Tài liệu Adaptive WCDMA (P15) doc

15 Wideband CDMA network sensitivity 15.1 THEORY AND PRACTICE OF MULTIUSER DETECTION Advanced wireless Code Division Multiple Access (CDMA) systems employing multiuser receivers described in Chapters 13 and 14 have gained a lot of attention during the recent years. In the beginning, the research was purely academic. In order to fully exploit CDMA capabilities, the third-generation wideband CDMA networks [1] have been planned to include interference cancellation (IC), as soon as it becomes feasible to implement (for details, see also Chapter 17). A number of overview papers [2–6] discuss basic features of multiuser detection (MUD) and IC techniques. Among linear IC schemes, decorrelat- ing detectors [7–9] belong to a major group of multiuser receivers. As it was discussed in Chapter 13, the basic idea of the decorrelator is to use the inverted cross-correlation matrix to subtract interference caused by other active users, that is, multiple access inter- ference (MAI). With perfect knowledge of code cross-correlations (of all active users), the effect of all MAI can be eliminated at the cost of noise enhancement. One important benefit of the ideal decorrelator is that it does not require knowledge of the users’ power levels (or amplitudes) and is thus robust to power fluctuations. On the other hand, the complexity and need for updating the matrix inversion can become a bottleneck at high user populations and fast fading environment. Also, in reality, the cross-correlation matrix must be estimated and that will lead to further imperfections. These imperfections are the focus of this chapter. Although other options, such as multistage or linear minimum mean square error (LMMSE) detectors discussed in Chapter 14, are also considered for these applications [4], in this chapter we will focus our attention on linear decorrelators and their operation in the presence of imperfections. In practice, performance of these detectors depends critically on the channel parameter estimation and errors that they produce. For these reasons, parameter estimation in multiuser communications has become an important research topic aiming to find feasible solutions for practical MUD applications. The Adaptive WCDMA: Theory And Practice. Savo G. Glisic Copyright ¶ 2003 John Wiley & Sons, Ltd. ISBN: 0-470-84825-1 520 WIDEBAND CDMA NETWORK SENSITIVITY performance of linear decorrelating detectors in the presence of time delay, carrier phase and carrier frequency errors is analyzed in Reference [10]. Methods for low-complexity amplitude and phase estimation with known or unknown delays are analyzed in Ref- erence [11]. Joint signal detection and parameter estimation (amplitudes and phases) is evaluated in Reference [12]. Adaptive symbol and parameter estimation algorithms based on recursive least squares (RLS) and extended Kalman filters (EKF) have been studied in Reference [13]. Sensitivity of multiple-access channels to several mismatches due to imperfect carrier recovery, timing jitter and channel truncation is analyzed in Reference [14]. The impact of timing (delay) errors to the performance of linear MUD receivers is illustrated in References [15,16]. The same authors have also considered the estimation problem in general in Reference [17]. Sensitivity analysis of near–far resis- tant DS-CDMA receivers to propagation delay estimation errors [18] shows that even quite small errors will destroy the near–far resistance of the decorrelating detector. Joint amplitude and delay estimation is evaluated in Reference [19] by using the EKF and the same authors study quasi-synchronous CDMA systems applying linear decorrelators in Reference [20]. The above references study mainly the link performance with quite limited code lengths and number of users. This is necessary in order to get analytically tractable performance results or to keep complexity of simulations at reasonable levels. For capacity evaluation, however, somewhat releasing assumptions and approximations are usually needed to get results for higher user populations and longer spreading codes. Capacity of the linear decorrelating detector for quasi-synchronous CDMA is evaluated in Reference [21]. Fur- thermore, comparison