Zero-Forcing Transceiver Design in the Multi-User MIMO Cognitive Relay Networks

Transcription

1 213 8th International Conference on Communications and Networking in China (CHINACOM) Zero-Forcing Transceiver Design in the Multi-User MIMO Cognitive Relay Networks Guangchi Zhang and Guangping Li School of Information Technology Guangdong University of Technology Guangzhou 16, China Liping Luo Department of Physics and Electronics Engineering Guangxi University for Nationalities Nanning 36, China Gaofei Huang Faculty of Mechanistic and Electric Engineering Guangzhou University Guangzhou 16, China Abstract The transceiver design in a cognitive radio networks is studied, all nodes are deployed with multiple antennas A primary point-to-point MIMO link is authorized to utilize the spectrum Ignoring the secondary users, the primary transmitter and receiver are designed based on the traditional singular value decomposition method The secondary users consist of multiple source-destination pairs, assisted by multiple two-hop non-regenerative relays The transceivers of the secondary users are supposed to cancel the interferences from the secondary users to the primary receiver, the interferences from the primary transmitter to the secondary users, and the inter-secondary-user interferences, in order to guarantee the communication quality of both the primary and secondary users Based on the zeroforcing method, the transceivers are designed to minimize the noise power amplified by the relays It is shown that the proposed transceiver design algorithm outperform the existed algorithm I INTRODUCTION Cognitive radio is a promising technology to improve the spectrum utilization and to alleviate the spectrum shortage [1] In the cognitive radio networks, the secondary users can share the spectrum with the primary users in overlay or underlay mode [2] In the overlay mode, the secondary users can access the spectrum only when the spectrum is not occupied by the primary users In the underlay mode, however, the secondary users can use the spectrum with the primary users at the same time, as long as the communication quality of the primary users is not affected Wireless relaying can provide high throughput and broad coverage in wireless communication networks [3] [6] The relaying way can be either regenerative or non-regenerative [7] When there are multiple antennas at the relays, transceivers should be designed to improve performance The related works usually consider relay beamforming design in the nonregenerative relaying systems [7] [11] The optimal relay beamforming filter has been designed to maximize capacity in the single-user single-relay two-hop systems [7] The zeroforcing distributed relay beamforming schemes have been proposed to cancel inter-user interferences for one-way [8] and This work was supported by the National Natural Science Foundation of P R China (61127 and ), the Natural Science Foundation of Guangdong Province (S and ), the Scientific and Technological Project of Guangzhou City (213J2271), and the Guangxi Natural Science Foundation (212GXNSFBA3162) two-way [9] multi-user relay systems respectively However, [8] and [9] only considered single-antenna relays A multiuser two-hop system which consists of multiple single-antenna source-destination pairs and multiple multi-antenna relays has been considered in [1] The zero-forcing relay beamforming filters have been designed to cancel inter-user interferences and to minimize the interference-plus-noise power The relay beamforming filter for a multi-antenna multi-user two-way relaying system has been designed based on the signal space alignment and zero-forcing methods in [11] However, this work only considered single-relay single-data-stream system Transceiver design is also one of the hot research topics in the cognitive radio networks Related research usually focus on the underlay spectrum sharing mode In [12], an opportunistic spectrum access scheme has been proposed, which allows the secondary user transmitting data on the spatial channel unused by the primary user, and the transceiver design and power allocation problems have been solved The primary and secondary users are both point-to-point singleuser systems Different from [12], [13] considered a different system configuration, there are multiple secondary user pairs An interference alignment scheme has been proposed