A SYMBOL RATE MULTI-USER DOWNLINK BEAMFORMING APPROACH FOR WCDMA Michael Joham, Wolfgang Utschick, and Josef A. Nossek 10th IEEE International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC’99) Osaka, Japan volume 2, pp. 228–232, September 12th–15th, 1999 c 2005 IEEE. Personal use of this material is permitted. However, per- mission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Munich University of Technology Institute for Circuit Theory and Signal Processing http://www.nws.ei.tum.de A SYMBOL RATE MULTI-USER DOWNLINK BEAMFORMING APPROACH FOR WCDMA Michael Joham, Wolfgang Utschick and Josef A. Nossek Institute for Circuit Theory and Signal Processing Munich University of Technology Arcisstr. 21, 80333 Munich, Germany [email protected] (m) Abstract - The downlink spectral efficiency of 3rd gener- where sk 2 {−1; +1g denotes the BPSK modulated ation mobile radio systems will be increasingly important (m) symbols. The spreading code ck (t) for the m-th symbol due to the asymmetric features of several services. On (m) of mobile k is composed of Q chips d [q] 2 {−1; +1g the average, the downlink data rates will be higher than k k and is of length T = Q T . In WCDMA the chiprate on the uplink. We propose to utilize adaptive antennas k k c equals 1=T = 4:096 Mchips/s. The chip-waveform at the base stations because spatial interference suppres- c p (t) has a square-root raised cosine spectrum with a sion is able to reduce the near-far effect in the downlink rrc rolloff factor of . Note that the chips (m) of single-user detection DS-CDMA systems. The algo- α = 0:22 dk [q] rithm that calculates the downlink beamforming vectors are changing from symbol to symbol because they are de- takes into account the correlation properties of the spread- fined as the multiplication of the q-th chip of the Orthogo- ing and scrambling codes. We presume an estimation of nal Variable Spreading Factor (OVSF) code belonging to the downlink channel parameters in terms of the directions mobile k and the (mQk + q)-th chip of the pseudo-noise of arrival, delays, and medium term average path losses. scrambling code. In this approach, we also presume that the phases of the different multi-paths are known. Therefore, the mobile II. DOWNLINK DATA MODEL stations have to transmit the values of the phases every We presume a channel with discrete multi-paths, thus, the slot. 0 (k ;m) In WCDMA the users are distinguished by different channel impulse response hk (t) is FIR: spreading codes [1] which change over time due to the Q scrambling of the transmitted sequences. In [2] the beam- 0 0 (k ;m) (k ;m) (3) forming vectors at the base stations were computed slot- hk (t) = hk;q δ(t − τk;q); q=1 wise, whereas in this contribution we favour a symbol rate X evaluation of the beamforming vectors. The optimization where δ(t) denotes the Dirac delta function. Each tap 0 approach in [2] compensates the non-ideal properties of (k ;m) hk;q 2 C belongs to the path q over which the m-th the utilized spreading codes, which results in the optimal symbol of the signal k0 of the base station is transmitted solution with respect to the signal to interference and noise to the mobile station k (cf. Figure 1).The channel param- ratio. However, the new approach optimizes the actual eters estimated in the uplink are reciprocal in terms of the values of the decision variables of the rake demodulators. M DOA (steering vector ak;q 2 C , where M is the number of antenna elements), the medium term average path loss I. SIGNAL MODEL pk;q 2 R, and the path delay time τk;q. We assume that the path losses pk;q are numbered in a descending order, WCDMA was proposed by ETSI as a standard for FDD thus, pk;1 is the path loss of the strongest path to mobile k. services [3]. The downlink baseband signal for the mobile However, the reciprocity does not hold for the path phase k 2 f1; :::; Kg may be expressed as shift 'k;q . To eliminate this lack of knowledge we propose a feedback of the phase shift 'k;q from the mobile station 1 (m) (m) k to the base station. Because of the lower data rates in sk(t) = sk ck (t − mTk); (1) the uplink this feedback does not decrease the system ca- m=0 pacity. Therefore, the base station is able to compute the X 0 (k ;m) Qk q-th tap of hk (t): (m) (m) ck (t) = dk [q]prrc(t − qTc); (2) 0 (k ;m) H (m) j'k;q q=1 hk;q = pk;qak;qwk0 e ; (4) X (1) hk (t) s1(t) mobile s2(t) (2) hk (t) station k base station sK(t) inter-cell interference, (K) noise n (t) hk (t) k Figure 1: The channel of mobile station k. (m) M ∗ where wk0 2 C is the base station beamforming vec- where (•) and E[•] denote the complex conjugate and the tor for the mobile k0 which has to be estimated and (•)H expectation value, respectively. denotes conjugate transpose. Note that the channel impulse responses change from symbol to symbol since we deploy symbol-wise beam- (m) III. PREDEFINITION OF THE RAKE FINGER forming. The alteration of the beamforming vector wk0 depends on the changing correlation properties of the WEIGHTS scrambled spreading codes which will be outlined in the following sections. We further assume that the mobiles are Since we propose a symbol-wise beamforming for the equipped with a conventional maximum ratio combining downlink, the channel impulse responses also change rake receiver [4] (cf. Figure 2). First, the rake receiver es- from symbol to symbol. The rake demodulator exploits (k;m) timates the channel impulse response hk (t). After the the pilot symbols at the beginning of each slot to estimate taps of the channel estimation are used to perform a max- (k;m) the channel impulse response hk (t). imum ratio combining, the resulting signal is correlated Our approach is to keep the beamforming vectors con- with the spreading code of mobile k. Thus, the decision stant during the transmission of the pilot symbols. Thus, signal of the rake demodulator k for the symbol m can be only the correlation properties of the spreading codes written as: change due to scrambling, while the channel impulse re- K Q Nf (m) (m) sponse remains constant. The resulting channel estima- uk = Re CCFk;k0 (τk;f − τk;q)vk;f tion of the rake receiver is the mean over the estimations ( k0 q=1 f X=1 X X=1 using every pilot symbol. Therefore, the rake receiver esti- mates a constant channel with mean correlation functions. H (m) (m) j'k;q pk;qak;qwk0 sk0 e : (5) Note that the mean correlation functions of the scrambled ) spreading codes are ideal, i. e. the mean cross correla- K; Q; and Nf are the numbers of mobile stations, paths, tion is approximately zero and the mean auto correlation (m) and rake fingers, respectively. CCFk;k0 (τ) denotes the is equal to the spreading factor for the time instant zero cross correlation function of the spreading codes of the and approximately zero otherwise (cf. Figure 3 and 4). mobiles k and k0 for the symbol m. Note that the cross As a consequence, only the paths belonging to the rake correlation function is equal to the auto correlation func- fingers have to be taken into account for the channel esti- 0 tion, if k = k . The rake finger weights vk;f are derived mation process. from the channel estimation taps. Hence, pilot The base station beamforming vector w for the ∗ k (k;m) pilot symbols is computed to maximize the power of the vk;f = E hk;f channel impulse response at the rake receiver k, while the h (m)iH −j'k;f pilot pilot E w 0 a (6) H = pk;f ( k ) k;f e ; transmitted power (wk ) wk is the same for all mo- h i v1 τ1 − c(t) v2 Sample at t = T Received Detection signal r(t) T signal u τ2 ( ) dt Re − 0 • {•} R vQ τQ − Figure 2: Rake receiver for BPSK. Example of the Autocorrelation Function Example of the Crosscorrelation Function 20 20 15 15 10 10 ) ) τ τ ccf( acf( 5 5 0 0 −5 −5 −20 −15 −10 −5 0 5 10 15 20 −20 −15 −10 −5 0 5 10 15 20 τ τ Mean of the Autocorrelation Function Mean of the Crosscorrelation Function 20 20 15 15 10 10 ) ) τ τ ccf( acf( 5 5 0 0 −5 −5 −20 −15 −10 −5 0 5 10 15 20 −20 −15 −10 −5 0 5 10 15 20 τ τ Figure 3: Instantaneous and averaged autocorrelation Figure 4: Instantaneous and averaged crosscorrelation function of a scrambled spreading code of length SF = function of a scrambled spreading code of length SF = 16. 16. biles. That leads to following optimization problem: solution is the eigenvector belonging to the largest eigen- H value of AkAk . Nf The resulting predefined rake finger weight reads as: pilot H 2 H pilot max (wk ) ak;f pk;f ak;f wk = wpilot k f=1 pilot H −j'k;f X vk;f = pk;f (wk ) ak;f e : (7) pilot H H pilot max(wk ) AkAk wk ; wpilot k IV.