The exploitation of redundancy and spectrum spreading

Aspects of signal-space geometry are used to study channel coding through redundancy and spectrum spreading in a multiple access communications relay system. The system noise is assumed to be additive, steady-state, gaussian, and white. Signal coding allows redundancy, which protects the information transfer from interference effects. The signal space is defined in terms of the bandwidth and the duration of the pulse, and consideration is given to the space generated by a set of signals. Maximum likelihood estimates are employed for reception in a noisy environment. Frequency hopping for spectrum spreading is shown to average the SNR, yielding an error probability after decoding that is a convex function of the SNR.