Mode Selection for Multi-Antenna Broadcast Channels

Transcription

1 Mode Selection for Multi-Antenna Broadcast Channels Gill November 22, 2011 Gill (University of Delaware) November 22, / 25

2 Part I Mode Selection for MISO BC with Perfect/Imperfect CSI [1]-[3] Gill (University of Delaware) November 22, / 25

3 System model BS Nt antennas Figure: MISO BC U users... MISO BC with U users in total (U N t ). N t antennas at BS, single antenna at each user. Single data stream for each user. Equal transmit power for each active user. Rayleigh fading channel with no pathloss. Gill (University of Delaware) November 22, / 25

4 System model (cont.) The received signal at the lth user: y l = P P M hh l q l x l + M M h H j q j x j + n l, (1) where M: number of active users, i.e., M = 1,2,,min{N t,u}. x l : the data symbol for lth user with energy constraint E[ x l 2 ] 1. BS allocates transmit power P equally to all active users ( P M ). h l : N t 1 channel vector for lth user. It is complex Gaussian with zero mean and unit variance. q l : N t 1 beamforming vector for lth user. n l : complex circular-symmetric Gaussian noise with zero mean and unit variance at lth user. j=1 j l Gill (University of Delaware) November 22, / 25

5 Perfect CSI [1] SU-MISO (matched filter precoding): q = h h R CSI (1) = E h [log 2 (1 + P h H q 2 )] = log 2 (e)e P 1 N t 1 = R BF (P,N t ), k=0 Γ( k, 1 P ) P k where Γ(α,x) = x tα 1 e t dt is the complementary incomplete gamma function. MU-MISO (zero-forcing): h H l q j = 0, l j M independent channels. R CSI (M) = M E h [log 2 (1 + M P hh l q l 2 )] l=1 = MR BF ( P M,N t M + 1). (2) (3) Mode selection: M opt = arg max R CSI(M). (4) 1 M min{n t,u} Gill (University of Delaware) November 22, / 25

6 the operating regions change if there are delay and channel quantization. SU/MU switching w/ perfect CSI simulation [2] rate is give R ( B BF region ZF region B. Zero-for Rate (bps/hz) γ=7.77 db 4 BF (simulation) BF (calculation) 2 ZF (simulation) ZF (calculation) SNR, γ (db) With del on the out h u[n D] interference Therefore, h SINR Fig. 1. Mode switching with perfect CSIT, N t =4. Figure: Mode switching with perfect CSI, N t = 4, M = N t, and γ = P. The SINR d which is de Theorem Gill (University of Delaware) November 22, / 25

7 Imperfect CSI [1] CSI delay model: the channel vector at time n h[n] = ρh[n 1] + e[n], (5) where e[n] is the channel error vector with i.i.d entries e i [n] CN(0,ɛ 2 e ), ɛ 2 e = 1 ρ 2. ρ = J 0 (2πf d T s ), where f d is the Doppler spread, T s is the symbol duration and J 0 is the zero-th order Bessel function of the first kind. Channel quantization: the channel direction information is fed back using a quantization codebook known at both Tx and Rx. E[ h H l N t ĥ l 2 ] = 1 2 B β(2 B, ), (6) N t 1 where h l = h l h l is the channel direction, ĥl is the quantized channel information, B is the code size, and β(x,y) is the Beta function. 1 2 N B t 1 E[ h H l ĥ l 2 ] 1 N t 1 2 B N t 1. (7) N t Gill (University of Delaware) November 22, / 25

8 Imperfect CSI (cont.) SU-MISO (matched filter precoding): q (QD) = ĥ[n 1] Lower bound of average achievable rate R QD (1) is expressed by (11) in [3] through removing channel error vector e[n]. MU-MISO (zero-forcing): ĥl[n 1] H q (QD) = 0, l j j Approximated average sum rate R QD (M) is expressed by (17) in [1], where the cross term of e[n] and h[n 1] is removed. Mode selection: M opt = arg max 1 M N t R QD (M). (8) Gill (University of Delaware) November 22, / 25

9 ral SU/MU switching w/ ANDimperfect KEY OBSERVATIONS CSI simulation [3] (19) IV. NUMERICAL RESULTS : VERIFICATION OF ANALYSIS I- i l- i --e-- M=1 (Simulation) 18 --M=1 (Approximation) "in ~ 12 Q) ~ M=2 (Simulation) - - M=2 (Approximation) -T- M=3 (Simulation) M=3 (Approximation) ----A-- M=4 (Simulation) ~ M=4 (Approximation) Q) :0 ssuming that ~ Q) 8 :E nt, and also :t. 6 the SINR can calculated. A 4 m, n), which 2-10 o (15) and (16) y( db) ated as Figure: ModeFig. switching I. Comparison with imperfect of simulations CSI, and N t = approximations 4, f c = 2GHz, forv different = 10km/hr, M, T s = 1ms, N; = 4, mobility v = 10 kmlhr, 1'8 = 1 msec, and B = 18. M B = 18 bits, users are (20) and ' randomly γ = P. selected from U users, U 2': N i, as follows. We first verify the derived approximations in Fig. I. We see Gill (University of Delaware) November 22, / 25

