Coding-Spreading Tradeoff for Lattice Codes

A fixed bandwidth expansion can be achieved either by coding or spreading, while each have different effect on the resultant signal space. Coding increases both Shannon and Fourier bandwidth whereas spreading only increases the Fourier bandwidth. In this document we are looking for the optimum combination of coding and spreading, in a Code Division Multiple Access (CDMA) system, that minimizes the average frame error rate under fading channel with multiple antennas at transmitter and receiver. Using the theory of lattice code, we show that in a system with K users, the optimum spreading factor N equals K. Simulation results support the analysis. In simulations we used Minimum Mean Square Error (MMSE), and Matched Filter (MF) as multi-user detector. We also assumed that receiver knows the Channel State Information (CSI). In case of multiple antennas Alamouti scheme [Ala98] at transmitter and Maximum Ratio Combining (MRC) at the receiver are applied.