  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.
