Tài liệu Adaptive WCDMA (P4) doc

4 Code tracking 4.1 CODE-TRACKING LOOPS Theoretically switching from code acquisition to code tracking in this chapter means switching from open loop maximization of likelihood function (equation 3.3) to the closed-loop tracker defined by equation (3.8) of Chapter 3. A variety of practical imple- mentation options are shown in the sequel. The baseband implementation of equation (3.8) of Chapter 3 is shown in Figure 4.1. The input signal is correlated with two locally gen- erated, mutually delayed, replicas of the pseudonoise (PN) code. After filtering, the useful component of the control signal e(t) will be proportional to D D (δ) = R c (δ − /2) − R c (δ + /2)(4.1) where R c (δ) is the auto correlation of the sequence. For the analysis of the tracking error variance, results from the standard phase lock loop theory can be used directly [1]. In Code Division Multiple Access (CDMA) system, the input signal in Delay lock loop (DLL) will be a complete Direct Sequence Spread Spectrum (DSSS) signal. In order to get rid of information, a noncoherent structure shown in Figure 4.2(a) may be used with the simplest form of the input signal r(t)= s(t)+ n(t) (4.2) and s(t) = Ab(t)c(t) cos ω 0 t(4.3) It can be shown that the direct current (DC) component of ε(t, δ) is A 2 D  (δ)/2where D  (δ)  = R 2 c  δ −  2  T c  − R 2 c  δ +  2  T c  (4.4) The tracking error variance can be expressed as [1] τ 2 δ 1 2ρ L  1 + 2 ρ if  (4.5) Adaptive WCDMA: Theory And Practice. Savo G. Glisic Copyright ¶ 2003 John Wiley & Sons, Ltd. ISBN: 0-470-84825-1 80 CODE TRACKING X VCO Loop filter − + e( t ,d) Spreading waveform generator Spreading waveform clock Delay-lock discriminator x 1 ( t ) x 2 ( t ) X Σ K 1 c ( t − T ^ d − 2 ∆ T c ) K 1 c ( t − T ^ d + 2 ∆ T c ) K 1 c ( t − T ^ d ) e ( t ) = D ∆ (d) + n Ac ( t − T d ) + n ( t ) D ∆ (d) R c 2 = ∆         2 ∆         2 ∆ d− T c − R c 2 d + T c Figure 4.1 Conceptual block diagram: baseband delay-lock tracking loop. X X BP filter B N − + BP filter B N + X X Spreading waveform generator Power divider (a) Local oscillator Low-pass filter Low-pass filter Power divider Voltage controlled oscillator g c Loop filter Abc cos w t ~ R 2 c ( ) 2 ( ) 2 e( t , d) D ∆ (d) 2 T c ) c ( t − T ˆ d − ∆ 2 T c ) c ( t − T ˆ d + ∆ Figure 4.2 (a) Full-time early–late noncoherent code-tracking loop, (b) Noncoherent tracking loop with interference cancellation (IC) DLL/IC [2]. Reproduced from Sheen, W. and Tai, C. (1998) A noncoherent tracking loop with diversity and multipath interference cancellation for direct-sequence spread-spectrum systems. IEEE Trans. Commun., 46(11), 1516–1524, by permission of IEEE. (c) Comparisons of DLL and DLL/IC tracking loops [2]. CODE-TRACKING LOOPS 81 PN code generator c [ t − tˆ( t ) − LT c − T D ] c [ t − tˆ( t ) − T D ] c [ t − tˆ( t )] c [ t − tˆ( t )] c [ t − tˆ( t ) − LT c ] c [ t − tˆ( t ) − LT c ] u 0 ( t ) u L ( t ) u L ( t ) u 0 ( t ) v 0 ( t ) v L ( t ) Noncoherent square-law discriminator Noncoherent square-law discriminator V.C.C Loop filter v L (t) v 0 ( t ) e 0 ( t ) e L ( t ) w L ( t ) w 0 ( t ) Tn LPF h 0 ( t ) 2 e − j w c t y ( t ) r ( t ) + + + + + + Complex signal flows LPF h 1 ( t ) LPF h 1 ( t ) − − Σ Σ Σ + + Σ Σ Σ − − (b) −5 20151050 10 −5 10 −4 10 −3 10 −2 10 −1 10 0 g b (dB) Mean-square tracking error ∆ = 0.5 f D = 83 Hz z 0 = 0.01 Γ 1 = 0 dB DLL/IC (ideal, analysis) DLL/IC (ideal, simulation) DLL/IC (simulation) Traditional DLL DLL/IC coherent (analysis) DLL/IC coherent (simulation) (c) Figure 4.2 (Continued). 82 CODE TRACKING where ρ L = 2A 2 N 0 B L ρ if = A 2 N 0 B N (4.6) Parameter ρ L is the loop signal-to-noise power ratio and ρ if is the signal-to-noise power ratio at the output of the intermediate frequency (IF) (band pass) filter. The first term in equation (4.5) represents σ 2 δ for a coherent loop. The second term is degradation due to the noncoherent structure. Other modifications of the code-tracking loops like τ -dither loop or double-dither loop can be seen in Reference [1]. 