed on an inverse eigenvalue problem. The paper presents an alternating projection algorithm that can design WBE sequences that satisfy equiangular side constraints. The proposed algorithm can be used to find Grassmannian frames as well as equiangular tight frames. Though one projection is onto a closed, but non-convex, set, it is shown that this algorithm converges to a fixed point, and these fixed points are partially characterized

Optimal CDMA signatures: a finite-step approach

A description of optimal sequences for direct-sequence code division multiple access is a byproduct of recent characterizations of the sum capacity. The paper restates the sequence design problem as an inverse singular value problem and shows that it can be solved with finite-step algorithms from matrix analysis. Relevant algorithms are reviewed and a new one-sided construction is proposed that obtains the sequences directly instead of computing the Gram matrix of the optimal signatures

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