Downlink Beamforming Method for Multimedia CDMA/TDD Systems

Transcription

1 Downlin Beamforming Method for Multimedia CDMA/TDD Systems Yoshitaa HARA Du-Kyu Par Yuiyoshi Kamio YRP Mobile Telecommunications Key Technology Research Laboratories Co., Ltd. 3-4 Hiari-no-oa, Yoosua , JAPAN. Phone: Fax: ABSTRACT This paper proposes a downlin beamforming method for multimedia CDMA / TDD systems. The proposed method determines the transmission weights so that the total transmitted power is minimized under a power-controlled CDMA system. In the decision process of downlin beamforming, each user s target signal-to-interference-plusnoise ratio(sinr) and the number of RAKE fingers are considered. Numerical results show that the proposed method has low complexity and good performance under multimedia CDMA systems.. INTRODUCTION CDMA has been standardized for the third generation cellular system and the application of antenna arrays is now under consideration for an improved CDMA system[] [9]. Using antenna arrays in base station(bs), we can reduce co-channel interference and improve system performance. There have been many investigations on beamforming methods for both uplin and downlin[] [9]. For uplin, we proposed an efficient sample matrix inversion(smi)- type algorithm with common correlation matrix(ccm- SMI), which achieves both low computational complexity and fast weight convergence[]. For downlin, an efficient beamforming method is also important for future multimedia communications, where users will have variable transmission rates and different target signal-tointerference-plus-noise ratio(sinr). The traffic characteristics are asymmetrical between uplin and downlin. So far, Liang[2] has proposed an adaptive downlin beamforming for multimedia CDMA systems, where virtual uplin concept is introduced to multimedia CDMA downlin. Since Liang s basic algorithm has large computational complexity, a simplified algorithm is also presented using equivalent one-path channel vector(eocv). However, the performance of the simplified algorithm degrades as angle spread of arrival paths becomes wider. In this paper, we propose a downlin beamforming method for multimedia CDMA/TDD systems, that has lower complexity and better performance than Liang s simplified algorithm. The beamforming is determined so that the total transmitted power is minimized under powercontrolled CDMA systems, considering each user s target SINR and the number of RAKE fingers. System-level simulation is employed to compare performance between our proposed method and Liang s simplified method. In section 2, CDMA downlin model is presented. In section 3, characterization of power control is described. In sections 4 and 5, we propose downlin beamforming method. In section 6, the system performance is evaluated. Section 7 is the conclusion. 2. CDMA DOWNLINK MODEL 2. Base Station Figure shows the configuration of BS transmit antenna arrays on CDMA downlin. We assume that the BS transmits signals s (t) c (t)d (t) for K different users simultaneously, where c (t) and d (t) (E[jc (t)j 2 ] E[jd (t)j 2 ]) are the -th user s spreading sequence with chip duration T c and the -th user s data with symbol duration T d, respectively. The BS controls the -th user s signal power P and weight w [w ;:::; w M ] T to achieve large capacity in CDMA downlin. The total transmitted signal is written as K p s(t) P c (t)d (t)w Λ : () 2.2 Signal The spreading sequence of each terminal is composed of orthogonal Walsh codes c W (t) and common long code c L (t) such as c (t) c W (t)c L (t)[3]. Denoting the processing gain as G T d T c, orthogonal Walsh codes and common long code have the following characteristics: G ρ 2 G p c W (pt c )c W2 (pt c ) E[c L (pt c ) Λ c L ((p + p)t c )] 6 2 ρ p otherwise : 2.3 Channel Model The impulse response of time-variant fading channel between the BS and the -th user can be modeled as h (t) L l a l ffi(t (l )T c ) (2)

