Downlink Beamforming for FDD Systems with Precoding and Beam Steering

Downlink Beamforming for FDD Systems with Precoding and Beam Steering Saeed Moradi, Roya Doostnejad and Glenn Gulak Department of Electrical and Computer Engineering University of Toronto Toronto, Ontario, Canada Email: {smoradi,gulak}@eecg.toronto.edu r.doostnejad@utoronto.ca Abstract A practical downlink beamforming technique is proposed for an FDD system to mitigate the interference and enhance the SINR performance at the mobile user. Most of the closed loop beamforming techniques require a large number of feedback bits that make them impractical for standards such as LTE where only a limited number of feedback bits is available in the feedback channel. Therefore, a downlink beamforming scheme is introduced at the base station where the antenna elements are grouped into a collection of ports. We propose to apply codebook beamforming over the ports and perform beam steering at each port to further direct the transmitted energy and reduce the interference to the rest of the users. Simulation results reveal that, with significantly fewer number of feedback bits, our proposed technique outperforms a diversity transmission scheme, especially in the low SNR regime, in a system with the same total number of antenna elements where a larger number of feedback bits is required. I. INTRODUCTION Multiple-input-multiple-output (MIMO) technology has been shown to offer potential for increasing the capacity and reliability in wireless communication systems. It can provide higher capacity through spatial multiplexing, and increased reliability with diversity transmission []. Due to the increasing demand for higher transmission rates and the growing number of users, interference has become one of the major limiting factors in the performance and capacity of wireless cellular systems. Beamforming is a widely used technique for interference reduction and directed transmission of energy in the presence of noise and interference. In multiple-antenna systems, beamforming exploits channel knowledge at the transmitter to maximize the signal-to-noise ratio (SNR) at the receiver by transmitting in the direction of the eigenvector corresponding to the largest eigenvalue of the channel []. Beamforming can also be used in the uplink or downlink of multiuser systems to maximize the signal-tointerference plus-noise ratio (SINR) of a particular user [3]. However, downlink beamforming for interference mitigation and, consequently, SINR enhancement at the mobile users is more challenging in Frequency Division Duplex (FDD) communication systems where the base station has only limited The authors gratefully acknowledge financial support from Ontario Centers of Excellence and the NSERC CRD programs. knowledge of the downlink channel. In FDD systems, uplink and downlink channels fade independently if the frequency separation between them is large enough compared to the coherence bandwidth of the channel. As a result, the uplink channel information may not be applied directly for downlink beamforming. There are two different schemes to address this issue. In closed loop beamforming, partial channel state information (CSI) is provided to the base station. In a typical limited feedback system, the transmitter and receiver share a pre-determined codebook and the receiver feeds back the index of the codeword that maximizes the received SINR for the current channel condition [4], [5]. A practical limitation of closed loop beamforming is that the required codebook size for a target bit error rate () grows with the number of transmit antennas. For instance, for a single-antenna user, roughly on the order of (the number of transmit antennas) feedback bits are needed to achieve near perfect-csi performance. In addition, for MIMO downlink channels, the feedback load per user must be scaled with both the number of transmit antennas as well as the system SNR in order to achieve near-perfect CSI performance and the full multiplexing gain [6]. However, in most of the practical systems, the user is provided with only a few bits of feedback. For instance, the number of feedback bits provisioned in the LTE standard for transmitting the Channel Quality Information (CQI) is only 4 bits [7]. On the other hand, in open loop beamforming for an FDD system, the required downlink channel information is estimated with the obtained uplink channel information at the base station. Some transformation is then required to convert uplink channel information to that of the downlink channel. For instance, the uplink direction of arrival (DOA) can be estimated from the received uplink data to calculate the optimal antenna beamforming weights for downlink transmission [8]. But the robustness of this method is substantially degraded in urban environments with large angular spread [9], [0]. Open loop beamforming algorithms based on spatial covariance, on the other hand, adjust the antenna pattern to the downlink propagation conditions [], [], [3]. In these schemes, the uplink channel spatial covariance matrix is obtained by taking an average, and a proper matrix transformation is then applied 978--444-968-8//$6.00 0 IEEE

