Chapter 4 Code Tracking Loops

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Horace Randolph Sullivan
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1 Chapter 4 Code Tracking Loops

2 4- Optimum Tracking of Wideband Signals A tracking loop making use of this optimum discriminator is illustrated in Figure 4-1.

4 4- Optimum Tracking of Wideband Signals

5 4.3 Baseband Delay-Lock Tracking Loop

6 4.3 Baseband Delay-Lock Tracking Loop.

7 4.3 Baseband Delay-Lock Tracking Loop

8 4.3 Baseband Delay-Lock Tracking Loop

9 4.3 Baseband Delay-Lock Tracking Loop

10 4-4 Noncoherent Delay-Lock Tracking Loop

11 4-4 Noncoherent Delay-Lock Tracking Loop Δ 1 1 N + + δ + N 1 1 Δ 1 1 δ N + + N D Δ ( δ )= δ N + Δ N 1 Δ δ N N 1 Δ δ N N for Δ 1.0 Δ Δ for N < δ < (1 + ) Δ Δ for (1 + ) < δ < Δ Δ for < δ < (1 ) Δ Δ for (1 ) < δ < (1 ) Δ Δ for (1 ) < δ < Δ Δ for < δ < 1+

12 4-4 Noncoherent Delay-Lock Tracking Loop Δ 1 1 N + + δ + N Δ 1 1 δ N + + N D Δ ( δ )= δ N + Δ N Δ 1 1 δ N + N 1 Δ δ N N for Δ 1.0 Δ Δ for N < δ < (1 + ) Δ Δ for (1 + ) < δ < ( 1) Δ Δ for ( 1) < δ < Δ Δ for < δ < Δ Δ for < δ < 1 Δ Δ for 1 < δ < 1+

17 4-5 Tau-Dither Noncoherent Tracking Loop (TDL) Fig Tau-dither noncoherent code tracking loop.

18 4-5 Tau-Dither Noncoherent Tracking Loop (TDL) Fig Equivalent tau-dither noncoherent code tracking loop.

19 4-5 Tau-Dither Noncoherent Tracking Loop (TDL) Fig Dithering loop switching functions: (a) q(t); (b) q 1 (t); and (c) q (t).

20 4-5 Tau-Dither Noncoherent Tracking Loop (TDL) ( ) ( ) ( ) Rε τ = E ε t, δ ε t + τ, δ (4 101) Δ Δ 1 c c c c q ( ) = K P R δ T 1 R δ + T R τ Δ Δ K1 P Rc δ Tc Rc δ Tc + Δ Δ + 8KP 1 σn Rc δ Tc + Rc δ + Tc Rq ( τ) 1 Δ Δ KP 1 σn Rc δ Tc c c + R δ + T Δ Δ + 4KP 1 Rc δ Tc Rc δ Tc Rn τ R b q τ E{ cos θd( t Td) θd( t + τ Td) } { () ( ) } n t n t R ( ) R ( ) b b τ q τ σn q τ σn + 4E ( ) ( )

21 4-5 Tau-Dither Noncoherent Tracking Loop (TDL) In Eq. (4-101), n b (t) represents any one of the four signals n 1I (t), n 1Q (t), n I (t), n Q (t) and σ n is the mean square value of n b (t) The discriminator output power spectrum is derived as listed in Eq. (4-10). It has been assumed in deriving Eq. (4-10) that only the first three harmonics of the dither frequency cause significant noise components within the tracking loop bandwidth

22 4-5 Tau-Dither Noncoherent Tracking Loop (TDL) 1 Δ Δ ε 1 c δ c c δ c δ ( ) ( ) S f = K P R (4 10) 4 T R + T f Δ Δ + KP 1 Rc δ Tc c c 4 n + R δ + T + σ δ ( f fq) + δ ( f + fq) + δ ( f + 3fq) + δ ( f 3fq) π π 9π 9π Δ Δ + KP 1 Rc δ Tc + Rc δ + Tc S f + S f f + S f + f + S f 3f + S f + 3f b b b b b π π 9π 9π ST ( f ) + S T ( f fq) + S T ( f + fq) + S T ( f 3fq) + S T ( f + 3fq) π π 9π 9π where ( ) ( ) ( ) ( ) ( ) n n q n q n q n q ( ) = ( ) ( ) S f S f S f T n n b b

23 4-5 Tau-Dither Noncoherent Tracking Loop (TDL) The first term of Eq. (4-10) is the desired error correction signal for code tracking. The remainder of the equation is undesired dither frequency clock components plus (signal noise) and (noise noise) components. The dither clock frequency must be selected to be large enough that the clock components of (4-10) are outside the tracking loop bandwidth. The power spectrum of n b ( f ) is KN f BN Sn ( f ) = b 0 elesewhere

24 4-5 Tau-Dither Noncoherent Tracking Loop (TDL) ( ) Fig Power spectral S f and ST ( f ) = Sn ( f ) S ( ) b n f b n b

25 Fig Typical power spectrum of noise and clock components at output of tau-dither discriminator. (for the particular case where f q = B N./4)

26 4-5 Tau-Dither Noncoherent Tracking Loop (TDL) σ δ For N>>1, the phase detector gain K d given by Eq. (4-79) is ( ) Kd Δ 1 K1P so that η = WL NW 0 L 8 R Δ 1 c δ Tc R Δ c δ T + + c + 8P 1 Δ/ π N BNWL 8 fq 8 3 fq (4 106) 8P ( 1 /) π B N 9π B Δ N

27 4-6 Double-Dither Noncoherent Tracking Loop The noise performance of TDL is inferior to that of DDL. The double-dither tracking loop is used to solve the gain-imbalance problem of DDL. The double-dither noise performance is the same as the DLL noise performance. The hardware complexity is increased.

28 4-6 Double-Dither Noncoherent Tracking Loop Fig Double-dither noncoherent code tracking loop.

29 4-6 Double-Dither Noncoherent Tracking Loop Fig. 4-0 DLL discriminator S-curve with gain imbalance.

30 4-6 Double-Dither Noncoherent Tracking Loop Fig. 4-0 DLL discriminator S-curve with gain imbalance.

31 ε 4-6 Double-Dither Noncoherent Tracking Loop When q(t) is a square wave whose frequency is well above the bandwidth of the loop filter, the time average of (4-11) is the desired tracking error. R Δ c δ q() t Tc P K1 K +, δ = q() t (4 114) Δ R c δ + q() t T c In this case, the discriminator S-curve crosses the origin as in Fig ( t )

32 4-7 Non-coherent Delay-Lock Tracking Loop with Arbitrary Data and Spreading Modulation The discussion of Section 4-4 was limited to systems that employ BPSK direct-sequence spreading modulation. In this section it will be shown that the same results apply to a system having an arbitrary constant-envelope phase modulation when the BPSK autocorrelation function is replaced by the autocorrelation function for the modulation being considered.. C

33 4-7 Non-coherent Delay-Lock Tracking Loop with Arbitrary Data and Spreading Modulation

Tracking of Spread Spectrum Signals

Chapter 7 Tracking of Spread Spectrum Signals 7. Introduction As discussed in the last chapter, there are two parts to the synchronization process. The first stage is often termed acquisition and typically