10 -th user in M>1at s SU/MU switching w/ imperfect CSI simulation [1], i, L + i), (22) for limited n in (21). th δ 1 =0. amforming he highest nd channel Dominant MU Mode B=30 B=20 B=10 (23) (M) given Normalized Doppler frequency, f T d s mode M array gain, MMT is to Fig. 2. The MU mode with the highest rate ceiling for different f d T s, with Figure: N t =4. MU mode with the highest rate with imperfect CSI, N t = 4. Gill (University of Delaware) November 22, / 25

11 Part II Mode Selection for MU-MIMO BC with Perfect/Delayed CSI Gill (University of Delaware) November 22, / 25

12 System model BS Nt antennas Figure: MIMO BC U users... MIMO BC with U users in total (U N t ). N t antennas at BS, N r antennas at each user (N r N t ). A user can have more than one stream. Equal transmit power for each stream. Rayleigh fading channel with no pathloss. Gill (University of Delaware) November 22, / 25

13 System model (cont.) The postprocessed signal at the lth user: P y l = G U H P l H l Q l x l + U M l l=1 M l l=1 U G H l H l Q j x j + G H l n l, (9) where M l : number of streams allocated to lth user, M l N r and M l = 0 for unscheduled user. Transmit power is equally allocated to all streams ( x l : M l 1 input vector for lth user with energy constraint E[ x l 2 ] I Ml. y l : M l 1 output vector for lth user. H l : N r N t channel matrix, complex Gaussian with zero mean and unit variance. Q l : N t M l beamforming matrix. G l : N r M l beamforming matrix. n l : complex Gaussian noise with zero mean and unit variance. j=1 j l P ). U M l l=1 Gill (University of Delaware) November 22, / 25

14 Problem description The sum capacity of the system U R = log I + P (G l=1 U H l Σ l G l + I) 1 G H l H l Q l Q H l H H l G l, (10) M l l=1 where Σ l = the lth user. U P U j=1,j l l=1 M l H l Q j Q H j H H l is the interference covariance matrix at Mode selection (stream allocation): M opt l = arg max 1 M l min{n r,n t,u} R(M l). (11) Gill (University of Delaware) November 22, / 25

15 Perfect CSI [4] SU-MIMO (SVD transceiver): H = UΛV H. Number of streams for a single user M = N r < N t. With perfect CSI, SVD is optimal for the point-to-point MIMO link. The average capacity is approximated as R SVD C(β,βP), (12) where C(β,P) = E[logdet(I Nr + P N t HH H )], as N t,n r, N t N r β. Gill (University of Delaware) November 22, / 25

16 Perfect CSI (cont.) MU-MIMO (block diagonalization (BD) precoding): G H l H l Q j = 0, l j BD is zero-forcing when N r = 1. When M l = N r, G H H H Q l l j = 0 H l Q j = 0. G does not affect transmission. Special case: assuming U = N t N r [4], Step 1: BD precoding: H l Q j = 0, l j. Step 2: SVD transceiver: H l Q l = UΛV H. The average rate is approximated as R BD UN r C iso (1, P ), (13) β where the spatial multiplexing gain of BD is UN r, compared to N r for the SVD system. Dual mode selection: SU-MIMO vs. MU-MIMO Gill (University of Delaware) November 22, / 25

17 SU/MU switching w/ perfect CSI simulation [4] SVD (simulation) SVD (approximation) BD (simulation) BD (approximation) be calculated selected. Rate (bps/hz) In this sec with BD pre system with perfect CSIT for the perfe SNR, γ (db) A. SU-MIMO Fig. 1. Approximations and simulations for SVD (SU MIMO) and BD (MU With CSI Figure: Mode switching with perfect CSI, N MIMO) systems with perfect CSIT, N t =4, N r =2. t = 4, N r = 2 and U = 2. channel cann receiver perfo which is on Gill (University of Delaware) November 22, / 25

18 Imperfect CSI [4] [5] special case: U = N t N r & M l = N r SU-MIMO: SVD transceiver based on the delayed channel. R (D) SVD R SVD. (14) MU-MIMO (BD precoding): H l [n 1] H Q (D) [n] = 0, l j (with Delayed j CSI). Upper bound of rate loss due to delay R (D) BD,l = R BD,l R (D) BD,l N r log [(N t N r ) P ] ɛ 2e,l + 1. (15) Nt Asymptotic average sum rate R (D) BD is expressed by (14) in [4] (as N t,n r, N t N r β). MU-MIMO (BD precoding) with quantized CSI is investigated in [5]. Gill (University of Delaware) November 22, / 25