to estimate the downlink channel spatial covariance with the null-constrained technique or frequency calibration [4]. However, the estimate of the uplink covariance matrix smooths out the channel fades and does not capture the fast fading characteristics of the channel. Moreover, the spatial covariance matrix transformation is computationally expensive. In this paper a downlink beamforming scheme for FDD systems is proposed that performs codebook precoding and beam steering to maximize the received SNR at the mobile user. In the proposed technique, antenna elements at the base station are grouped into arrays or ports with an equal number of elements. The element spacing at each port is half wavelength, λ/, and the spacing between the ports is larger, typically 5λ or more. The precoding is performed over the ports which now require fewer bits of feedback to achieve the target. We then propose to apply beam steering at each port to further direct the transmit energy toward the desired user and avoid causing interference to the rest of the users. In other words, by trading off spatial multiplexing with diversity gain, the beam steering is performed to adjust to the low capacity of the feedback channel. This makes the proposed system model very appealing to FDD systems where the target can not be achieved when the number of transmit antennas limited to only few available feedback bits. It tackles this problem while keeping the same multiplicity of total transmit antenna elements and grouping them into fewer ports which then require fewer feedback bits for codebook beamforming. Simulation results imply that the achieved beam steering gain outperforms the diversity gain especially in the low SNR regime for the same multiplicity of total transmit antennas. This paper is organized as follows. The system model is introduced in Section II. The proposed technique is explained in Section III. Section IV introduces two methods for driving the optimal beam steering vectors. Section V presents simulation results. Finally, Section VI concludes the paper. II. SYSTEM MODEL In the proposed architecture, the base station is equipped with ports each having an antenna array of N elements. Element spacing at each array is λ/ and the spacing between the ports is larger, typically 5λ or more. The receiver is assumed to have M R antennas. In practical communication systems, mobile users usually have up to or receive antennas. If we consider each array at the base station as one transmitting port, then the corresponding MIMO channel between the base station and the mobile user can be written as H = h h h MT h h h MT h MR h MR h MR. () Considering the N antenna elements at each port, the M R Input Data Fig.. station. S/P s s s MT Codebook Beamformer x x x MT Beamformer Beamformer Beamformer Transmitter N N N Array Array Array M R Receiver Proposed system model for single-user transmission at the base ( N) MIMO channel can be written as h h h MT where Ĥ = h h h MT h M R h M R h MT M R, () h j i =[hj i,, hj i,,, hj i,n ] (3) is the channel vector from the jth port (antenna array) at the base station to the ith antenna at the user, and h j i,n is the channel fading between the nth antenna element of the jth port at the base station to the ith antenna at the user. For a flat fading assumption, the N downlink channel vector from the jth port at the base station to the ith antenna at the user can then be written in terms of the corresponding downlink spatial signature as L h j i (t) =aj D (t) = α j l (t)v D(θ l ), (4) l= where α j l is the downlink multipath flat fading coefficient of the lth dominant path for the jth port, L is the number of dominant paths, and downlink steering vector v D (θ) is defined as v D (θ) =[,e jπd cos θ/λd,...,e jπ(n )d cos θ/λd ], (5) where d is the antenna element spacing at the base station, θ is the DOA of the phased array, and λ D is the downlink wavelength. III. DOWNLINK BEAMFORMING FOR FDD SYSTEMS In a Time Division Duplex (TDD) system, the same frequency band is used for uplink and downlink transmissions, and the reciprocity principle can be applied to obtain the downlink channel information needed for calculating the downlink beamforming vector. However, in a Frequency Division Duplex (FDD) system, there is a frequency separation between