2 2 M w w * w 2 w M w w 2 * * Copier Transmit BF(User) Transmit BF(User2) Transmit BF(UserK) w K Power & Weight Controller P K P 2 P Signal S (t) Signal2 S 2 (t) SignalK S K (t) Figure : Base station transmit antenna arrays. where a l [a l ;:::; a lm ] T is the propagation vector of the l-th path for the -th user and a lm is the amplitude of the l-th path in the m-th antenna. 2.4 RAKE Receiver The -th user uses a R -finger RAKE receiver in which the r-th finger despreads the l-th path(l r). The outputs of different fingers are combined using RAKE combining weight w ;RK [w ; ;:::; w ;R ] T. 2.5 Target SINR and Power Control Variable bit rate multimedia services such as voice, data, and video, are considered. Depending on their traffic characteristics, each user of such services has a broad range of target SINRs. To achieve the performance requirements, closed-loop power control is used so that the received SINR of the -th user corresponds to the target SINR fl. 2.6 Downlin Beamforming Criterion The downlin beamforming is performed user by user to minimize the total transmitted power of the BS under a power-controlled CDMA system. The minimum total transmitted power(mttp) type demands can be put mathematically as [][2] J K jjw jj 2 P! min (3) with constraint fl : In the remaining of the paper, we present a downlin beamforming method that satisfies the MTTP-type demands. 3. CHARACTERIZATION OF POWER CONTROL 3. SINR Characteristics An exact expression for output SINR of the -th user s RAKE receiver is given by (appendix A.) A ;d 8 < : K i d6 GP jg y (Ay ; w ) Λ j 2 P i jg y (Ay ;d w i) Λ j 2 + N jg j 2 (4) [a ; d :::a ;L O (M (R L d)) ] L» d<r L [a ; d :::a ;R d ] R L» d» [O (M d) a ; :::a ;R d ] <d» R (5) where N represents the outer-cell-interference-plusnoise power before despreading, A ;d is a M R matrix, O (p q) is a p q zero matrix, and y denotes the complex conjugate transpose. We consider a case of RAKE combining weight g proportional to desired signal level, such that g [w y a ;;:::; w y a ;R] T (A y w ; ) Λ : (6) Then, can be rewritten in the following form: ' K i d6 K i GP ja y ; w j 2 P i R jay ;d w ij 2 + N GP w y Ψw Ψ A ; A y R ; Ψ R L l (7) P i w y iψ w i + N (8) d6 l A ;d A y ;d a ;l a y ;l (9) a ;l a y ;l Ψ () R In deriving (7), we use the relation of (appendix B.) j(a y ; w ) y (A y ;d w i)j 2 ' R jay ; w j 2 ja y ;d w ij 2 : () 3.2 Power Control Closed-loop power control is used so that the received SINR corresponds to the target SINR. We consider iterative power control schemes where the transmitted power is updated by P (n+) (fl (n) ) P (n) fl ψ K i P (n) i w y iψ w i + N! Gw y Ψ w ; (2)

3 where P (n) is the transmitted power for the -th user at the n-th step and (n) denotes the received SINR measured by the -th user at the n-th step. Using (2), the transmitted power for all users can be expressed as P (n+) DF T P (n) + DN (3) P (n) [P (n) ; :::; P (n) K ]T D diag " fl N [N ;:::;N K ] T [F ] ;i w y Ψ i w Gw y ; :::; Ψw # fl K Gw y KΨKw K In a perfect power-controlled system, the iteration converges to P lim n! P (n) [I DF T ] DN: (4) Therefore, the total transmitted power J W T P can be expressed as J W T [I DF T ] DN W T D T [I F T D] N Q T N (5) Q [I DF] DW W [jjw jj 2 ;:::; jjw M jj 2 ] T : The total transmitted power J can be represented by the weighted sum of the elements in Q. The elements in Q depend on w, while N is independent of w. In the next section, we describe the weight decision algorithm