dth to data rate, BHIRS. At this point, it is reasonable to expact that if one were to plot I' versus BHIRS with E/No as a parameter, than at each value of E/N, there would exist an optimum filter bandwidth in the sense of minimizing the loop's squaring loss. Figure 2.14 illustrates the validity of this statement for the case of an ideal filter with S'L as determined from (2.54) together with (2.14), (2.59), and (2.61). The corresponding minimum tracking jitter performance as described by (2.54) is illustrated in Figure 2.15. In both of these figures, the value of was chosen equal to four. Comparing Figure 2.15 with Figure 2.8, we observe that over the entire range of parameter variations cho- sen, the TDL is approximately 1.06 dB poorer than the DLL. 5 As is 5The comparison here is made on the basis of equal o Emin and the signal-to-noise ratio penalty of 1.06 dB is obtained directly from the computational data rather than the curves themselves. BHTd=4 N = 2 -10.0 -11.0 -12.0 -14.0 Es/No==2dB -15.0 BHIR5 coding. Figure 2.14. Squaring loss variations versus BHIR, for various values of ENo; ideal filter, Manchester The Tau-Dither Loop 85=100 = BHTd = 4 = -10.0 Es/No,dB Figure 2.15. Linear tracking jitter performance of non-coherent TDL; ideal filter. increased (typically by lowering the dither frequency relative to the arm fil- ter bandwidth), the performance penalty also increases approaching 1.5 dB in the limit as approaches infinity. Clearly, this situation is never reached in practice, nor in theory, since the assumption made in the analy- sis that the dither frequency be large relative to the loop bandwidth breaks down. It is perhaps interesting to see how the optimized performance results presented in this chapter compare with the early results of Gill [3] and Hartmann [6]. In particular, both these authors performed their analyses neglecting the band-limiting effect of the arm filters. Thus, if one sets KL = M2 = M4 = 1 in (2.29), and substitutes ENo(BRs) for PH one arrives at Gill's result6 for the normali