Hierarchy Based Construction of Signature Matrices for Simplified Decoding in Overloaded CDMA

Abstract

The overloaded CDMA system, as the solution to the capacity limit of its conventional counterpart, has drawn frequent interest of the researchers in the past. While there exists numerous proposals on the construction of uniquely decodable (UD) signature matrices for overloaded CDMA system with very high value of overloading factor, most of them lag the efficient multiuser detector (MUD) for noisy transmission. Here, by efficient, we imply the MUD to have acceptable BER performance and simplified in design. Whereas the lack of efficiency of several MUDs is primarily due to the impact of excess level of multiple access interference (MAI) because of the rise in the number of active users, its random nature prohibits its accurate estimation and elimination. Under such constraints, if the signature matrices can be intelligently constructed so as to generate a defined and controlled pattern (hierarchy) of MAI so that the designed MUD will exploit the knowledge of this hierarchy to remove the MAI completely and attain better error performance at much lower cost of complexity. We consider this as the motivation for research in this thesis. First, we propose the ternary signature matrix with orthogonal subsets (TSMOS), where the matrix with index-k comprises of k orthogonal subsets with each having different number signatures, and all subsets besides the first (largest) one are of ternary type. The correlation (interference) pattern among the signatures is mapped into a twin tree hierarchy, which is further leveraged to design a simplified MUD using the linear decoding blocks like matched filter (MF) to provide errorfree and better error performance for noiseless and noisy transmission respectively. Next, we generalize the construction of TSMOS to multiple structures i.e.; Type I, Type II, Type III and mixed versions and reveal the complementary feature of 50% signatures of the largest (binary) subset that further results in their optimality. Further, we propose the non-ternary version of SMOS (called as 2k-SMOS), where the binary alphabets in each of the k subsets are different from each other. With vii no complementary feature, 50% signatures of its largest subset are also found to be optimal. The superiority of 2k-SMOS over TSMOS is also verified for an overloading capacity of 150%. Next, we propose and discuss the hybrid SMOS (HSMOS), where the subsets from TSMOS and 2k-SMOS are used as the constituents to produce multiple SMOS structures, of which TSMOS and 2k-SMOS are treated as the special cases. For better understanding of the features of the whole family of SMOS (with an overloading capacity of 200%), the gradual change in the twin tree hierarchy and BER performance of the left and right child of the individual subsets are studied. Similar to SMOS, we also introduce the hierarchy based low density signature (HLDS) matrix, where any UD matrix satisfying particular criterion can be considered as the basis set. For hadamard matrix as the basis set, we design a MUD that uses the MF to implement the decision vector search (DVS) algorithm, which is meant to exploit the advantageous hierarchy of constellation of the transmitted vector to offer errorfree decoding. For noisy channel, the marginal degradation in the level of BER of the MUD (DVS) as compared to the optimum joint maximum likelihood decoder (MLD) is worthy to be overlooked when compared with the significant gain achieved in terms of complexity. For the smallest dimension of the hadamard matrix as the basis, the MUD is further simplified to offer recovery using a comparison driven decision making algorithm, also known as comparison aided decoding (CAD). Despite simplicity, the error performance of the MUD (CAD) is observed to be very close to that of MUD (DVS).