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 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 cell capacity can be upper and lower bounded by closed form expressions. We compare 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.