Semidefinite relaxation based multiuser detection for M-ary PSK multiuser systems

Abstract

Because of the powerful symbol error performance of multiuser maximum-likelihood (ML) detection, recently, there has been much interest in seeking effective ways of approximating multiuser ML detection (MLD) with affordable computational costs. It has been illustrated that for the synchronous code division multiple access (CDMA) scenario, the so-called semidefinite relaxation (SDR) algorithm can accurately and efficiently approximate multiuser MLD. This SDR-MLD algorithm, however, can only handle binary and quadratic phase shift keying (PSK) symbol constellations. In this sequel, we propose an extended SDR algorithm for MLD with -ary PSK (MPSK) constellations. For the synchronous CDMA scenario, the proposed SDR algorithm provides an attractive polynomial-time complexity order of 3 5 , where is the number of users. Simulation results indicate that the proposed detector provides improved symbol error performance compared with several commonly used multiuser detectors.Index Terms-M-ary phase shift keying, maximum likelihood detection, multiuser detection, relaxation methods, semidefinite programming.

Semidefinite relaxation for detection of 16-QAM signaling in MIMO channels

“…Otherwise, SDR is only an approximation of ML, and there is no strict relation between and . Instead, there are a few standard techniques for approximating based on [10]:…”

“…Other results that motivate the use of the SDR show that many of the other conventional detectors, such as the MMSE, are relaxations of the SDR and are, therefore, inferior (at least before the discretization) [5]. There are many works on practical low-complexity implementations of the SDR algorithm that are suitable for MIMO channels with a large number of multiple inputs [6], [9], [10]. Another important feature of the SDR is that its solution can be easily modified to provide soft decisions as required in state-of-the-art communication systems [8].…”

“…In [10] and [11], the SDR was generalized to the detection of -phase shift keying ( -PSK) signaling. In our letter, we propose to extend these works to the detection of other constellations used in digital communications.…”

Capacity-achieving probability measure for a reduced number of signaling points

“…If the resulting matrixŜ has rank one, then the relaxation is tight. Otherwise, special techniques are required to convert the SDP relaxation solution back to the solution of an binary quadratic problem, see, e.g., [22,23]. Using any of these relaxation techniques, we then obtain the set of estimators fsg: Before remapping it back to vector b; it has to be checked whether the estimator fulfills the average power constraint and find the one which maximizes the channel capacity among all those.…”

“…Figure 4 compares different SDP relaxation techniques. The blue curve depicts the channel capacity obtained by applying the dominant eigenvector approximation, see [23], to acquire the SDP relaxation. The green and red curve are obtained by using randomization with 30 loops, i.e., an estimator of s is obtained after each randomization loop.…”