to minimize the total transmitted power J. 4. DOWNLINK BEAMFORMING METHOD 4. Weight Decision Algorithm In the downlin beamforming based on MTTP type demands, the weight w is determined so that the total transmitted power J is minimized. Since Q can be elementwise minimal[][2] and N is independent of w, the minimization of J can be achieved by optimal weight w which minimizes the elements in Q. We can obtain optimal weights w in the following weight decision algorithm [Weight Decision Algorithm A]. Estimate Ψ and Ψ based on received signal in uplin. Set initial vector Q () [Q () ;:::;Q() K ]T. 2. Update weight( ;:::;K) w (n) arg maxf (w) (6) f (w) Q(n) Φ (n) w w y Φ (n) w K i wy Ψ Q (n) i Ψ i + I: (7) 3. Update Q (n) ( ;:::; K) Q (n+) D (n) F (n) Q (n) + D (n) W (n) (8) D (n) diag " fl Gw (n)y Ψ w (n) ; :::; Ψ i w (n) Gw (n)y K fl K Ψ Kw (n) K [F (n) ] ;i w (n)y W (n) [jjw (n) jj2 ;:::; jjw (n) M jj2 ] T Procedures 2. and 3. are iteratively carried out n w times until w are converged. Using the converged weights w ( ;:::;K), we can perform downlin beamforming to satisfy the MTTP-type demands. 4.2 Weight in Procedure 2. The weight to maximize f(w ) is given by the generalized eigenvector e with largest eigenvalue in Ψe Φe [5][]. 4.3 Feature of Algorithm A Algorithm A considers all arrival paths and the effect of RAKE receiver. The algorithm reduces the total transmitted power of the BS and increases supportable users within a maximum tolerable transmitted power. Algorithm A has a single iterative algorithm, while Liang s basic algorithm needs double iterative algorithms. 5. Simplified Downlin Beamforming 5. Weight Decision Algorithm Let us present a simplified beamforming with modification of procedure 2. in the following form. [Weight Decision Algorithm B]. Same with algorithm A 2. Update weight( ;:::;K) w (n) arg max Q(n) wy a ;max a y ;max w w y Φ (n) w Φ (n) a ;max (9) 3. Same with algorithm A Here, a ;max is the response vector for the -th user spath with largest power. Algorithm B performs beamforming for an arrival path with largest power. 5.2 Feature of Algorithm B Algorithm B computes all users weights w (n) using a common matrix inversion Φ (n). Considering that algorithm A and Liang s simplified method need individual matrix inversion for different users weights, algorithm B has lower computational complexity than algorithm A and Liang s simplified method. Algorithm B #

4 Table : Simulation parameters Spreading code Long random code + Walsh code Processing gain G 64 Number of antennas (BS) M 4 Number of RAKE fingers (MS) R 4 Number of users K 5 6 Number of paths L 4 Channel Path loss Maximum transmission power 4-path Rayleigh channel -3[dB] J max(n G)7dB Outage Probability - -2 n w 2 n w 6 n w 3 n w 2 n w performs downlin beamforming for a path with largest power, while Liang s simplified method performs beamforming for EOCV. The performance among algorithms A, B, and Liang s simplified algorithm is evaluated by computer simulation Number of Users Figure 2: Weight convergence of algorithm A ( :2ß, L 4, R 4). 6. SIMULATION 6. Parameters System-level simulations are performed to evaluate performance of the proposed downlin beamforming. The BS is equipped with halfwavelength-spaced circular four antennas(m 4) and transmits signals for K users(k 5 to 6). The signals are spread by individual Walsh codes and common long code with chip synchronization. The direction of the -th active user is randomly distributed in [; 2ß). Power loss between the BS and each user is set to - 3[dB] and 4-path Rayleigh channel with the same average power for each path is assumed. The arrival angle of the -th user s path is assumed Gaussian random variable with