A Symbol Rate Multi-User Downlink Beamforming Approach for Wcdma

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

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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 ∈ {−1, +1} 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] ∈ {−1, +1} 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 ∈ 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 ∈ C , where M is the number of antenna elements), the medium term average path loss I. SIGNAL MODEL pk,q ∈ 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 ∈ {1, ..., K} may be expressed as shift ϕk,q . To eliminate this lack of knowledge we propose a feedback of the phase shift ϕk,q from the mobile station ∞ (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) jϕk,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 ∈ 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) jϕk,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 −jϕk,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

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 −jϕk,f X vk,f = pk,f (wk ) ak,f e . (7) pilot H H pilot max(wk ) AkAk wk , wpilot k IV. SYMBOL-WISE BEAMFORMING pilot H pilot s. t.: (wk ) wk = 1, After predefining the rake finger weights during the trans- M×Nf where Ak = [ak,1pk,1, . . . , ak,Nf pk,Nf ] ∈ C . The mission of the pilot symbols, we can compute the base (m) station beamforming vector wk of the mobile k for each and T K symbol m providing the demanded value of the decision θ = [θ1, . . . , θK ] ∈ R+ . variable u(m) at the output of rake k. Also, we deploy the k The parameter θ ∈ R of the constraint in Equation (10) ability of power reduction due to the gain of the antenna k + is the absolute value of the demanded decision signal of array. the rake receiver k. The needed θ can be chosen indi- It is convenient to introduce following abbreviations: k vidually for each mobile k, therefore, fast transmit power −jϕk,q M bk,q = pk,qak,qe ∈ C control (TPC) can be easily implemented by adapting θk (m) (m) (m) M depending on the TPC commands. z 0 0 w 0 k = sk k ∈ C . The solution of the optimization problem of Equation Thus, the rake decision signal of the mobile station k can (10) can be written as: (m) − be written as: uk = 1 x(m) = (Γ(m))T Γ(m)(Γ(m))T θ. (11) K Q Nf (m) H (m) = Re CCF 0 (τ − τ )v b z 0 .  k,k k,f k,q k,f k,q k  k0 q=1 f V. LOOK-DIRECTION BEAMFORMING  X=1 X X=1  (8)  (m) (m)  We compare the symbol-wise downlink beamforming al- After collecting the vectors zk0 in a vector z and transforming to a real-valued representation, we end up gorithm with a slot-wise downlink beamforming algo- with following representation of the output signal of the rithm, where the base station beamforming vectors are rake receiver k: chosen to form a beamforming pattern which shows in the look-direction of the respective mobile station. This Q Nf approach does not take into account the changing corre- (m) (m) T (m) (m) T (m) uk = (γk,f,q) x = (γk ) x , (9) lation properties of the utilized spreading codes. We also q=1 f X X=1 presume a DOA estimation in the uplink, but we deploy where the steering vector ak,q of the “strongest” path q form the base station to the mobil k. The strongest path – the look- T x(m) = Re{z(m)}T , Im{z(m)}T ∈ R2MK , direction – is determined by the largest transmission value pk,q. Because the look-direction beamforming only re- h i T gards one single path, the index q can be dropped , thus, (m) (m) T (m) T MK z = (z1 ) , . . . , (zK ) ∈ C , the steering vector and the path transmission factors are and h i denoted by ak and pk, respectively. The idea is to trans- Q Nf mit into the direction from where most of the uplink signal (m) (m) 2MK γk = γk,f,q ∈ R , power was received. Thus, the beam shaped by the vec- q=1 f=1 tor w can equally be formed by use of the steering vector X X k T ak. To consider the near-far effect we have to multiply the (m) (m) T (m) T 2MK γk,f,q = Re{gk,f,q} , Im{gk,f,q} ∈ R , beamforming vector with the reciprocal of the path trans- misson factor. Consequently, the resulting beamforming with h i vector reads as: g(m) CCF(m) k,f,q = k,1 (τk,f − τk,q ), . . . , 1 w = a ∈ CM . (12) h T k k (m) ∗ MK pk . . . , CCFk,K (τk,f − τk,q) ⊗ (vk,f bk,q) ∈ C , i where ‘⊗’ denotes the Kronecker product. VI. SIMULATION RESULTS Our goal is to provide the demanded level for the decision signal of every rake receiver, in other words, we have Our simulation scenario includes K = 14 mobiles, where to fulfill K requirements. Note that the number of degrees Q = 7 paths connect each mobile with the base station. of freedom is larger than the number of restrictions. We The directions of arrival ak,q and the path transmission can use the remaining degrees of freedom to reduce the factors pk,q, k = 1, . . . , K and q = 1, . . . , Q, are con- transmitting power at the base station. This leads to fol- stant. The path phase shifts ϕk,q and the delay times τk,q lowing optimization problem: are uniformly distributed within the intervals [0, 2π] and [−τmax, +τmax], respectively. The delay spread τmax is (m) 2 Γ(m) (m) min kx k2, s. t.: x = θ. (10) 2µs which is about the half of a symbol time for the used x(m) spreading factor SF = 16. The rake receiver oversamples where with OSF = 4 and has Nf = 3 fingers. The transmission 2 T power kwkk2 is set to 1 =ˆ 0 dB and is the same for Γ(m) (m) (m) (m) (m) K×2MK = s1 γ1 , . . . , sK γK ∈ R both the slot-wise and symbol-wise beamforming. Also, P h i Table 2: BERs for look-direction slot-wise downlink beamforming and symbol-wise downlink beamforming

