Analysis of CDMA systems that are characterized by eigenvalue spectrum

Abstract

Abstract. -An approach to analyze the performance of the code division multiple access (CDMA) scheme, which is a core technology used in modern wireless communication systems, is provided. The approach characterizes the objective system by the eigenvalue spectrum of a cross-correlation matrix composed of signature sequences used in CDMA communication, which enable us to handle a wider class of CDMA systems beyond the basic model reported by Tanaka in Europhys. Lett., 54 (2001) 540. The utility of the scheme is shown by analyzing a system in which the generation of signature sequences is designed for enhancing the orthogonality.Introduction. -Over the last decade, the scope of statistical mechanics has rapidly expanded beyond its original goal of analyzing many-body problems that arise when dealing with material objects. Information theory is a major source of problems, and research activity aimed at solving these problems is becoming popular. Identifying information bits with Ising spins, many problems in information theory, such as error correcting/compression codes [1-10] and cryptosystems [11,12], can be formulated as virtual many-body systems that are subject to disordered interactions. Analysis of the formulated problems using techniques of statistical mechanics has provided various nontrivial results that have not been obtained by conventional methods of information theory [13,14].Code division multiple access (CDMA), which is a core technology used in modern wireless communication, is an example of the successful application of such a statistical mechanical approach. This technology realizes simultaneous communication between multiple users and a single base station by modulating each user's bit signal (symbol) into a sequence of random pattern, termed the signature sequence [15]. CDMA has already been employed in thirdgeneration mobile phone systems and wireless LANs.Tanaka (2001) showed that the replica method of statistical mechanics enables the accurate assessment of the communication performance of a basic CDMA model in which users' sequences are generated independently of each other in a large system limit [16,17]. This research

Rigorous dynamics of expectation-propagation-based signal recovery from unitarily invariant measurements

“…Compare (10) and (18) to the SE equations. The FPs of the SE equations were proved in [27] to correspond to those of an asymptotic energy function that describes the Bayes-optimal performance-derived in [30] via the replica method. Thus, the Bayes-optimal performance derived in [30] is achievable when the SE equations have a unique FP, or equivalently when the compression rate δ is larger than the BP threshold.…”

“…Note that the condition B H t ′ M t = Q H t ′ H t is a constraint imposing V ∈ U N , and follows from (28) and (30). In order to investigate the dynamics of the error recursions, the distribution of the Haar matrix V conditioned on X t,t ′ is analyzed.…”

“…More precisely, we derive SE equations for individual elements of the signal vector in the large system limit. This implies the achievability of the Bayes-optimal performance conjectured in [30], when the compression rate is larger than the BP threshold, while the converse theorem is still open, i.e. there are no algorithms outperforming the EP-based algorithm in the large system limit.…”

“…The structure (198) in the upper-left block follows from the orthogonality between the first t + t ′ rows ofV . Similarly, (199) is due to the orthogonality between the first t + t (28) and (30) imply that B t ′ and H t are so. Thus, (210) and (211) are full rank.…”

“…By investigating the properties of the SE equations, they conjectured that, for unitarily invariant measurement matrices, the FPs of the SE equations are the same as those of an asymptotic energy function that describes the Bayes-optimal performance in the large system limit, which were derived in [30] via the replica method. In other words, the EP-based algorithm was conjectured to achieve the optimal performance in the large system limit, when the compression rate is larger than the BP threshold.…”