a mean and a standard deviation of. We statistically evaluate the system performance based on 2 times simulation trials, where each trial has independent fading channels. Each user has 4-finger RAKE receiver, and the exact expression for the received SINR is given by (22). Therefore, system-level simulation is established based on (22). For multimedia services, standard data rate with fl 3[dB], middle data rate with fl 6[dB], and high data rate with fl 9[dB] are considered. In each simulation trial, we choose K( 5;:::; 6) users randomly among 8 users with standard data rate, 4 users with middle data rate, and 4 users with high data rate. For closed-loop power control, each user transmits the ratio of the received SINR to the target SINR, ff fl, to the BS on uplin. The BS changes the transmitted power for the -th user by ff. We assume that all the beamforming and power control procedures are perfectly performed within the coherence time of fading channels. In the simulation, downlin beamforming is performed firstly and power control is carried out afterward. The total transmitted power is variable due to fading and number of users. The maximum transmitted power J max of the BS is J max P N 7[dB], and an outage occurs in case of JP N > 7[dB], where P N denotes the noise-plusoutercell-interference power in each user. In performance evaluation, we examine six beamforming methods with the following specifications. [Method] Algorithm A [Method2] Algorithm B [Method3] Liang s simplified method [2] [Method4] Modified algorithm A where all the diagonal elements of D are set to 9[dB]. [Method5] Eigenbeamforming with w arg max w y Ψ w [Method6]Simple beamforming for arrival path with largest power (w a ;max ) In above methods, methods 4, 5, and 6 do not consider variable bit rate multimedia traffic. 6.2 Weight Convergence Figure 2 shows the outage probability of algorithm A versus the number of users under iterations n w 2; 3; 6;, and 2. It is found that there is little difference in outage probability characteristics between n w and 2. Therefore, good weight convergence can be achieved by setting n w. 6.3 Outage Probability Figures 3 and 4 show the outage probabilities versus the number of users K under :2ß and :2ß, respectively. In figure 3, there is little difference in outage probability characteristics among methods, 2, and 3. On the contrary, in figure 4, the performance degradation is found in method 3. This is because EOCV in method 3 induces estimation error under wide angle spread. Methods and 2 have almost the same performance and outperform other methods including method 3. From these results, method 2(algorithm B) achieves

5 Outage Probability Method Method2 Method3 Method4 Method5 Method Number of Users K Figure 3: Outage probability versus number of users ( :2ß, L 4, R 4). Outage Probability - Method -2 Method2 Method3 Method4 Method5-3 Method Number of Users K Figure 4: Outage probability versus number of users ( :2ß, L 4, R 4). good performance under various angle spread, in spite of its low computational complexity. It is also seen that outage probability of a CDMA system can be reduced by precise downlin beamforming for multimedia traffic with variable target SINR. 7. CONCLUSIONS We proposed a downlin beamforming method for multimedia CDMA/TDD systems. The proposed method determines the transmission weights so that the total transmitted power is minimized under power-controlled CDMA systems. In the weight decision process, we consider each user s target SINR and the number of RAKE fingers. The simulation results show that the proposed downlin beamforming has low complexity and good performance under multimedia CDMA systems. The system