uplink and downlink that results in independent fading of the uplink and downlink channels. As a result, the uplink channel information may not be applied directly for downlink beamforming. Therefore, in a typical FDD system, the base station is often provided with a few bits of feedback to perform codebook precoding. The selected codevector by the user usually maximizes the received SINR. This codevector is in fact the quantized direction of the downlink channel. For achieving a near perfect-csi performance, the number of required feedback bits for quantization of the downlink channel vector grows with the number of transmit antennas at the base station [6]. However, in practical systems such as LTE, the user is provided only with a few bits of feedback. To tackle this issue, we propose to group the available antennas at the base station into a collection of ports with the same total number of elements. In this system model, the codebook precoding is performed over the ports, and then beam steering is performed at each port to further direct the transmit energy toward the desired user and avoid causing interference to the rest of the users. On the other hand, spatial multiplexing is traded off to perform the beam steering and adjust to the low capacity of the feedback channel. As shown in Fig., the signal vector s =[s,s,,s MT ] is first precoded with code vector c. Then, the beam steering vector w =[w, w,, w MT ] is applied where w j is used for the beam steering at the jth port. As a result, the received signals at the mobile user can be written as H = r = Hx + n, (6) where H is the M R effective channel matrix defined as h w h w h MT w MT h w h w h MT w MT h M R w h M R w h MT M R w MT, (7) and x =[x,x,,x MT ] T is the vector of precoded messages, and n is the M R complex Gaussian white additive noise vector at the mobile user. IV. OPTIMAL BEAM STEERING VECTOR In this section, we propose two approaches to obtain optimal beam steering vectors maximizing the received SNR at the mobile user in FDD transmission. In the first scheme, we linearly transform the uplink channel obtained by the base station to estimate the downlink channel information. In the second approach, DOA information of the uplink signal is derived to calculate the downlink steering vector. A. Transformation of Uplink Channel Information A linear approach can be used to transform uplink spatial signatures into the downlink ones. Assume a j U (t 0) and a j D (t 0) are uplink and downlink spatial signatures sampled at time t = t 0 for the jth port, respectively. Although the exact transformation of a j U to aj D is a nonlinear function, a linear transformation can be applied to obtain an estimation of the downlink spatial signatures. If A U and A D represent N P Avg. Estimation error (db) 0 5 0 5 0 (a) 5 0 0 30 40 50 60 70 80 90 00 Δ f (MHz) (b) Fig.. The proposed technique for converting uplink spatial signatures to the downlink ones with a linear transformation. (a) Block diagram of the proposed technique. (b) Effect of computing matrix Φ from only channel direction information (CDI) compared to complete channel knowledge (CQI). Δ f is the frequency separation between the uplink and downlink channels. array responses of uplink and downlink, respectively, for P samples from the jth port, then a linear transformation can be written as CQI CDI A D = ΦA U. (8) A least squares solution for the N N transformation matrix Φ is then given by Φ = A D A H U (A U A H U ). (9) Thus, as shown in Fig. (a), an estimation of downlink spatial signature for the jth port can be found as â j D = Φaj U. (0) Assuming the interference is spatially white (single user case), the optimal beamforming vector for the jth port is given by [5] w j =[â j D ]H. () In general, computing the matrix Φ defined in (9) requires complete knowledge of the uplink and downlink test spatial signatures. However, it is not practical to obtain complete knowledge of the downlink test spatial signatures at the base station. In fact, a mobile user can only feedback its optimal codevector as the quantized direction of the corresponding downlink spatial signature, and not its magnitude. Thus, the

effectiveness of this technique needs to be investigated when only the channel direction information (CDI) is provided to the base station as opposed to the ideal scenario where the complete channel quality information (CQI) is available. Fig. (b) shows the accuracy of estimation of downlink spatial signatures from the uplink ones from only the direction of the uplink and downlink test spatial signatures. Δ f is the frequency separation between the uplink and downlink channels. The estimation error is calculated as the normalized average distance between the actual test vectors and the estimated ones obtained from transforming with matrix Φ. As seen from this figure, the matrix Φ calculated from only channel direction information (CDI) results in almost the same performance of having complete channel quality information (CQI). It is expected that uplink and downlink channels fade independently for fairly large frequency separations. Hence, the effectiveness of this technique needs to be investigated against the frequency separation of uplink and downlink channels. This