against an adaptive receiver employing the minimum mean square error (MMSE) criterion is presented. Outage probability bounds when using a zero forcing detector are presented in Reference [22]. Capacity gains over conventional matched fil- ter–based systems were shown to be significant. A linear interference canceller is applied to microcellular CDMA in Reference [23] in which uplink capacities are estimated for different propagation scenarios. Besides the multiuser detectors, an advanced CDMA receiver will be using also a RAKE receiver with multipath combining. Linear multipath-decorrelating receivers in frequency-selective fading channels, discussed in Chapter 13, have been compared to the conventional RAKE receiver in Reference [24]. The conclusion was that decorrelators can avoid error floors demonstrated by plain RAKE receivers. These components will be also imperfect. Performance of RAKE combining techniques (selection, equal gain and maximal ratio diversity) in the presence of chip and phase synchronization errors is reported in Reference [25]. As expected, the maximal ratio combiner (MRC) outperforms other combiners and quite drastic capacity losses are seen because of synchronization errors and fading. Diversity methods in Rayleigh fading have also been evaluated and compared in References [26,27]. Capacity evaluation of CDMA networks [28] and comparison of CDMA and time divi- sion multiple access (TDMA) systems have been an important and controversial issue. One of the reasons for such a situation is the lack of a systematic, easy to follow math- ematical framework for this evaluation. The situation is complicated by the fact that a lot of parameters are involved and some of the system components are rather complex resulting in imperfect operation. The analysis of an advanced CDMA network should in SYSTEM MODEL 521 general take all these elements into account including their imperfections and come up with an expression for the system capacity in the form that can be used in practice. In Reference [29] a systematic analytical framework for the capacity evaluation of wideband CDMA networks with nonlinear IC was presented. In this chapter we extend the model to networks employing linear decorrelating detec- tors. This approach should provide a relatively simple way to specify the required quality of MAI canceller (decorrelator) and RAKE receiver in a CDMA system, taking into account all their imperfections. A flexible, complex signal format is used that enables us to model all currently interest- ing wideband CDMA standards. For such a signal we first derive a complex decorrelator structure. This is the first time that a complete decorrelator is described for the CDMA signal with two independent data and two independent code streams. This type of the signal is used in all CDMA standards. In the next step all imperfections in the operation of such a system are modeled and analyzed by using the concept of a network sensitivity function. This provides the necessary information to the designer on how much of the theoretically promised ideal performance will be preserved in a real implementation. The theory is general and some examples of practical sets of channel and system parameters are used as illustration. 15.2 SYSTEM MODEL In order to be able to discuss implementation problems in the existing standards, the complex envelope of the signal transmitted by user k ∈{1, 2, ,K} in the nth symbol interval t ∈ [nT , (n + 1)T ] will be written as s k = A k e j φ k0 S (n) k (t − τ k )(15.1) where A k is the transmitted signal amplitude of user k, τ k is the signal delay, φ k0 is the transmitted signal carrier phase and T is the symbol interval. S (n) k (t) can be repre- sented by S (n) k (t) = S (n) k = S k = S ik + jS qk = d ik c ik + jd qk c qk (15.2) In this equation, b ik and b qk are two information bits in the I and Q channels, respectively, generated with bit interval T . c ik and c qk are the kth user pseudo-noise codes in the I and Q channels, respectively, generated with chip interval T c and having a period T /T c . Equations (15.1) and (15.2) are general and different combinations of the signal parame- ters cover most of the signal formats of practical interest. For