4.1.1 Effects of multipath fading on delay-locked loops In this section, the effects of a specular multipath fading channel on the performance of a DLL are discussed. For this type of environment, the two-path channel model becomes h(τ ) = √ 2P{δ(τ − τ 1 ) e jθ1 + g 2 e jθ 2 δ(τ − τ 1 − τ d )} (4.7) where θ 1 is a constant phase shift, and g 2 and θ 2 are Rayleigh- and uniform-distributed random variables, respectively. When τ d = 0, the channel becomes the familiar frequency nonselective Rician-fading model. In order to present some quantitative results, the following important system param- eters are needed: the power ratio of the main path to the second path R  = 1/E[g 2 2 ], the bit signal-to-noise ratio (SNR) (SNR in data bandwidth) γ d  = PT b /N 0 , the loop SNR γ L 0  = P/N 0 B L | = 1 and the ratio ς 0 = γ L 0 /γ d where T b is the duration of an infor- mation bit, and B L is the closed-loop bandwidth for the case when g 2 = 0. That is, B L =  ∞ −∞ |H(f)| 2 df where H(s) is the closed loop transfer function. By using the standard phase lock loop theory [3], the tracking error variance for this case has been evaluated and the results are shown in Figure 4.3. Effects of multipath fading on the nor- malized mean time to lose lock (MTLL) and tracking error versus early–late discriminator offsets /2 are shown in Figures 4.4 and 4.5, respectively. Figures 4.4 and 4.5 demonstrate performance degradation of DLL due to the pres- ence of multipath components. In order to improve the system performance in such an environment, some research results are reported in which multipath IC is used. The receiver block diagram is shown in Figure 4.2(b). For the input signal received through L + 1 equidistantly modeled paths, the upper half of the block diagram is used to regenerate multipath interference (MPI) for each path. In the first step, input signal r(t) is correlated with L + 1 delayed replica of the local code to separate L + 1 narrowband signal components. After processing delay T D ,the wideband components u 0 (t), . . . , u L (t) are regenerated separately and summed up again. At this point r(t − T D ) is created together with all individual components u l (t) available separately. Now in L + 1 branches, signal r(t − T D ) − u l (t) = v l (t), representing the CODE-TRACKING LOOPS 83 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 10 −2 10 −1 10 0 Delay spacing t d ( T c ) Tracking error (rms) R = 5 dB R = 10 dB R = 15 dB No multipath g d = 5 dB g d = −2.5 dB Figure 4.3 Effects of multipath fading on the tracking error performance with various delay spacings ( = 0.5,ζ 0 = 100) [3]. Reproduced from Sheen, J. W. and St ¨ uber, G. (1994) Effects of multipath fading on delay locked loops for spread spectrum systems. IEEE Trans. Commun., 42(2/3/4), 1947 –1956, by permission of IEEE. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10 −1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 10 12 10 13 10 14 Normalized mean time to lose lock Early-late discriminator offset ∆ R = 5 dB R = 10 dB R = 15 dB No multipath g d = −5 dB g d = 0 dB Figure 4.4 Effects of multipath fading on the MTLL performance with various early–late discriminator offsets (τ d = 0.5,ζ 0 = 100) [3]. Reproduced from Sheen, J. W. and St ¨ uber, G. (1994) Effects of multipath fading on delay locked loops for spread spectrum systems. IEEE Trans. Commun., 42(2/3/4), 1947–1956, by permission of IEEE. 84 CODE TRACKING 0.9 R = 5 dB No fading Tracking error (rms) 10 0 10 −1 10 −2 0.1 0.2 0.3 0.4 0.6 0.7 0.8 g d = 0 dB g d = 2.5 dB Early-late discriminator offset ∆ 0.5 Figure 4.5 Effects of multipath fading on the tracking error performance with various delay spacings ( = 0.5,ζ 0 = 100) [3]. Reproduced from Sheen, J. W. and St ¨ uber, G. (1994) Effects of multipath fading on delay locked loops for spread spectrum systems. IEEE Trans. Commun., 42(2/3/4), 1947 –1956, by permission of IEEE. interference for path l is regenerated. In the lower path of the receiver block diagram, these signals are used to generate the clean signal per path r(t− T D ) − v l (t) = w 0 (t), whichisusedinthelth DLL to create a control signal e l (t) for the voltage controlled clock (VCC). All the individual control signals summed up represent the overall control signal for VCC. For the simulation environment defined in Table 4.1, the tracking error performance for standard DLL and DLL with IC DLL/IC is presented in Figure 4.2c. One can see that while the performance of the standard DLL is very poor, the performance of the DIL/IC loop for the appropriate signal-to-noise ratio is good. The problem of multipath IC will be visited again later in the context of multiuser detection in which in addition to the multipath the multiple access interference (MAI) will be also present at the front end of the receiver. 