, one need only plot curves of squaring loss for the "one-delta" loop whereupon all other cases can be derived from these curves by appropriately modifying the data rate Rs. Tables 2.1 and 2.2 present closed form results for M2 and M4, corre- sponding to one- and two-pole Butterworth filters and NRZ or Manchester coded data [18]. Also for an n-pole Butterworth filter [17], KL=n-1 (2.31) (2.32) The Delay-Locked Loop Table 2.2 Evaluation of M4 for one- and two-pole Butterworth filters. Signal X Noise Distortion, M4; 2B/R,)exp(-2BH/R; 4BH/Rs 5 {4BH/R,COS(2BH/R,) + 5[cos(2BH/Rs) - sin(2BH/R)]}exp(-2B/Rs 16BH/Rs Manchester Code 4BH/Rs 16BH/Rs {4BH/R,cos(2B/R,), + 5[cos(2BH/R) - sin(2BH/Rs)]}exp(-2B/Rs) 16BH/Rs where fc is the 3 dB cutoff frequency of the equivalent low-pass filter H(j). Figures 2.4 to 2.6 plot SL of (2.30) in dB versus BHIRS with EJN as a para- meter for N = 2, the case of Manchester coded data and one-, two-, and infi- nite-pole (ideal) Butterworth filters for H(s) respectively. We observe that at each value of E/No, there exists an optimum filter bandwidth in the sense BHIRS Figure 2.4. Squaring loss variations versus BRs for various values of E/No; one- pole Butterworth filter, Manchester coding. Pseudonoise Code Tracking in Direct-Sequence Receivers yL,dB BHIRS Figure 2.5. Squaring loss variations versus BH/Rs for various values of E/No; two- pole Butterworth filter, Manchester coding. of minimizing the loop's squaring loss. From (2.29), such optimization of SL is equivalent to minimizing the loop's tracking jitter. Similar optimization behavior of squaring loss as a function of BHIRS can also be observed for NRZ data. As examples, Figures 2.7 and 2.8 illustrate O Smin versus E&/No with Ss 1/BLTs (the ratio of data rate to loop bandwidth) as a parameter for two- Es/No=-2dB BHIRS Figure 2.6. Squaring loss variations versus BHIR, for various values of E/No; ideal filter, Manchester coding. The Tau-Dither Loop Ss = 100 oemin -10.0 -9.0 -80 -7.0 -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0 Es/No,dB Figure 2.7. L