can be observed in Fig. (b) where the power of the average estimation errors tends to 0 db as the Δ f becomes as large as 00 MHz. This indicates that the beam steering technique using the transformation of the uplink channel information is less effective for large frequency separations between the uplink and downlink channels. A practical channel model such as 3GPP SCM [6] can be used for modeling FDD channels. However, a more accurate channel model for FDD uplink and downlink channels is required to generate the corresponding spatial signatures. Thus, besides SCM channel model, we use the FDD channel model introduced in [7], [8] where the spatial signature for a multi-delay channel with L dominant paths is modeled as L a T (t) = α l (t)v(θ l ). () l= Then, uplink and downlink complex path fading coefficients can be modeled as α U,l (t) = K U d.β U,l(t). Γ η/ l (t), (3) α D,l (t) = K D d.β D,l(t). Γ η/ l (t), where K U and K D are uplink and downlink propagation constants, d is the distance to the mobile user, and η is the K d η/ path loss exponent. The term accounts for large scale fading, β l models the fast fading factor, and Γ l describes the slow fading of the lth path. As a result, samples of the uplink and downlink spatial signatures for a given propagation link between jth antenna at the base station and ith antenna at the mobile user are generated by a T U,i,j(kT) = K U d η/ i,j a T D,i,j(kT) = K D d η/ i,j [ L β U,i,j,l (kt)v U (θ i,j,l ) ] Γ i,j,l, (4) l= [ L β D,i,j,l (kt)v D (θ i,j,l ) ] Γ i,j,l. (5) l= =, N= =, N= =, N=4 =4, N= =4, N= =4, N=4 0 4 0 5 0 5 0 5 30 =, N= =, N= =, N=4 =4, N= =4, N= =4, N=4 (a) 0 5 0 5 0 5 30 (b) Fig. 3. Performance of the proposed system model for several antenna configurations ( ports and N elements at each port) at the base station, and a single receive antenna, with transformation of uplink channel information (Δ f =0MHz) for the beam steering. 4-QAM modulation is used. SNR is defined as the total transmit power to the receiver noise power ratio. (a) performance under FDD channel model in [7]. (b) performance under SCM channel model in [6]. B. DOA Estimation For the flat fading assumption, the uplink spatial signature from the ith antenna at the mobile user to the jth port at the base station can be modeled as a j U (t) α i,j(t)v U (θ j ) (6) where α i,j is the uplink fading coefficient, and θ j is the direction of the path with the largest power. In an FDD system, uplink and downlink fading coefficients are uncorrelated in general. However, since the DOA is mostly decided by the physical environment and the scatterers, uplink and downlink DOAs are identical [8]. Thus, the DOA can be derived through the uplink sounding, and used later to estimate the downlink channel. As a result, the downlink steering vector can be obtained from the uplink channel as v T D(θ j )=Ψv T U (θ j ), (7) where Ψ is a diagonal matrix that captures the frequency shift between the uplink and downlink, and defined as Ψ = diag(,e jφ,,e jφn ), (8)

where φ n = ( ) π(n )d cos θ j, n =,...,N. (9) λ D λ U Once the downlink steering vector is estimated, the beamforming vector for the jth port can be chosen as w j = v D (θ j ) H. (0) As a result, the effective channel fading element H i,j in eq. (7) can be written as H i,j = h j i w j = α i,j.v D (θ j )v D (θ j ) H = Nα i,j, () since v D (θ j ) = N. Thus, since α i,j and h i,j in eq. () have the same distribution, the effective channel matrix in (7) can be modeled as H = N α, α, α,mt α, α, α,mt α MR, α MR, α MR,. () Consequently, the effective channel matrix H can be approximated as H NH. (3) As discussed in [9], for the Zero-Forcing receiver, this system results in roughly 0 log N performance enhancement over the traditional V-BLAST scheme. V. SIMULATION RESULTS In this section we provide the simulation results for the proposed techniques. The mobile user is assumed to have a single receive antenna. We examine the proposed techniques for =, 4 ports and N =,, 4 elements at each port at the base station. The downlink channel has the Rayleigh fading distribution, and complex additive white Gaussian noise (AWGN) is added to the faded signal at the receiver. 4-QAM and 6-QAM modulations are used to modulate the symbols at the base station. Full diversity transmission is adopted at the base station, and the mobile user makes use of a MMSE receiver to demodulate the received signal. The 3GPP LTE Householder codebooks [0] of sizes 4 and 6, for two and four transmit ports, respectively, is shared by the base station and the mobile user. Thus, the feedback channel is assumed to have a capacity of up to 4 bits. As discussed in Section IV-A, the uplink and downlink channels are generated according to both the SCM channel model and the FDD channel model introduced in [7], [8]. Since the physical environment can be assumed unchanged from the uplink to the downlink channel, the same angle of arrival (AOA) and angle of departure (AOD) is used for generating uplink and downlink channels with the SCM channel model. Fig. 3(a) shows the performance of the proposed system model with transformation of uplink channel information for the beam steering versus SNR defined as the ratio of total available transmit power at the base station to the noise power at the receiver. A fixed frequency separation of Δ f =0MHz 0 4 0 5 =, N= =, N= =, N=4 =4, N= =4, N= M =4, N=4 T 0 6 0 5 0 5 0 5 0 4 0 5 =, N= =, N= =, N=4 =4, N= =4, N= =4, N=4 (a) 0 6 0 5 0 5 0 5 30 (b) Fig. 4. Performance of the proposed system model for ports and N elements at each port at the base station, and a single receive antenna, with DOA estimation for the beam steering. No DOA estimation error is considered. SNR is defined as the total transmit power to the receiver noise power ratio. (a) performance for 4-QAM modulation. (b) performance for 6-QAM modulation. is assumed. For instance, if we compare the performance for the two cases of ( =4,N=)which corresponds to a traditional 4 system of single antenna array, and ( =, N = ) which has the same total number of antenna elements but grouped into two ports of two-element arrays, it can be observed that the beam steering gain outperforms the diversity transmission for the low SNR range. However, for the high SNR regime, the diversity gain of transmitting with more transmit ports outperforms the proposed system model with beam steering gain. The later employs two ports for transmitting up to two different symbols, but requires only bits of feedback. However, the former uses four antennas for transmitting up to four different symbols, but requires 4 bits of feedback. As a result, at the expense of lower spatial multiplexing, we have achieved better performance with fewer feedback bits. This suggests that the proposed system model is very well suited for diversity transmission cases with a low capacity feedback channel. Fig. 3(b) shows similar performance under SCM channel modeling. Fig. 4(a) shows the performance of the proposed system model with DOA estimation for the beam steering with no DOA estimation error. Similarly, with fewer required

a significantly larger number of feedback bits is required. This makes the proposed system model very suitable for a practical diversity transmission case where a low capacity feedback channel with only a few number of feedback bits is available. 0 4 0 5 =, N=, θ e =5 =, N=, θ e =5 =, N=, θ e =30 =4, N=4, θ e =5 =4, N=4, θ e =5 =4, N=4, θ e =3 0 6 0 5 0 5 0 5 Fig. 5. Performance of the proposed system model for two antenna configurations for various DOA estimation errors, θ e, for the beam steering where the actual DOA is θ =45degrees. feedback bits, the same performance is achieved with this technique. Compared to Fig. 3(a), the beam steering gain in the DOA estimation technique outperforms the diversity gain for a larger low SNR range. In addition, the DOA estimation technique performs better than the previous result where the transformation of uplink channel information is used for the beam steering. For instance, for the target =, the required SNR with DOA estimation for beam steering is approximately 0 db, however, beam steering with the uplink channel transformation method needs roughly 8 db of SNR to achieve this target. This is due to the fact that the maximum possible gain from beam steering is achieved when the exact DOA information is available and the array is beamformed with the conjugate transpose of the array output with the same DOA angle. Fig. 4(b) shows the performance of the proposed system model with DOA estimation for the beam steering for 6-QAM modulation. It can be seen that similar performance results are achieved for the higher order modulation schemes. Fig. 5 examines the performance against the error in DOA estimation for various θ e =5, 5, 3, 30 degrees of error in the DOA estimation when the actual DOA is θ = 45 degrees. It can be seen that, if the transmitted signal at the array output is assumed to be a single path, the beam steering loss due to the error in DOA estimation increases for the larger array sizes (number of elements at each port) at the base station. VI. CONCLUSION This paper presented a practical downlink beamforming technique for an FDD system to reduce the interference and improve the SNR performance at the mobile user. We proposed to group the antennas at the base station to apply codebook beamforming over the ports and perform beam steering at each port to further direct the transmitted energy. Simulation results reveal that, with significantly fewer number of feedback bits, our proposed technique either outperforms or performs very closely, especially in the low SNR regime, to a traditional system with the same total number of antenna elements where REFERENCES [] A. Paulraj, D. Gore, R. Nabar, and H. 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