(,B) replaced by (3.117) Note that for b = 0, Di(e, B) of (3.116) and Din(E, B) of (3.117) reduce, respectively, to D() of (3.69) and Din(E) of (3.71). Comparing (3.115) with (3.73), it is clear that the bit error probability per- formance conditioned on fixed frequency and time synchronization errors is given by (3.78) together with (3.75) and (3.77) where D(,B) and Din(E, B) are used in place of D(s) and Din(E) in (3.75). Frequency Synchronization of Non-Coherent FH / MFSK Systems B = 0.40 SIGNAL-TO-NOISE RATIO, Eb/NJ, dB Figure 3.27. 4-ary FSK with frequency error (minimum orthogonal tone spacing) (reprinted from [13]). Figures 3.27, 3.28, and 3.29 are the analogous results for performance in the presence of frequency error alone to those in Figures 3.18, 3.19, and 3.20, which depict performance in the presence of timing error alone. Comparing Figure 3.28 with Figure 3.19, for example, we observe that in the case of frequency error, the loss of orthogonality is the dominant degra- dation component for all B, whereas, as previously mentioned, for time syn- chronization error, loss of orthogonality dominates only for large error values. Returning to Figure 3.21, we observe that increasing the MFSK tone spac- ing to twice its minimum orthogonal value has a more pronounced effect on the performance improvement achieved in the presence of frequency error alone than that when timing error alone is present, particularly when the syn- chronization errors are large. When both time and frequency errors exist simultaneously, Figure 3.30 illustrates a set of curves that represent contours of constant Eb/N, degradation for a fixed bit error probability. Both 4-ary and 8-ary FSK results are provided. Time and Frequency Synchronization of Frequency-Hopped Receivers 4-ARY FSK Pb =10-2 MINIMUM ORTHOGONAL TONE SPACING NORMALIZED FREQUENCY ERROR, B Figure 3.28. Performance degradation due to frequency error (reprinted from [13]). Pb=10-2 = MINIMUM ORTHOGONAL TONE SPACING NORMALIZED FREQUENCY ERROR, B from [13]). Figure 3.29. 8-a