example, in WCDMA/FDD mode the uplink signal format can be expressed as (c d d d + jc c d c )c s c sl (15.3) where c d and c c are data and control channel codes, d d and d c are data and control channel information bits and c s and c sl are scrambling and scrambling long (optional) 522 WIDEBAND CDMA NETWORK SENSITIVITY codes for user k. Equation (15.3) can be written in the form of equation (15.2) with the following mapping: c ik = c d c s c sl c qk = c c c s c sl d ik = d d d qk = d c (15.4) Equation (15.3) may be further modified to include complex scrambling codes. The model of channel impulse response consists of discrete multipath components represented as h (n) k (t) = L  l=1 h (n) kl δ(t − τ (n) kl ) = L  l=1 H (n) kl e j φ kl δ(t − τ (n) kl ) (15.5) h (n) kl = H (n) kl e j φ kl (15.6) where L is the number of multipath components of the channel, h (n) kl and τ (n) kl ∈ [0,T m ) are the complex coefficient (gain) and delay, respectively, of the lth path of user k at symbol interval with index n and δ(t) is the Dirac delta function. We assume that T m is the delay spread of the channel. In what follows, indices n will be dropped whenever this does not produce any ambiguity. It is also assumed that T m <T and an indication for the necessary modifications in the case when T m >T is provided whenever appropriate. The overall received signal during N b symbol intervals can be represented as r(t) = Re  e j ω 0 t N b −1  n=0  k  l a kl S (n) k (t − nT − τ k − τ kl )  + Re{z(t)e j ω 0 t} (15.7) where a kl = A k H (n) kl e j kl = A kl e j kl , A k H (n) kl = A kl ,  kl = φ 0 + φ k0 − φ kl , φ 0 is the fre- quency downconversion phase error, z(t) is a complex zero mean additive white Gaussian noise (AWGN) process with two-sided power spectral density σ 2 and ω 0 is the carrier angular frequency. In what follows, we will drop the noise term for simplicity reason and focus only on proper representation of the MAI. For a correct representation of the overall signal, the noise term will be reintroduced again in equation (15.35). In order to be able to model system imperfections, both I and Q signal components should be represented separately as an explicit function of all parameters that are estimated in the receiver and because these estimates are imperfect they may include some errors. The complex matched filter of user k will create two correlation functions for each path and by omitting the noise terms these signals can be represented as y (n) ikl =  (n+1)T +τ k +τ kl nT +τ k +τ kl r(t)c ik (t −nT − τ k + τ kl ) cos(ω 0 t + ˜  kl ) dt =  k   l  y ikl (k  l  ) (15.8) SYSTEM MODEL 523 where ˜  kl is the estimate of  kl and y ikl (k  l  ) = y iikl (k  l  ) + y iqkl (k  l  ) = A k  l  [d ik  ρ ik  l  ,ikl cos ε k  l  ,kl + d qk  ρ qk  l  ,ikl sin ε k  l  ,kl ] (15.9) and y (n) qkl =  (n+1)T +τ k +τ kl nT +τ k +τ kl r(t)c qk (t − nT − τ k + τ kl ) sin(ω 0 t + ˜  kl ) dt =  k   l  y qkl (k  l  ) (15.10) y qkl (k  l  ) = y qqkl (k  l  ) + y qikl (k  l  ) = A k  l  [d qk  ρ qk  l  ,qkl cos ε k  l  ,kl − d ik  ρ ik  l  ,qkl sin ε k  l  ,kl ] (15.11) with ρ x,y being the cross-correlation functions between the corresponding code compo- nents x and y. A scaling factor 1/2 is dropped in the above equations for simplicity. Basically by dropping this coefficient for both signal and noise, the signal-to-noise ratio (SNR) that determines the system performance will not change. Each of these components is defined with three indices (i or q, user and path). Parameter ε a,b =  a − ˜  b where a and b are defined with two indices (user and path). Let the L-element vectors  L (·) of matched filter output samples for the nth symbol interval be defined as y (n) ik = L (y (n) ikl ) = (y (n) ik1 ,y (n) ik2 , ,y (n) ikL ) T ∈ C L (15.12) y (n) qk = L (y (n) qkl ) = (y (n) qk1 ,y (n) qk2 , ,y (n) qkL ) T ∈ C L (15.13) y (n) k = y (n) ik + jy (n) qk (15.14) y (n) = K (y T(n) k ) ∈ C KL (15.15) y = N b (y T(n) ) ∈ C N b KL (15.16) Let in general R (n) (i) ∈ (−1, 1] KL×KL be a cross-correlation matrix with the follow- ing partition: R (n) (i) =        R (n) 1,1 (i) R (n) 1,2 (i) ··· R (n) 1,K (i) R (n) 2,1 (i) R (n) 2,2 (i) ··· R (n) 2,K (i) . . . . . . . . . . . . R (n) K,1 (i) R (n) K,2 (i) ··· R (n) K,K (i)        ∈ R KL×KL = K (R (n) k,k  (i)) (15.17) 524 WIDEBAND CDMA NETWORK SENSITIVITY For the final representation of the complex matched filter output signal, given by equations (15.49) and (15.50), we now define four specific matrices of the form given by equation (15.17) with the following notation: R ii(n) (i) = K (R ii(n) k,k  (i)) (15.18) R qi(n) (i) = K (R qi(n) k,k  (i)) (15.19) R iq(n) (i) = K (R iq(n) k,k  (i)) (15.20) R qq(n) (i) = K (R qq(n) k,k  (i)) (15.21) where matrices R ab(n) k,k  (i) ∈ R L×L , ∀k, k  ∈{1, 2, ,K} in equations (15.18) to (15.21) have elements (R ii(n) k,k  (i)) l,l  = cos ε k  l  ,kl ×  ∞ −∞ c (n) ik (t − τ k − τ kl )c (n−i) ik  (t + iT − τ k  − τ k  l  ) dt (15.22) (R qi(n) k,k  (i)) l,l  = sin ε k  l  ,kl ×  ∞ −∞ c (n) qk (t −τ k − τ k,l )c (n−i) ik  (t +iT − τ k  − τ k  l  ) dt (15.23) (R iq(n) k,k  (i)) l,l  =−sin ε k  l  ,kl ×  ∞ −∞ c (n) ik (t −τ k − τ k,l )c (n−i) qk  (t +iT − τ k  − τ k  l  ) dt (15.24) (R qq(n) k,k  (i)) l,l  = cos ε k  l  ,kl ×  ∞ −∞ c (n) qk (t − τ k − τ k,l )c (n−i) qk  (t + iT − τ k  − τ k  l  ) dt ∀l, l  ∈{1, 2, ,L} (15.25) In order to simplify the notation, we present equation (15.22) as R = ρ cos ε and its estimation as ˆ R =ˆρ cos ˆε(15.26) In general, the estimated phase difference ˆε between the two users (e.g. users with index k = 1andk = 2) can be represented as ˆε = φ 1 − φ 1 − φ 2 − φ 2 = ε + ε (15.27) where ε = φ 1 − φ 2 and ε =−(φ 1 + φ 2 ). The noise samples at the output matched filters for different users are uncorrelated. So, if φ is a process with zero mean and variance σ 2 φ ,thenε is a zero mean process with variance 2σ 2 φ . The estimated correlation function can be represented as ˆρ = ρ + ρ ∼ = ρ +ρ  ε τ = ρ  1 + ρ  ε τ ρ  = ρ(1 + s ρ )(15.28) SYSTEM MODEL 525 where ρ  is the slope of the ρ function at the point of zero delay estimation error and ε τ = τ 1 − τ 2 (15.29) is the difference between the two delay estimation errors. For a given class and code length, ρ  is a parameter [30]. If τ is a zero mean variable with variance σ 2 τ ,thenε τ is a zero mean variable with variance 2σ 2 τ . The second component of equation (15.26) can be represented as cos ˆε = cos(ε +ε) = cos ε cos ε − sin ε sin ε = (1 −ε 2 /2) cos ε − ε sin ε = (1 +s ε ) cos ε (15.30) where s ε =−(ε 2 /2 + ε · tan ε) (15.31) Now, equation (15.26) becomes ˆ R = R +R (15.32) where R = ρ cos ε R = ρ cos ε(s ε + s ρ + s ε s ρ ) (15.33) Whenever k  = k, the average value of the cross-correlation ρ = 0 and parameter R can be considered as an additional noise component with a zero mean and variance σ 2 R = ρ 2 [(1 + 2σ 2 ρ  σ 2 τ /ρ 2 )(3σ 4 φ + 2σ 2 φ ) + 2σ 2 ρ  σ 2 τ /ρ 2 ] (15.34) Similar expressions can be derived for the estimation of equations (15.23) to (15.25). In the case when multipath delay spread produces severe intersymbol interference (ISI), the overall received signal should be further modified. When the delay spread is limited to less than one symbol interval, then for an asynchronous network the vector equation (15.15) can be expressed as [4] y (n) (R, H, A, d) = R (n) (2)H (n−2) Ad (n−2) + R (n) (1)H (n−1) Ad (n−1) + R (n) (0)H (n) Ad (n) + R (n) (−1)H (n+1) Ad (n+1) + R (n) (−2)H (n+2) Ad (n+2) + n (n) (15.35) where A = diag(A 1 ,A 2 , ,A K ) ∈ R K×K (15.36) 526 WIDEBAND CDMA NETWORK SENSITIVITY is a diagonal matrix of transmitted amplitudes, H (n) = diag(H (n) 1 , H (n) 2 , ,H (n) K ) ∈ C KL×K (15.37) is the matrix of channel coefficient vectors H (n) k = (H (n) k,1 ,H (n) k,2 , ,H (n) k,L ) T ∈ C L (15.38) d (n) = (d (n) 1 ,d (n) 2 , ,d (n) K ) T ∈  K (15.39) is the vector of the transmitted data and n (n) ∈ C KL is the output vector due to noise. This component is due to processing the second term of equation (15.7) that was dropped for simplicity in derivation of equations (15.8) to (15.34). It is easy to show that R (n) (i) = 0 KL , ∀|i| > 2andR (n) (−i) = R T(n+1) (i),where0 KL is an all-zero matrix of size KL × KL. Thus, the concatenation vector of the matched filter outputs (15.16) has the expression y(R, H,A, d ) = RHAd + n = RHh + n(15.40) where R =         R (0) (0) R T(1) (1) R T(2) (2) ··· 0 KL R (1) (1) R (1) (0) R T(2) (1) ··· 0 KL R (2) (2) R (2) (1) R (2) (0) ··· 0 KL . . . . . . . . . . . . . . . 