ry FSK performance degradation due to frequency error (reprinted Frequency Synchronization of Non-Coherent FH /MFSK Systems SOLID: 4-ARY FSK DASHED: 8-ARY FSK MINIMUM ORTHOGONAL TONE SPACING Pp = 10-2 NORMALIZED FREQUENCY ERROR, B Figure 3.30. Performance degradation due to time and frequency synchronization errors (reprinted from [13]). 4-ARY FSK Pb = 10-2 MINIMUM ORTHOGONAL TONE SPACING NORMALIZED FREQUENCY ERROR, B Figure 3.31. Performance degradation due to frequency error with chip combining (reprinted from [13]). Time and Frequency Synchronization of Frequency-Hopped Receivers 4 -ARY FSK Pb = 10- (E,B)=(.3,0) MINIMUM ORTHOGONAL TONE SPACING (.2,.2) (0, .3) (.2,0) (.1,.1) (0,.2) (.1, O) (0,.1) NUMBER OF CHIPS COMBINED, m Figure 3.32. Effect of chip combining on degradation due to synchronization errors (reprinted from [13]). Finally, when m-diversity and non-coherent combining are superimposed on the basic FH/MFSK system of above, then again all of the results of Section 3.2.3.2 apply after making the same replacements of D(,B) and Din( E, B) for D(s) and Din(e). In this regard, Figure 3.31 provides, for fre- quency error alone, the analogous results to Figure 3.22. Again we observe that increasing m improves performance; however, a comparison of the two figures reveals that the reduction of loss of orthogonality by non-coherent combining plays a more prominent role with frequency errors than with tim- ing errors. When both time and frequency errors are present and fixed, Figure 3.32 illustrates the performance degradation as a function of m, the number of chips combined. 3.3.3.1 Average Error Probability Performance in the Presence of Frequency Synchronization Error Estimation If the estimator B of (3.106) is used for FH frequency synchronization and and E is the fixed normalized time synchronization error, then a residual fre- quency offset v(B) B - B arises, which, as in our previous discussions, affects system performance by reducing the signal energy available for the Frequency Synchronization of Non-Co