Errorless Codes for Over-Loaded CDMA with Active User Detection

In this paper we introduce a new class of codes for over-loaded synchronous wireless CDMA systems which increases the number of users for a fixed number of chips without introducing any errors. In addition these codes support active user detection. We derive an upper bound on the number of users with a fixed spreading factor. Also we propose an ML decoder for a subclass of these codes that is computationally implementable. Although for our simulations we consider a scenario that is worse than what occurs in practice, simulation results indicate that this coding/decoding scheme is robust against additive noise. As an example, for 64 chips and 88 users we propose a coding/decoding scheme that can obtain an arbitrary small probability of error which is computationally feasible and can detect active users. Furthermore, we prove that for this to be possible the number of users cannot be beyond 230.

I. INTRODUCTION

In Direct-Sequence Code Division Multiple Access (DS-CDMA) due to practical conditions it is desirable to use binary antipodal signatures (spreading codes) in conjunction with BPSK modulation. In these systems we can obtain errorless transmission using orthogonal codes (e.g. Hadamard codes) under the assumption of noiseless channel. This is only true if the number of users does not exceed the spreading factor (under-loaded or fully-loaded CDMA). When the number of users exceeds the spreading factor, such orthogonal codes do not exist. Also, using Pseudo-Noise (PN) spreading signatures creates interference that cannot be completely removed and results in errors in the Multi-User Detection (MUD) receiver [1]–[3]. There are papers that discuss double orthogonal codes for increasing capacity [4]–[5]. These codes are non-binary complex codes (equivalent to phases for MC-OFDM) and thus are not a fair comparison to binary codes.