erent FH / MFSK Systems 8-ARY FSK pb=10°2 = MINIMUM ORTHOGONAL TONE SPACING NORMALIZED TIMING ERROR, E Figure 3.20. 8-ary FSK performance degradation due to timing error (reprinted from [13]). 4-ARY FSK Pb=10-2 K = I MINIMUM ORTHOGONAL TONE SPACING K =2 TWICE MINIMUM ORTHOGONAL SPACING NORMALIZED ERROR, E OR B Figure 3.21. Performance degradation due to synchronization errors for different tone spacings (reprinted from [13]). Time and Frequency Synchronization of Frequency-Hopped Receivers inant cause of the degradation, whereas for large timing errors the loss of the orthogonality component plays an equally, if not more, important role. Figure 3.20 illustrates similar performance degradation results for 8-ary FSK. These results, when compared with the corresponding 4-ary FSK perfor- mance results of Figure 3.19, indicate that increasing the number of tones M decreases the performance degradation due to the timing synchroniza- tion error. Finally, Figure 3.21 demonstrates the effect of increasing the MFSK tone spacing to twice its minimum orthogonal value. The additional results shown there for frequency error will be explained later on in the chap- ter when we discuss that subject. 3.2.3.2 Conditional Error Probability Performance-m-Diversity with Non-Coherent Combining When the same MFSK symbol is transmitted on m different hops, and the symbol decision is based on the non-coherent combining of the m corre- sponding detector outputs for that tone, then, assuming all m chips are jammed, the conditional pdf for the spectral estimates formed in the receiver is given by p(r)) 0; otherwise (3.80) where for the correct tone, r corresponds to Vj, and V'n = nD(s) (3.81) with D() defined in (3.69). For the M - 1 incorrect tones, r corresponds to rin, and = YnDin(E) (3.82) with Din(E) defined in (3.70) or (3.71). Thus, following the steps leading to the evaluation of (3.75), we can immediately write down the corresponding result for FH/MFSK with m-diversity and non-coherent combining, namely, Ps(E) Im-1[V2my,D,(e)y] M - 