Finding sub‐optimum signature matrices for overloaded code division multiple access systems

Abstract

The objective of this paper is to design optimal signature matrices for binary inputs. For the determination of such optimal codes, we need certain measures as objective functions. The sum-channel capacity and Bit Error Rate (BER) measures are typical methods for the evaluation of signature matrices. In this paper, in addition to these measures, we use distance criteria to evaluate the optimality of signature matrices. The Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are used to search the optimum signature matrices based on these three measures (Sum channel capacity, BER and Distance). Since the GA and PSO algorithms become computationally expensive for large signature matrices, we propose suboptimal large signature matrices that can be derived from small suboptimal matrices.

Set of uniquely decodable codes for overloaded synchronous CDMA

“…To overcome this capacity hard limit, numerous UD [1][2][3][4][5][6][7][8][9][10][11][12][13][14], and non-UD [15][16][17][18][19] construction based systems have already been proposed. For the non-UD based approaches like O/O CDMA, PN/O CDMA [15], improved O/O CDMA [16], the maximisation in system capacity is achieved by collaborating two different sets of code (signature).…”

Twin tree hierarchy: a regularized approach to construction of signature matrices for overloaded CDMA

“…The concept of overloading in CDMA as a solution to the strict capacity limit of its conventional counterpart has drawn frequent interest of the researchers in the past and continuously evolved though several phases. The existing research in the field can be broadly classified into problems like the following: (i) designing of the signature matrices (uniquely decodable (UD) and non‐UD ); (ii) development of reusing techniques for the existing non‐overloaded matrices; (iii) designing of multi user detectors (MUD) ; (iv) adding system level improvisations for improved error performance ; and (v) study of capacity and performance under different channel and input conditions , for synchronous or asynchronous transmission. For matrix C being considered as UD over x , the inequality C x 1 ≠ C x 2 is true for x 1 and x 2 denoting two different input vectors, whereas its major applications in literature are recorded in the field of multiuser encoding for physical layer network coding , overloaded CDMA , and T‐user channels .…”

“…However, selection of the core matrix with relatively large dimension, on the other hand, leads to the rise in design complexity of the MUD, which is due to the growth in the number of secondary users (note that Hadamard refers to primary users), usually detected through the method of joint MLD . Very recently, in , efforts have been focused to optimize the interference existing in the code space to offer better error performance for noisy transmission. However, hardly any attempt has been exercised to linearize the structure of the MUD so that the rise in complexity as compared to the conventional decoding can be maintained at a moderate level.…”