quency (due to variation of the channel in time), we say the channel is doubly dispersive. We also note that while the dominant effect of time dispersion in a channel is ISI, the dom- inant effect of frequency dispersion is ICI. Hence, in order to design prototype filters that address both time and frequency dispersions, it has been argued [5] that one should choose a pulse-shape p(t) with similar behavior along time and frequency. In particular, if p(t) is selected to be a SR-Nyquist along the time axis, it should also be ensured that P(f) is an SR-Nyquist along the frequency axis. To this end, the pulse-shape, p(t), with the following property may be adopted: P(f) = p(nf), for a constant scaling factor N, (5.20) i.e. a function that has the same form in both the time and frequency domain. 5 Filter Bank Multicarrier Modulation The parameter n in (5.20) is related to the symbol spacing in time, T, and frequency, F, and is given by =Time (5.21) Also, as one may understand intuitively, T and F are, respectively, chosen proportional to time dispersion, AT, and frequency dispersion, Av, of the channel, i.e. T/F = At/Av. Hence, the following identity also holds. (5.22) The definitions for At and Av are usually vague. The time dispersion At may be thought of as a coarse estimate of the duration of the channel impulse response, equivalently, the span of the multipaths of the channel. Similarly, the frequency dispersion Av may be thought of as a coarse estimate of the span of Doppler spread of the channel. The design of the prototype filter for time-varying channels is closely tied to the ambiguity function; e.g. see [16]: (5.23) where T is a time delay and V is a frequency shift. Let p(t) be a prototype filter and Pn.k(t) be a time frequency translated version of the same, which is defined as (5.24) We note that xx,A,((n-m)T,(l-k)F), (5.25) where a denotes proportionality. The proportionality factor is a phase shift due to the delays of mT and nT whose value is irrelevant to our discussion here. Using (5.25), one may no