on of Frequency-Hopped Receivers which has the power spectral density (3.2) [f-(fIF-sf)](Th-t) The non-coherent demodulator forms a filtered measure of the average power in x(t) by demodulating it with quadrature reference signals V2 cos 2nf IFT and V2 sin 2nf IFt and summing the squares of the resultant filtered low-pass signals. Thus, if |H(j2pf)p denotes the squared magnitude of the low-pass filter transfer function, then the non-coherent demodulator out- put has an average value (3.3) Assuming first that the bandwidth of the demodulator low-pass filters is much larger than the hop rate 1/T and, in addition, the frequency error is small (relative to this bandwidth), then (3.3) simplifies to s(1-17) (3.4) i.e., a triangular correlation curve for width 2Th. In general, the non- coherent demodulator low-pass filter bandwidth must be chosen large enough to accommodate the information modulation bandwidth, the max- imum system frequency error, and the hop frequency modulating spectrum. Thus, for slow frequency hopping (SFH), wherein the information symbol rate dominates this choice, the above assumption of a large low-pass filter bandwidth relative to the hop rate is valid and hence no significant filter- ing of the correlation curve occurs in accordance with (3.4). For fast fre- quency hopping (FFH) where the low-pass filter bandwidth is chosen on the order of the hop rate, significant filtering occurs and the correlation curve must be computed from (3.3). As an example of the filtering distor- tion of the triangular correlation function, consider the case of single-pole low-pass filters with single-sided noise bandwidth B. Then evaluation of FH Acquisition Techniques (3.3) with of = 0 yields (3.5) which is plotted against t/Th in Figure 3.3 with BT as a parameter. We observe from this figure that in the neighborhood of T = 0, the predominant effect of the filtering is a reduction of the correlation peak by an amount approximately given by 1/4BT and a corresponding broadening of the tri- angular shape. When additi