to allow multiple secondary users to use the same spectrum with a primary user pair In the cognitive radio networks, the secondary link can use relay to improve throughput, enlarge coverage area, and reduce interference The transceivers need to be designed in such networks The optimal relay beamforming filter to maximize the capacity of the underlay two-hop MIMO cognitive radio networks has been found in [14] Furthermore, the optimal relay beamforming filters for the multi-hop MIMO cognitive radio networks have been designed in [1] However, [14] and [1] considered single source-destination pair in the secondary link, the transceiver design problem for the cognitive radio networks with multiple secondary source-destination pairs and multiple relays needs to be studied In this paper, transceiver design for an underlay cognitive radio network consisting of one primary user pair and multiple secondary user pairs is studied The secondary user pairs are assisted by multiple two-hop non-regenerative relays Each node in the network is employed with multiple antennas The IEEE

2 Primary Users Secondary Users M S M1 S 1 MK S K H RlS H RlSi Fig 1 H DiS H DS J1 R 1 JL R L H DSi System Model H DiRl H DRl precoder at each transmitter, receiver at each receiver, and beamforming filter at each relay are designed in a zero-forcing fashion to cancel the interferences from the primary transmitter to the secondary users, the interferences from the secondary users to the primary receiver, and the inter-secondary-user interferences The transceivers have been designed to minimize the total noise power amplified by the relays Computer simulation results have been provided to show the performance of the proposed transceiver design scheme In this paper, capital boldface letters are referred to matrices, and lowercase boldface letters are referred to vectors The superscripts T and H stand for transposition and Hermitian transposition Z 1, Z 1/2, det(z), tr(z), Z F, and vec(z) denote the inverse, square root, determinant, trace, Frobenius norm, and vectorization of a matrix Z, and null(z) denotes the null space of Z I M stands for the M M identity matrix II SYSTEM MODEL The underlay cognitive radio network considered in this paper is shown in Fig 1 The primary transmitter and receiver are denoted as S and D respectively, and S and D are deployed with M and N antennas respectively The secondary users consists of K source-destination pairs, which are assisted by L two-hop relays The ith source and destination are denoted as S i and D i respectively (i =1,,K), and the lth relay is denoted as R l (l =1,,L) The source S i and destination D i are deployed with M i and N i antennas respectively, and R l is employed with J l antennas The matrix H BA denotes the channel matrix from A to B, A {S,,S K, R 1,,R L } and B {R 1,,R L, D,,D K } The entries of all channel matrices are identically independent distributed (iid) complex Gaussian random variables with zero mean and unit variance The direct links from the sources {S i } to the destinations {D i } have been ignored due to deep path loss The input-output relation between S and D is r = U H H DS V s + U H n D (1) the d 1 vector s and r denote the transmitted signal at S and the received signal at D, and d is the the N D N1 D 1 NK D K number of parallel data streams The M d matrix V denotes the precoder at S, and V H V = I d TheN d matrix U denotes the receiver at D, and U H U = I d The d d diagonal matrix P is the power allocation matrix of S with P = E[s s H ], tr(p ) = P PU, P PU is the transmit power of S and E[ ] denotes mathematical expectation The N 1 vector n D is noise signal, whose entries are iid Gaussian variables with zero mean and σ 2 variance The interferences from the secondary users will be canceled, so (1) does not include any interference signal Let H DS = U Λ V H be a singular value decomposition (SVD) of H DS, with two unitary matrices U and V with dimension N N and M M respectively, and N M diagonal matrix Λ Thed columns of U and V form U and V, respectively The power allocation matrix P can be obtain based on the water-filling method [16] With the help of L two-hop relays, K secondary sourcedestination pairs access the same spectrum with the primary link at the same time The data transmission is over two timeslots of equal length In the first time-slot, S i (i =1,,K) transmit