mobile station 1 2 3 4 5 6 7 BER ± slot-wise 1.95 · 10−2 0.43 · 10−2 8.63 · 10−2 4.88 · 10−2 0.14 · 10−2 1.62 · 10−2 0.92 · 10−2 BER ± symbol-wise 3.35 · 10−3 2.49 · 10−3 0.41 · 10−3 0.01 0.05 · 10−3 5.57 · 10−3 0.19 · 10−3 mobile station 8 9 10 11 12 13 14 BER ± slot-wise 0.66 · 10−2 0.15 · 10−2 1.20 · 10−2 0 0.01 · 10−2 0 0 BER ± symbol-wise 1.06 · 10−3 4.01 · 10−3 6.60 · 10−3 0 0 0 0

the additive white Gaussian noise which models the in- spread τmax is small enough so that we can neglect the tercell interference and noise is the same for all mobiles signal portions due to the previously and afterwards trans- and both beamforming methods and we chose a value of mitted symbols. This assumption holds as long as the path −10 dB with respect to the transmission power. The sim- attenuations of the weaker paths is large – the transmis- ulation parameters are listed in Table 1. Each slot con- sion factors are small – enough. In the case of mobile 9, the weaker paths are very strong (0.98, 0.9, 0.8, 0.5), thus, the probability that the assumption does not hold is higher Table 1: Simulation parameters than for mobile 5 (0.6, 0.5, 0.4, 0.2). parameter value M 3 VII. CONCLUSION K 14 Q 7 We presented a new symbol-wise downlink beamforming OSF 4 algorithm which presumes a feedback of the path phase shifts from the mobile stations to the base station. The Nf 3 algorithm takes into account the channel parameters esti- Tc 0.2441µs mated in the uplink and the correlation properties of the T1, . . . , T14 3.9062µs scrambled spreading sequences. Although these proper- SF1, . . . , SF14 16 slot length 2560 symbols ties are bad, we are able to reduce the disadvantageous τmax 2µs interference caused by intersymbol and co-channel inter- transmission power 1 =ˆ 0 dB ference. Our simulation results have shown that the BER noise and intercell-interference 0.1 =ˆ − 10 dB performance and, therefore, the system capacity can be trials 150 increased signiﬁcantly by regarding the correlation properties of the scrambled spreading codes and adapting the downlink beamforming vectors symbol-wise. sists of 2560 symbols or 40960 chips which is equal to the length of the used Gold scrambling sequence. The results VIII. REFERENCES shown in Table 2 and 3 are the mean of 150 simulations. [1] E. H. Dinan and B. Jabbari. Spreading Codes for Di- rect Sequence CDMA Cellular Networks. IEEE Com- Table 3: Mean BERs for look-direction slot-wise down- munications Magazine, September 1998. link and symbol-wise downlink beamforming [2] C. Brunner, M. Joham, W. Utschick, M. Haardt, and slot-wise symbol-wise J.A. Nossek. Downlink Beamforming for WCDMA mean BER 1.47 · 10−2 1.70 · 10−3 based on Uplink Channel Parameters. In Proceedings of the 3rd European Personal Mobil Communications Conference, 1999. We observe a signiﬁcant improvement of the BER [3] E. Dahlman, B. Gudmundson, M. Nilsson, and with the symbol-wise beamforming compared to the slot- J. Skold. UMTS/IMT-2000 Based on Wideband wise look-direction method. However, the BER for mo- CDMA. IEEE Communications Magazine, Septem- bile 9 is higher for symbol-wise beamforming than for ber 1998. slot-wise beamforming. The explanation can be found in the very large path transmission factors p9,q of mobile 9. [4] J. G. Proakis. Digital Communications. McGraw- In the development of the symbol-wise downlink beam- Hill, Inc., 1995. forming algorithm we made the assumption that the delay