4.1.2 Identification of channel coefficients After code synchronization (acquisition and tracking), signal despreading can be per- formed. If the processing gain is large, T b /T c ≥ 1, after despreading, the received low-pass equivalent discrete time signal is y k = x k c k + n k (4.8) CODE-TRACKING LOOPS 85 Table 4.1 Simulation parameters • PN Code: m-sequence with the generating polynomial 1 + x + x 6 • Data modulation: binary phase shift keying (BPSK) with R b = 10 kb s −1 • Chip rate: 630 Kb s −1 • Sampling rate: 8 samples per chip period • Total simulation time: 70 000 T b •  = 1/2 • Fading channel: Jake’s model (independent paths with Rayleigh fading) with maximum Doppler shift of 83 Hz • Low-pass filters: Elliptic filters (eighth order) with 3-dB bandwidths of 3 R b and R b for h 1 (t) and h 2 (t), respectively • In the simulations, the tracking range is limited to [−T c ,T c ], that is, whenever |ε| > 1. A reacquisition process will be initiated. The initial tracking error is assumed to be ε = 0.2. Only the first-order loop [F(s)= 1] with  = 1/2 is to be considered for simplicity •  k = E|g k | 2 /E|g 0 | 2 ,ζ 0 = B L 0 /R b is the normalized average loop bandwidth • Received average SNR. γ b = PT b E|g 0 | 2   1 +  L k=1  k  /N 0 . where c k is the channel coefficient. At this stage we will assume that the residual fading is frequency nonselective because all multipath components are resolved in the despreading process in each finger of the RAKE receiver. If x k is a known training symbol and if the SNR is high, a good estimate of c k can be easily computed from equation (4.8) as c k ≈ y k /x k  =˜c k (4.9) where y k is the received signal. However, most of the received symbols are not training symbols. In these cases, the available information for estimating c k can be based upon prediction from the past detected data bearing symbols x i (i < k). This scheme will be referred to as decision feedback adaptive linear predictor (DFALP). Using a standard linear prediction approach we formulate the predicted fading channel coefficient at time k as ˆc k = N  i=1 b ∗ i ˜c k−i  = b(k) H ˜c(k) (4.10) where ˜c(k) = (˜c k−1 , ˜c k−2 , .,˜c k−N ) T (4.11) is a vector of past corrected channel coefficient estimates and b(k) = (b 1 ,b 2 , .,b N ) T (4.12) are the filter (linear predictor) coefficients at time k. The superscript T stands for transpose and H stands for Hermitian transpose. The constant N is the order of the linear predictor. The block diagram of the receiver is shown in Figure 4.6. 86 CODE TRACKING Delay D f T Soft viteberbi decoder Tentative decision Adaptive linear predictor or y k / x k LPF Delay T ˆ y k / x k ˆ y k / x k ˆ Figure 4.6 The DFALP algorithm for tracking phase and amplitude of frequency nonselective fading channels [4]. Reproduced from Liu, Y. and Blostein, S. (1995) Identification of frequency nonselective fading channels using decision feedback and adaptive linear prediction. IEEE Trans. Commun., 43(2), 1484–1492, by permission of IEEE. 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 10 20 30 40 50 60 Normalized fading bandwidth f m T Predictor order N and number of LPF taps 2 D f + 1 Predictor order N and Number of LPF taps 2 D f + 1 Figure 4.7 Recommended linear predictor order N and the number of LPF taps for the DFALP algorithm [4]. Reproduced from Liu, Y. and Blostein, S. (1995) Identification of frequency nonselective fading channels using decision feedback and adaptive linear prediction. IEEE Trans. Commun., 43(2), 1484–1492, by permission of IEEE. The updating process for the filter coefficients is defined as b(k + 1) = b(k) + µ(˜c k −ˆc k ) ∗ ˜c(k) (4.13) Simulation results for predictor order N and the number of taps 2D f + 1 of the low-pass filter for the minimum bit error rate (BER) are shown in Figure 4.7. CODE TRACKING IN FADING CHANNELS 87 4.2 CODE TRACKING IN FADING CHANNELS The previously presented material on code tracking was based on the assumption that except for the additive white Gaussian noise the channel itself does not introduce any additional signal degradation or that only a flat frequency nonselective fading per path was present. For some applications like land and satellite mobile communications, we have to take into account the presence of severe fading due to channel dynamics. In this section we will present one possible approach to code tracking in such an environment. 