signals to R l (l =1,,L) The received signals at the relays are given by y Rl = H Rl S i V i s i +H Rl S V s +n Rl, l =1,,L (2) the d i 1 vector s i denotes the signal transmitted by S i, d i is the number of parallel data streams of the S i -D i link The M i d i matrix V i denote the precoder at S i P i = E[s i s H i ] is the d i d i power allocation matrix, tr(p i )=P Si, and P Si is the transmit power of S i LetP S be the total transmit power of the sources, P Si = P S /K TheJ l 1 vector n Rl denotes noise signal, whose entries are iid Gaussian variables with zero mean and σ 2 variance In the second time-slot, relay R l forwards the received signal to the destinations The transmit signal of R l is generated by filtering y Rl through beamforming filter W l, and is given by x Rl = W l y Rl, l =1,,L (3) The transmit power of R l is = tr [ ( K V i P i Vi H H H R l S i + σ 2 ) ] I Jl W H l (4) P Rl i= The total transmit power of all relays is P R = L P R l The received signal at D i after the receiver U i is given by r Di = V i s i + k=1 W l H Rl S k V k s k + W l H Rl S V s + U H i H DiS V s + W l n Rl + U H i n Di () 664

3 n Di is the noise signal at D i The maximum rate from S i to D i is given by R i (W, V i, U i )= 1 [ ] 2 log 2 det I + Ĥ DiS i P i Ĥ H D is i Q 1 i Q i = + k=1 Ĥ DiS i = (6) V i (7) W l H Rl S V P V H H H R l S Wl H H H D ir l U i + σ 2 W l W H l H H D ir l U i + σ 2 I di (8) W = {W 1, W 2,,W L } denotes the set of all relay beamforming filters The sum rate of the secondary users is given by R sum (W, V, U) = R i (W, V i, U i ) (9) V = {V 1, V 2,,V K } denotes the set of all precoder matrices of the sources, and U = {U 1, U 2,,U K } denotes the set of all receiver matrices of the destinations It can be seen from ()-(9) that interferences from the primary transmitter and among the secondary users degrade the sum rate of the secondary users III TRANSCEIVER DESIGN FOR THE SECONDARY USERS The non-regenerative relays amplify the noise signal components when forwarding the desired signals Ensuring canceling the interferences from the secondary users to the primary receiver, the interferences from the primary transmitter to the secondary users, and the interferences among the secondary users, the zero-forcing precoders V = {V 1,,V K }, receivers U = {U 1,,U K }, and relay beamforming fiters W = {W 1,,W L } are designed to minimize the total amplified noise power received at the destinations The problem is described as follows min σ 2 W l 2 F (1) W,V,U s t U H H DS i V i =, i =1,,K (11) U H H DR l W l =, l =1,,L (12) U H i H DiS V =, i =1,,K (13) W l H Rl S k V k =, i {1,,K}, k {, 1,,K}, k = i (14) tr [ ( K V i P i Vi H H H R l S i i= +σ 2 I Jl ) W H l ] = PR (1) (11) means the interferences from {S i } to D are canceled, (12) means the interferences from the {R l } to D are canceled, (13) means {D i } cancel the interferences from S, (14) means the inter-secondary-user interferences and the interferences from S amplified by {R l } are canceled, (1) means the total relaying power constraint The precoders V should satisfy (11) Let H DS i = U H H DS i, (16) W l H Rl S k V k P k Vk H H H R l S k Wl H H H D ir l U i then V i can be constructed by selecting d i bases from null( H DS i ) Note that the dimension of null( H DS i ) is T i = M i d,sod i T i The receivers U should satisfy (13) Let H DiS = H DiS V, (17) then U i can be constructed by selecting d i bases from null( H H D is ) The dimension of null( H H D is ) is Q i = N i d, so d i Q i Hence, the number of data streams of each sourcedestination pair should satisfy d i min(m i d,n i d ) (18) After obtaining V and U, we find W as follows Let H DiR l = (19) H DR l = U H H DR l (2) H Rl S i = H Rl S i V i (21) Employing the property of Kronecker product [17] (12) can be expressed as vec(abc) =(C T A)vec(B) (22) Bw = (23) I J1 H DR 1 B = I JL H DR L w = (24) [ vec(w 1 ) T,,vec(W L ) T ] T (2) L The dimension of B is d J l L J l 2 The above equation has non-zero solutions when J l >d, l =1,,L Let H Rl S i =[ H Rl S,, H Rl S i 1, H Rl S i+1,, H Rl S K ] (26) then employing (22), (14) can be turned into A i w = (27) [ ] A i = H T R1Si H DiR 1,, H T RLSi H DiR L (28) and i {1,,K} Stack the K equations in (27), we have Aw = (29) 66

