Sequential detection versus conventional detection: A comparative study

M-ary sequential detection algorithms are discussed in terms of the advantage measure A, the number of possible signals M, and the signal-to-noise ratio SNR. The advantage measure A is defined as the logarithm of the ratio of the error probability of the optimum conventional detector to that of the optimum sequential detector with the same values of M and SNR. It increases as the SNR increases but decreases when M increases. For M → ∞, the advantage measure A diminishes to zero, so that application of the sequential approach is useless for large values of M. Thus, the sequential approach is most useful for binary detection with high signal-to-noise ratios. These results are demonstrated for detection of equiprobable orthogonal signals received in white Gaussian noise.