4.2.1 Channel model A channel with multipath propagation can be represented by a time-varying tapped-delay line, with impulse repose given by h(τ, t) = N β −1  l=0 β l (t)δ(τ − lT s )(4.14) where T s is the Nyquist sampling interval for the transmitted signal, N β is the number of received signal replicas through different propagation paths and β l (t) represents the complex-valued time-varying channel coefficients. So, for the transmitted signal s(t) the received signal r(k) sampled at t = kT s , will consist of N β mutually delayed replicas that can be represented as r(k)= N β −1  l=0 β  (k)s[(k − l)T s + τ(k)] + n(k) (4.15) In this equation, n(k) are samples of the noise with E{n(k − i)n ∗ (k − j)}=σ 2 n δ i,j (4.16) In the RAKE receiver, each signal component is despread separately and then combined into a new decision variable for final decision. For the combining that provides maximum signal-to-noise ratio, signal components are weighted with factors β l . So the synchroniza- tion for the RAKE receiver should provide a good estimate of delay τ and all channel intensity coefficients β l l = 0, 1, .,N β − 1. The operation of the RAKE receiver will be elaborated later and within this section we will concentrate on the joint channel (β l )and code delay (τ ) estimation using the extended Kalman filter (EKF) [5,6]. For these purposes, the channel coefficients and delay are assumed to obey the follow- ing dynamic model equations. β  (k + 1) = α  β  (k) + w l (k); l = 0, 1, .,N β − 1 τ(k+ 1) = ζτ(k)+ w τ (k) (4.17) 88 CODE TRACKING where w l (k) and w τ (k) are mutually independent circular white Gaussian processes with variances σ 2 wl and σ 2 τ , respectively. In statistics, these processes are called autoregressive (AR) processes of order k,wherek shows how many previous samples with indices (k, k − 1,k− 2, .,k− K + 1) are included in modeling a sample with index k + 1. In equation (4.17), the first-order AR model is used. The more the disturbances in signal are expected due to Doppler, the higher the variance of w l and the lower α l should be used. Var i an c e o f w τ will not only depend on Doppler but also on the oscillator stability. A comprehensive discussion of AR modeling of wideband indoor radio propagation can be found in Reference [7]. 4.2.2 Joint estimation of PN code delay and multipath using the EKF From the available signal samples r(k) given by equation (4.15) we are supposed to find the minimum variance estimates of β l and τ These will be denoted by ˆ β l (k|k) = E{β l (k)|r(k)} ˆτ(k|k) = E{τ(k)|r(k)} (4.18) where r (k) is a vector of signal samples r(k) ={r(k),r(k− 1), .,r(0)} (4.19) From equation (4.15) one can see that r(k) is linear in the channel coefficients β l (k), but it is nonlinear in the delay variable τ(k). A practical approximation to the minimum variance estimator in this case is the EKF. This filter utilizes a first-order Taylor’s series expansion of the observation sequence about the predicted value of the state vector, and will approach the true minimum variance estimate only if the linearization error is small. The basic theory of extended Kalman filtering is available in textbooks [6]. Having in mind that in the delay-tracking problem, the state model is linear, while the measurement model is nonlinear, we have x(k + 1) = Fx(k) + Gw (k) z(k) = H(x (k)) + n(k) (4.20) In this equation, x(k) represents the N β + 1 dimensional state vector and z(k) is the scalar measurement r(k) In terms of the previous notation we have x(k) = [τ(k),β 0 (k), β 1 (k), .,β N β −1 (k)] T F =        ζ 0 ··· 0 0 α 0 . 0 00α 1 ··· 0 . . . . . . . . . . . . . . . 00··· α N β −1        (4.21) [...]... S y k / dk _ (l ) Ck Linear predictor (kalman filter) ^ (l )* Ck +1 ^ dk Control S ( ) (b) Figure 4.15 Receiver block diagram: (a) generic block diagram of Rake receiver and (b) The decision feedback adaptive linear predictor (ALP) algorithm for tracking a complex multipath coefficient in one RAKE finger TURBO PROCESSOR AIDED RAKE RECEIVER SYNCHRONIZATION FOR UMTS W-CDMA 105 will be despread in L RAKE . error variance can be expressed as [1] τ 2 δ 1 2ρ L  1 + 2 ρ if  (4.5) Adaptive WCDMA: Theory And Practice. Savo G. Glisic Copyright ¶ 2003 John Wiley. symbols x i (i < k). This scheme will be referred to as decision feedback adaptive linear predictor (DFALP). Using a standard linear prediction approach