On chip-matched filtering and discrete sufficient statistics for asynchronous band-limited CDMA systems

The problem of generating discrete sufficient statistics for signal processing in code-division multiple-access (CDMA) systems is considered in the context of underlying channel bandwidth restrictions. Discretization schemes are identified for (approximately) band-limited CDMA systems, and a notion of approximate sufficiency is introduced. The role of chip-matched filtering in generating accurate discrete statistics is explored. The impact of approximate sufficiency on performance is studied in three cases: conventional matched filter (MF) detection, minimum mean-squared-error detection, and delay acquisition. It is shown that for waveforms limited to a chip interval, sampling the chip-MF output at the chip rate can lead to a significant degradation in performance. Then, with equal bandwidth and equal rate constraints, the performance with different chip waveforms is compared. In all three cases above, it is demonstrated that multichip waveforms that approximate Nyquist sinc pulses achieve the best performance, with the commonly used rectangular chip pulse being severely inferior. However, the results also indicate that it is possible to approach the best performance with well-designed chip waveforms limited to a chip interval, as long as the chip-MF output is sampled above the Nyquist rate.