Outage probability for a zero forcing multiuser detector with random signature sequences

The performance of linear interference suppression in a DS-CDMA (direct-sequence code division multiple access) system using random codes varies over the user-population due to the random set of interfering sequences. As a result, the capacity of such systems depends on the distribution of the interfering signature sequences and consequently the distribution of the signal-to-interference ratio (SIR). For a zero-forcing or decorrelating solution, the SIR can be expressed in terms of the the near-far resistance (NFR) associated with the detector. Using a statistical characterization of the NFR, we derive analytical bounds on the outage probability in such systems. The analysis is based on application of the Wilson-Hilferty approximation of the chi-squared distribution valid on the range 1≪K≪N where K is the number of users in a cell and N is the processing gain. We show that the cell capacity can be upper and lower bounded by closed form expressions. We compare the cell capacity using zero forcing detection with conventional matched filter detection. Results show a ten fold capacity increase using zero forcing detection in a single cell system and a three fold increase in a multiple cell system