Maximum Likelihood Energy Detection of Mary Orthogonal Signals

The literature on energy detection is extended by applying it to the processing of M´ary orthogonal communication signals of arbitrary time-bandwidth product. Guassian noise channel transition probabilities are derived for maximum likelihood energy detection, modified to the extent of including an erasure threshold. Relations and computational techniques are described for determining the symbol erasure and error probabilities for general signal alphabet sizes (M) and time-bandwidth products. When time of arrival is known exactly and Doppler is negligible, gible, it is determined that energy detection is inferior to noncoherent matched filter detection. For time-bandwidth products of the order of 100 and error probabilities around 10 3, a loss of about 5 dB occurs which is attributable to a lack of knowledge of the detail signal structure. However, for problems where time of arrival and/ or Doppler are unknown, energy detection will perform nearly as well as matched filter detection of, for example, spread spectrum signals, and is also simpler to implement. General energy detection performance curves are given in terms of required signal energy for specific error and erasure probabilities, as a function of M´ary and time-bandwidth product.