Asynchronous code-division random access using convex optimization

Many applications in cellular systems and sensor networks involve a random subset of a large number of users asynchronously reporting activity to a base station. This paper examines the problem of multiuser detection (MUD) in random access channels for such applications. Traditional orthogonal signaling ignores the random nature of user activity in this problem and limits the total number of users to be on the order of the number of signal space dimensions. Contention-based schemes, on the other hand, suffer from delays caused by colliding transmissions and the hidden node problem. In contrast, this paper presents a novel pairing of an asynchronous non-orthogonal code-division random access scheme with a convex optimization-based MUD algorithm that overcomes the issues associated with orthogonal signaling and contention-based methods. Two key distinguishing features of the proposed MUD algorithm are that it does not require knowledge of the delay or channel state information of every user and it has polynomial-time computational complexity. The main analytical contribution of this paper is the relationship between the performance of the proposed MUD algorithm in the presence of arbitrary or random delays and two simple metrics of the set of user codewords. The study of these metrics is then focused on two specific sets of codewords, random binary codewords and specially constructed algebraic codewords, for asynchronous random access. The ensuing analysis confirms that the proposed scheme together with either of these two codeword sets significantly outperforms the orthogonal signaling-based random access in terms of the total number of users in the system.