APPROXIMATE LOWER BOUND ON THE SNR OF MATCHED FILTERS
B. V. K. Vijaya Kumar
Venugopal V. Veeravalli
Abstract
For the simple binary detection problem of detecting a known signal in
the presence of additive noise, the matched filter is well known to
yield the highest output signal-to-noise ratio (SNR). When the
detection is carried out in discrete time, selecting an optimal filter
length for a specific detection problem is important. Bounds on the
SNR of the matched filter can assist in this selection. Exact bounds
on the SNR can be computed in terms of the eigen values of the noise
covariance matrix, but these bounds can be difficult to compute. An
approximate lower bound on the SNR has recently been suggested by
Martinez and Thomas. A supplement to this bound which is more accurate
for small values of filter length is discussed in this paper. Some
examples which delineate a comparison between the two approximate
bounds are presented.