0 KL 0 KL 0 KL ··· R (N b −1) (0)         ∈ R N b KL×N b KL (15.41) H = diag(H (0) , H (1) , ,H (N b −1) ) ∈ C N b KL×N b K (15.42) A = diag(A, A, ,A) ∈ R N st K×N b K (15.43) d = (d T(0) , d T(1) , ,d T(N b −1) ) T ∈  N b K (15.44) h = Ad is the data-amplitude product vector and n is the Gaussian noise output vector with zero mean and covariance matrix σ 2 R.Ifwedefine y ii = y(R ii ,H,A,d i ) (15.45) y qi = y(R qi ,H,A,d q ) (15.46) y iq = y(R iq ,H,A,d i ) (15.47) y qq = y(R qq ,H,A,d q ) (15.48) then we have y i = y ii + y qi (15.49) y q = y iq + y qq (15.50) CAPACITY LOSSES 527 On the basis of these equations in the sequel, a complex decorrelator receiver structure is derived. 15.2.1 Complex decorrelator As a starting point, we represent equations (15.49) and (15.50) as y i = y ii + y qi = ii d i + qi d q + n i (15.51) y q = y iq + y qq = iq d i + qq d q + n q (15.52) where =RHA(15.53) and we use an additional step to produce  ii−1 y i = d i + ii−1  qi d q + ii−1 n i  iq−1 y q = d i + iq−1  qq d q + iq−1 n q  qi−1 y i = qi−1  ii d i + d q + qi−1 n i  qq−1 y q = qq−1  iq d i + d q + qq−1 n q (15.54) From the last set of equations one can show that the data estimates should be obtained as ˆ d = ˆ d i + j ˆ d q ˆ d q = sgn{D qi y i + D qq y q } D qi ={ qi−1  ii − qq−1  iq } −1  qi−1 D qq =−{ qi−1  ii − qq−1  iq } −1  qq−1 (15.55) and similarly ˆ d i = sgn{D ii y i + D iq y q } D ii ={ ii−1  qi − iq−1  qq } −1  ii−1 D ii ={ ii−1  qi − iq−1  qq } −1  ii−1 (15.56) Bearing in mind that all current wideband code division multiple access (WCDMA) standards are based on using complex signal formats, future research in the field of multiuser detectors should be focused on the structures defined above. 15.3 CAPACITY LOSSES The starting point in the evaluation of CDMA system capacity is parameter Y bm = E bm /N 0 , the received signal energy per symbol per overall noise density in a given 528 WIDEBAND CDMA NETWORK SENSITIVITY reference receiver with index m. For the purpose of this analysis, we can represent this parameter in the general case as Y bm = E bm N 0 = ST I oc + I oic + I oin + η th (15.57) where I oc ,I oic and I oin are the power densities of intracell, intercell and overlay type inter- network interference, respectively, and η th is the thermal noise power density. Parameter S is the overall received power of the useful signal and T = 1/R b is the information bit interval. Contributions of I oic and I oin to N 0 have been discussed in Chapter 8 and in a number of papers, for example, in Reference [28]. In order to minimize repetition in our analysis, we will parameterize this contribution by introducing η 0 = I oic + I oin + η th (15.58) and concentrate on the analysis of the intracell interference, I oc , in a CDMA network based on advanced receivers using imperfect RAKE, and MAI cancellation based on an imperfect decorrelator. An extension of the analysis to include both intercell and internetwork interference is straightforward. A general block diagram of the receiver is shown in Figure 15.1. If for user m an L 0 -finger RAKE receiver (L 0 ≤ L) with combiner coefficients w mr (r = 1, 2, ,L 0 ) and an imperfect decorrelator is used, the SNR will become Y bm = r (L 0 ) m ς 0 ηR b /S (15.59) where ς 0 = L 0  r=1 w 2 mr = w m w T m ; w m = (w m1 ,w m2 , ,w mL 0 )(15.60) Bank of matched filters Other users Rake receiver of user m Demodulation & decoding Information output Imperfect parameter estimation Complex decorrelator Figure 15.1 General receiver block diagram. [...]... frequency hopping (FH) and direct sequence (DS) configurations Owing to simplicity, DS configuration has been accepted for civil applications in mobile communication systems (e.g Standards ANSI-95, IS-665, WCDMA UMTS) For large bit rates, DS system will have low processing gain and performance of a RAKE receiver will be considerably degraded In the presence of near–far effect (imperfect power control or . topic aiming to find feasible solutions for practical MUD applications. The Adaptive WCDMA: Theory And Practice. Savo G. Glisic Copyright ¶ 2003 John Wiley. parameter estimation (amplitudes and phases) is evaluated in Reference [12]. Adaptive symbol and parameter estimation algorithms based on recursive least