19 SU/MU switching w/ imperfect CSI simulation [4] iance matrix, SVD (simulation) SVD (asymptotic) BD (simulation) BD (asymptotic) N t =6 u[n]+i Nr +I Nr. (12) Rate (bps/hz) N t =4 ound for the system. This eful insights. tion through be used to SNR (db) d for Figure: the rate ModeFig. switching 2. Comparison with imperfect of simulationcsi, and Napproximation t = 4 or 6, Nresults, r = 2, Nf t c =4or= 2GHz, 6, v = 10km/r, and T N r =2, f c =2GHz, terminal speed is 10 km/hr, and delay is 1 msec. s = 1ms. ect CSIT, the tem is upper Gill (University of Delaware) November 22, / 25

20 Mode selection schemes with BD with perfect CSI Mode selection schemes: tree-based search (TMS) [6], successive projections(sp) [7]. User selection: ZFBF semiorthogonal user selection (ZFBF-SUS) [8]. Mode selection user and antenna selection. Each user only selects a subset of receive antennas and disables the remaining ones. one stream corresponds to one receive antenna. Activate the best antenna of the best user at each iteration. Norm-based user/antenna selection algorithm [9]. Capacity-based user/antenna selection algorithm [9]. Gill (University of Delaware) November 22, / 25

21 Robust mode selection schemes with delayed CSI Delayed CSI at BS, perfect CSI at user. Robust user/antenna selection with BD [10] Residual interference due to delayed CSI. Capacity with delayed CSI is estimated using rate loss upper bound (15). The best antenna of the best user with the largest estimated capacity at each iteration. Gill (University of Delaware) November 22, / 25

22 Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings Mode selection w/ imperfect CSI simulation [4] earch scheme 12 capacity vs. speed na set as Φ at which fulfill ed achievable r and receive (12) eedy scheme me under the ity estimation CSIT aware ction sers inactive nna j of user capacity(bps/hz) Greedy Naive Greedy Delayed CSIT Aware SVD Exhaust Naive Exhaust Delayed CSIT Aware speed(km/h) Figure: Average Fig. 1. sumaverage capacity sum capacity vs. speed versuswith speed, imperfect N T =4, N R CSI, =2, P K = =4, 10dB, N t = 4, N r = 2, U = 4, f f c = c = 2GHz, and THz, s = P 1ms. =10dB and the delay is 1ms. ]. (13) capacity vs. SNR Gill (University of Delaware) November 22, / 25

23 Conclusions and future work Conclusions: ZF or BD is applied to decide the beamforming vector/matrix due to its analytical simplicity. Neither SU-MIMO nor MU-MIMO can dominate at all values of SNR. Future work Simulations: Exhaustive search to find out which mode set is the best. Robust mode selection with BD with quantized CSI. Robust mode selection scheme with MMSE transceiver for MIMO BC. Theoretical analysis: capacity approximation of MIMO BC with any number of streams at each user. SU/MU switching. Gill (University of Delaware) November 22, / 25

24 Reference [1] J. Zhang, M. Kountouris, J. G. Andrews, and R. W. Heath, Jr., Multi-mode transmission for the MIMO broadcast channel with imperfect channel state information, IEEE Trans. Commun., vol. 59, no. 3, pp , Mar [2] J. Zhang, J. G. Andrews, and R. W. Heath, Jr., Single-user MIMO vs. multiuser MIMO in the broadcast channel with CSIT constraints, in Proc. of Allerton Conf. on Comm. Control and Comp., Sep [3] J. Zhang, M. Kountouris, J. G. Andrews, and R. W. Heath, Jr., Achievable throughput of multi-mode multiuser MIMO with imperfect CSI constraints, in Proc. of Int. Symp. Inform. Theory, June-July [4] J. Zhang, J. G. Andrews, and R. W. Heath, Jr., Block diagonalization in the MIMO broadcast channel with delayed CSIT, in Proc. of Globecom 2009, pp. 1-6, Nov [5] N. Ravindran and N. Jindal, Limited feedback-based block diagonalization for the MIMO broadcast channel, IEEE J. Sel. Areas Commun., vol. 26, no. 8, pp , Oct Gill (University of Delaware) November 22, / 25

25 Reference (cont.) [6] Y.-U. Jang, H. M. Kwon, and Y. H. Lee, Adaptive mode selection for multiuser MIMO downlink systems, in Proc. of Veh. Technol. Conf. Spring, vol. 4, pp , May [7] A. Tolli and M. Juntti, Scheduling for multiuser MIMO downlink with linear processing, in Proc. of Int. Symp. Personal, Indoor Mobile Radio Commun., pp , Sep [8] T. Yoo and A. Goldsmith, On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming, IEEE J. Sel. Areas Commun., vol. 24, no. 3, pp , Mar [9] R. Chen, Z. Shen, J. G. Andrews, and R. W. Heath Jr., Multimode transmission for multiuser MIMO systems with block diagonalization, IEEE Trans. Signal Processing, vol. 56, no. 7, pp , July [10] J. Xu and L. Qiu, Robust multimode selection in the downlink multiuser MIMO channels with delayed CSIT, in Proc. IEEE Int. Conf. Commun., June Gill (University of Delaware) November 22, / 25