Is a Large Bandwidth Mandatory to Maximally Exploit the Transmit Matched-Filter Structure?

Transmitted signals can be focused in time or space, i.e., at a particular receiver location, by introducing a prefilter in the transmitter. Prefiltering also allows containing intersymbol and multiuser interference. Performance bounds in terms of signal-to-noise ratio gain, which is achievable by prefiltering, depend on both transmitted signal bandwidth and channel characteristics. This paper analyzes the aforementioned dependence for transmit matched filters, which are also known as time-reversal prefilters, and channels with multipath. Theoretical results show that single-cluster channels verify a condition by which the gain is monotonic nondecreasing with bandwidth. Multicluster channels, such as those described by the Saleh-Valenzuela model, seem to follow a similar behavior, as suggested by simulation of the IEEE 802.15.3a channel model. As such, the transmit matched filter is particularly suitable for signals with large bandwidths, as in acoustics and ultrawideband communications.