4 The dimension of A is K d Kk= i A =[A T 1,,A T K] T (3) d k L J 2 l Let C =[A T, B T ] T (31) Since (23) and (29) are supposed to be satisfied at the same time, w null(c) A non-zero solution of w can be found when K L Jl 2 > d i d k + d J l (32) The dimension of null(c) is N C = Jl 2 k= d i K k= d k d L J l (33) ASVDofC is C = U C Λ C VC HPickN C column vectors c 1, c 2,,c NC which are corresponding to the zero singular values, and form matrix Then w can be written as C null =[c 1, c 2,,c NC ] (34) w = C null a (3) the N C 1 vector a denotes the addition weights for the vectors Applying (22), we have H DiR l W l 2 F = w H A DiRw (36) I J1 H H D ir 1 H DiR 1 A DiR = I JL H H D ir L H DiR L (37) The optimization target function (1) can be written as σ 2 H DiR l W l 2 F = a H à np a (38) à np = σ 2 C H null power constraint (1) can be rewritten as P R = E l = B pc = ( K ) A D ir C null Applying (22), the (E T/2 l I Jl )vec(w l ) 2 F = a H B pc a (39) H Rl S i P i H H R l S i + σ 2 I Jl, l =1,,L (4) i= E /2 1 E T/2 1 I J1 E /2 L ET/2 L I J L (41) Average sum rate (bps/hz) Porposed Fig 2 Average sum rate of the secondary users vs (K =2sourcedestination pairs and L =3relays) B pc = C H nullb pc C null (42) Thus the transceiver design optimization problem is transform into the problem below Let min a H à np a a (43) s t a H B pc a = P R and this problem can be transformed to b =1/ P R B 1/2 pc a (44) min b b H B H/2 pc à np B 1/2 pc b s t b H b =1 (4) Take eigenvalue decomposition to B H/2 pc à np B 1/2 pc, and the eigenvector b corresponding to the smallest eigenvalue is the optimal solution of the above problem So the optimal solution of w is w = P R C null B 1/2 pc b (46) The solution w can be unvectorized into the relay beamforming filter set W = {W 1,,W L } IV SIMULATION RESULTS Computer simulations have been carried out to the performances of the proposed transceiver design algorithm The signal-to-noise ratio (SNR) of the primary user is defined as SNR PU = P PU /σ 2 (47) and the SNR of the secondary users is defined as =(P S + P R )/σ 2 (48) In the simulations, P S = P R, and equal power allocation scheme is applied at each source, ie P i = (P S /Kd i )I di, i = 1,,K The proposed algorithm is compared with the existing scheme The existing scheme has 666

5 Average rate (bps/hz) Proposed Fig 3 Average rate of the primary user vs (K = 2 sourcedestination pairs and L =3relays) Average sum rate (bps/hz) Proposed Fig 4 Average sum rate of the secondary users vs (K =4sourcedestination pairs and L =relays) Average rate (bps/hz) Proposed Fig Average rate of the primary user vs (K = 4 sourcedestination pairs and L =relays) the same zero-forcing precoders and receivers at {S i } and {D i } with the proposed algorithm, but has simple relay beamforming filters, which are written as W l = γi Jl,,,L, P R / L tr(e l) restricts the total power to be γ = P R The antenna numbers of the primary transmitter and receiver are M = N =2, the data stream number is d =1, and the SNR of the primary user SNR PU =1dB Two system configurations of the secondary users have been considered In the first configuration, the secondary users include K =2 source-destination pairs and L = 3 relays The antenna numbers of the secondary sources and destinations are M i = N i =3(i =1, 2), the antenna numbers of the relays are J l =3(l =1, 2, 3), and the data stream numbers are d i =2 The average sum rate of the secondary users versus the SNR of the secondary users is shown in Fig 2 When 6dB, the sum rate using the proposed algorithm is slightly lower than the existing scheme This is because the interference power is low and is not the main cause degrading the rate performance when the SNR is low When > 6dB, the sum rate using the proposed algorithm grows significant with the SNR, but the rate performance of the existed algorithm grows much slower When =2dB, the sum rate of the proposed algorithm is more than two times of the rate of the existed algorithm This is because the proposed algorithm cancels interferences which is the main rate degrading cause in the high SNR regime The average rate of the primary link versus the SNR of the secondary users is shown in Fig 3 Since the proposed algorithm cancels the interferences from the secondary users to the primary receiver, the average rate of the primary link is unaffected by the secondary user However, applying the existed scheme, the rate of the primary link decrease rapidly with the growing SNR of the secondary users This is because the