Performance Limits in CDMA PN Code Acquisition

This paper addresses timing acquisition aspects in direct-sequence code division multiple access (DS-CDMA) systems. Various chip waveform shaping schemes are considered,including both one-chip long full-response pulses, and partial response ones occupying several chip periods. Different figures of merits are considered in a comparative analysis that seeks to establish performance limits in terms of correct timing detection capability, false alarm rate, bandwidth occupancy, multiple access interference (MAI), and inter-chip interference (ICI). A waveform design algorithm is formulated to optimize system performance in terms of signal-to-interference-ratio (SIR) subject to other signalling constraints, and a solution based on the use of prolate spheroidal wave functions (PSWF) is derived. Numerous waveform design examples are then constructed to illustrate acquisition detection capability versus system load for both faded and unfaded cases. A comparative assessment of the performance of conventional signalling waveforms against the optimized ones is also presented. In particular, the numerical results show that the half-sine pulse used in Minimum Shift Keying (MSK) is quasi-optimal within the full-response category, while Root-Raised Cosine (RRC) Nyquist filtering with 22% rolloff (used in third generation CDMA standards) is also close to optimal when considering many-chip-long pulses