Performance Analysis of CDMA Signature Optimization with Finite Rate Feedback

We analyze the performance of CDMA signature optimization with finite rate feedback. For a particular user, the receiver selects a signature vector from a signature codebook to avoid the interference from other users, and feeds the corresponding index back to this user through a finite rate and error-free feedback link. We assume the codebook is randomly constructed where the entries are independent and isotropically distributed. It has been shown that the randomly constructed codebook is asymptotically optimal. In this paper, we consider two types of signature selection criteria. One is to select the signature vector that minimizes the interference from other users. The other one is to select the signature vector to match the weakest interference directions. By letting the processing gain, number of users and feedback bits approach infinity with fixed ratios, we derive the exact asymptotic formulas to calculate the average interference for both criteria. Our simulations demonstrate the theoretical formulas. The analysis can be extended to evaluate the signal-to-interference plus noise ratio performance for both match filter and linear minimum mean-square error receivers.