signals from the relays cause great interferences when using the existing non-zero-forcing scheme In the second configuration, the secondary users include K = 4 source-destination pairs and L = relays The antenna numbers of the secondary sources and destinations are M i = N i =4(i =1,,4), the antenna numbers of the relays are J l =6(l =1,,), and the data stream numbers are d i =3 The average sum rate of the secondary users versus the SNR of the secondary users is shown in Fig 4 The results are similar to the first configuration When 1dB, the sum rate using the proposed algorithm is slightly lower than the existing scheme When > 1dB, the sum rate using the proposed algorithm grows significant with the SNR, but the rate performance of the existed algorithm grows much slower When =2dB, the sum rate of the proposed algorithm is more than two times of the rate of the existed algorithm The average rate of the primary link versus the SNR of the secondary users is shown in Fig By using the proposed scheme, the average rate of the primary link is unaffected by the secondary user The rate of the primary user applying the 667

6 existing scheme decrease rapidly with the growing SNR of the secondary users V CONCLUSION The transceiver design problem has been considered in a MIMO cognitive relay network with point-to-point MIMO primary link and multiple two-hop secondary source-destination pairs assisted by multiple relays Ensuring canceling interferences from the secondary users to the primary receiver, interferences from the primary transmitter to the secondary users, and the inter-user interferences among the secondary users, a zero-forcing scheme has been proposed to minimize the noise power amplified by the relays Simulation results show the novelty of the proposed algorithm REFERENCES [1] S Haykin, Cognitive radio: brain-empowered wireless communications, IEEE J Select Areas Commun, vol 23, no 2, pp 21-22, 2 [2] L Luo, P Zhang, G Zhang, and J Qin, Outage Performance for Cognitive Relay Networks with Underlay Spectrum Sharing, IEEE Commun Lett, vol 1, no 7, pp , 211 [3] J N Laneman, D N C Tse, and G W Wornell, Cooperative diversity in wireless networks: Efficient protocols and outage behavior, IEEE Trans Inf Theory, vol, no 12, pp , 24 [4] G Zhang, G Li, and J Qin, Fast antenna subset selection algorithms for multiple-input multiple-output relay systems, IET Commun, vol 3, no 11, pp , Nov 29 [] G Zhang, W Zhan, and J Qin, Power Allocation in Decode-and- Forward Cooperative OFDM Systems Using Perfect and Limited Feedback, Chinese Journal of Electronics, vol 19, no 2, pp , 21 [6] G Zhang, W Zhan, and J Qin, Transmit antenna selection in the Alamouti-coded MIMO relay systems, Wireless Personal Commun, vol 62, no 4, pp , 212 [7] X Tang and Y Hua, Optimal Design of Non-Regenerative MIMO Wireless Relays, IEEE Trans Wireless Commun, vol 6, no 4, pp , 27 [8] C Esli, S Berger, and A Wittneben, Optimizing Zero-Forcing Based Gain Allocation for Wireless Multiuser Networks, Proc ICC 27, Glasgow, pp 82-83, 27 [9] C Wang, H Chen, Q Yin, A Feng, and A F Molisch, Multi-User Two-Way Relay Networks with Distributed Beamforming, IEEE Trans Wireless Commun, vol 1, no 1, pp , 211 [1] A El-Keyi and B Champagne, Cooperative MIMO-beamforming for multiuser relay networks, Proc ICASSP 28, Las Vegas, NV, pp , 28 [11] H Chung, N Lee, B Shim, and T Oh, On the Beamforming Design for MIMO Multipair Two-Way Relay Channels, IEEE Trans Veh Tech, vol 61, no 7, pp , 212 [12] S M Perlaza, N Fawaz, S Lasaulce, and M Debbah, From Spectrum Pooling to Space Pooling: Opportunistic Interference Alignment in MIMO Cognitive Networks, IEEE Trans Signal Process, vol 8, no 7, pp , 21 [13] M Amir, A El-Keyi, and M Nafie, Constrained Interference Alignment and the Spatial Degrees of Freedom of MIMO Cognitive Networks, IEEE Trans Inf Theory, vol 7, no, pp , 211 [14] Q Li, L Luo, and J Qin, Optimal relay precoder for non-regenerative MIMO cognitive relay systems with underlay spectrum sharing, Electronics Lett, vol 48, no, pp , 212 [1] Q Li, R Feng, and J Qin, Optimal relay precoding for spectrum sharing multi-hop MIMO cognitive radio networks, Electronics Lett, vol 48, no 24, pp , 212 [16] E Telatar, Capacity of multi-antenna gaussian channels, Euro Trans Telecommun, vol 1, no 6, pp 8-9, 1999 [17] X Zhang, Matrix Analysis and Applications Beijing, China: Tsinghua University Press,