A detector of a spatially distributed target in white Gaussian noise is developed. A reasonable distribution for the a priori target scatterer density is assumed, and a detector that incorporates this a priori knowledge is given. A simple detector form results, whose detection performance is robust over different scattering densities.

The design of M average-energy-constrained signals in additive white Gaussian noise is addressed. The long-standing strong simplex conjecture, which postulates that the regular simplex signal set maximizes the probability of correct detection under an average-energy constraint, is disproven. A signal set is presented that performs better than the regular simplex signal set at low signal-to-noise ratios for all M/spl ges/7. This leads to the result that, for all M/spl ges/7, there is no signal set of M signals which is optimal at all signal-to-noise ratios. Furthermore, the optimal signal set at low signal-to-noise ratios is not an equal energy set for any M/spl ges/7. The regular simplex is shown to be the unique signal set which maximizes the minimum distance between signals. It follows that a signal set which maximizes the minimum distance is not necessarily optimum. However, the regular simplex is shown to be globally optimum in the sense of uniquely maximizing the union bound on error probability at all signal-to-noise ratios.>

In 1982, Delsarte and Piret constructed a concatenated code for which the error probability decreases exponentially with the block length for a subclass of symmetric channels called regular channels. In the case of arbitrary discrete memoryless channels, they were not able to prove an exponential bound, but one for which the error probability decreases as (log N/N)/sup /spl alpha// where /spl alpha/ is related to the random coding exponent and N is the block length. The present author shows that indeed, the codes also satisfy the much stronger exponential bound for arbitrary discrete memoryless channels and hence are good in this sense. It is also indicated that the codes are valid for the bandlimited additive Gaussian noise channel.>