Probability of error in bandlimited spread spectrum binary communication systems
Abstract
The performance of a pseudonoisemodulated spread spectrum binary communication system is analyzed to determine the probability of error in the presence of bandlimiting, Gaussian noise, and synchronization errors. It is shown that the correlation receiver is an optimum receiver in the presence of white gaussian noise with no bandlimiting. Synchronization errors are introduced into the analysis in the form of a timing delay between the received code and local code. Bandlimiting is modeled by a causal lowpass filter at the input of the correlation receiver. Probability of error in detecting the binary message symbols is analyzed first by developing upper bounds based on the correlation properties of maximal length pseudonoise sequences and the decaying response typical of causal filters. Then, the average probability of error is computed using a series expansion of the characteristic function of the intersymbol interference. Results show that for large spreading ratios, the effects of intersymbol interference are negligible. Synchronization errors in addition to bandlimiting further degrade the performance, but less dramatically than in the case of the infinitebandwidth system.
 Publication:

Ph.D. Thesis
 Pub Date:
 December 1975
 Bibcode:
 1975PhDT........58H
 Keywords:

 Digital Systems;
 Error Analysis;
 Probability Theory;
 Telecommunication;
 Pulse Modulation;
 Random Noise;
 Synchronism;
 Time Lag;
 Communications and Radar