capacity is also increased by precise downlin beamforming for multimedia traffic with variable target SINR. The proposed downlin beamforming method will be useful for future multimedia communications. Appendix A: instantaneous received SINR An exact expression for instantaneous SINR at output of RAKE receiver is represented by [8] K P [R i I ] r;r 2 G (ay ;l w i ) Λ (w y i a ;l 2 ) Λ i (l ;l 2)2U l U l fl ;l 2 l (r r 2 )jl 6 r ;» l ;l 2» Lg: R N can be approximated as [9] R N ff N + P () N G I ' N I: (2) G R (ff) where N is the equivalent interference-plus-noise power before despreading. Using (5), R S and R I are rewritten as R S P (A y ; w ) Λ (w y A ;) Λ R I K i d6 P i G (Ay ;d w i) Λ (w y ia ;d ) Λ : Therefore, we can get in the following form: K i d6 GP jg y (Ay ; w ) Λ j 2 P i jg y (Ay ;d w i) Λ j 2 + N jg j 2 :(22) g y R Sg g y R Ig + g y R : (2) Ng where R S, R I, and R N are the correlation matrices among RAKE fingers for desired signal, intra-cell interference, and outer-cell interference, respectively, and y denotes the complex conjugate transpose. Element (r ;r 2 ) of R S, R I is given by [R S ] r;r 2 P (a y ;r w ) Λ (w y a ;r 2 ) Λ Appendix B: Derivation of () Elements of A y ; w [v ;:::; v R ] T and A y ;d w i [v 2 ;:::; v 2R ] T are represented by v r a y ;r w (23) v 2r 8 < : ; r d» a y ;r d w i;» r d» R ; r d R + (24)

6 For simplicity, we assume that v ; ;:::; v R, v 2; ;:::; v 2R have independent and identical distribution. Then, we have E[j(A y w ; ) y (A y ;d w i)j 2 ] E[jv Λ v 2 + v Λ 2v 22 + ::: + v Λ Rv 2R j 2 ] (25) R p E[jv p j 2 ]E[jv 2p j 2 ] (26) R E[jAy ; w j 2 ] R p E[jv 2p j 2 ] (27) [2] F. Rasid-Farrohi, K. J. R. Liu, and L. Tassiulas, Transmit beamforming and power control for cellular wireless systems, IEEE J. Selected Areas Commun., vol. 6, no. 8, pp , Oct R E[jAy ; w j 2 ]E[jA y ;d w ij 2 ] (28) In converting (25) into (26), we use E[v p ]E[v p ]. Although (28) is derived for ensemble average, we use the following approximation for instantaneous value: j(a y ; w ) y (A y ;d w i)j 2 ' R jay ; w j 2 ja y ;d w ij 2 : References [] Y. Hara, Multi-user adaptive arrays for CDMA base station, EPMCC2, no. 24.3, Feb., 2. [2] Y.-C. Liang, F. Chin, and K. J. R. Liu, Downlin beamforming for DS-CDMA mobile radio with multimedia services, IEEE Trans. on Commun., vol. 49, no. 7, pp , July 2. [3] F. Adachi, M. Sawahashi, and H. Suda, Wideband DS- CDMA for next generation mobile communications system, IEEE Commun. Mag., vol. 36, pp , Sept [4] M. D. Anna and A. H. Aghvami, Performance of optimum and suboptimum combining at the antenna array of a W- CDMA system, IEEE J. Select. Areas Commun., vol. 7, no. 2, pp , Dec [5] H. Liu, Signal processing applications in CDMA communications, Chapter 4, pp. 8 2, Artech House Publishers, 2. [6] A. F. Naguib, Space-time receivers for CDMA multipath signals, Proc. ICC 97, pp , June, 997. [7] S. Tanaa, A. Hanada, M. Sawahashi, and F. Adachi, Experiments on coherent adaptive antenna array diversity for wideband DS-CDMA mobile radio, IEEE J. Select. Areas Commun., vol. 8, no. 8, pp , Aug. 2. [8] Y. Hara, D. Par, and Y. Kamio, Analysis of RAKE receiver in W-CDMA systems with downlin beamforming, Proc. of VTC2 Fall, Oct. 2. [9] Y. Hara, D. Par, and Y. Kamio, Performance analysis of RAKE receiver in W-CDMA downlin, IEICE Trans. on Commun., Vol.J84-B, No., pp , Nov. 2. [] C. Farsah and J. A. Nosse, Spatial covariance based downlin beamforming in an SDMA mobile radio system, IEEE Trans. Commun., vol. 46, no., pp , Nov [] F. Rasid-Farrohi, L. Tassiulas, and K. J. R. Liu, Joint optimal power control and beamforming in wireless networs using antenna arrays, IEEE Trans. on Commun., vol. 46, no., pp , Oct. 998.