Resource Allocation for OFDM and Multi-user. Li Wei, Chathuranga Weeraddana Centre for Wireless Communications

Transcription

1 Resource Allocation for OFDM and Multi-user MIMO Broadcast Li Wei, Chathuranga Weeraddana Centre for Wireless Communications University of Oulu

2 Outline Joint Channel and Power Allocation in OFDMA System Resource Allocation in Multi-user MIMO System

3 Joint Channel and Power Allocation in OFDMA System Background Existing lots of resource allocation algorithms for OFDMA systems Existing lots of resource allocation algorithms for OFDMA systems Two problems Throughput maximization and power minimization Focus on the efficiency and fairness tradeoff Resource based fairness Utility based fairness Weighted throughput maximization under total power or individual power constraints ([1 6, 8, 10, 12]) Weighted power minimization under individual data rate constraints ([7-9]) Non-convex optimization ([13])

4 Joint Channel and Power Allocation in OFDMA System We consider two problems in OFDMA downlink 1, weighted throughput maximization under total power constraint 2, Throughput maximization under total power constraint and individual user data rate requirement

5 Joint Channel and Power Allocation in OFDMA System Weighted throughput maximization under total power constraint Problem formulation

6 Joint Channel and Power Allocation in OFDMA System Weighted throughput maximization under total power constraint An relaxation is used to solve the problem

7 Joint Channel and Power Allocation in OFDMA System Weighted throughput maximization under total power constraint Using primal decomposition p m Master problem Secondary problem p km

8 Joint Channel and Power Allocation in OFDMA System Weighted throughput maximization under total power constraint The secondary problem is maximizing a convex function, therefore the maximum solution must be at the extreme points The optimal

9 Joint Channel and Power Allocation in OFDMA System Weighted throughput maximization under total power constraint Solving master problem Because the following function is non-concave The conventional gradient or sub-gradient for convex optimization cannot be utilized Weighted waterfilling can provide a suboptimal solution

10 Joint Channel and Power Allocation in OFDMA System Weighted throughput maximization under total power constraint The summarization of approximate primal decomposition method (APD)

11 Joint Channel and Power Allocation in OFDMA System Weighted throughput maximization under total power constraint Numerical results Numerical results Capacity regions under deterministic channel 2 users and 8 subcarriers

12 Joint Channel and Power Allocation in OFDMA System Weighted throughput maximization under total power constraint Numerical results Numerical results Mean ratio and variance comparison of APD and WSRmax v.s. Exhaustive searching under random generated channels 2 users and 8 subcarriers

13 Joint Channel and Power Allocation in OFDMA System Weighted throughput maximization under total power constraint Numerical results Numerical results Mean ratio and variance comparison of APD v.s. WSRmax The number of users are 2, 4 and 8 The number of subcarriers are 128, 256 and 512

14 Joint Channel and Power Allocation in OFDMA System Throughput maximization under total power constraint and individual user data rate requirement Problem formulation

15 Joint Channel and Power Allocation in OFDMA System Throughput maximization under total power constraint and individual user data rate requirement Dual problem and decomposition Secondary problem Master problem

16 Joint Channel and Power Allocation in OFDMA System Throughput maximization under total power constraint and individual user data rate requirement The secondary problem is a weighted sum maximization problem Subgradient method can be used to solve the master problem

17 Joint Channel and Power Allocation in OFDMA System Throughput maximization under total power constraint and individual user data rate requirement Numerical results

18 Joint Channel and Power Allocation in OFDMA System Throughput maximization under total power constraint and individual user data rate requirement Numerical results Average number of the satisfied users Average throughput of each user

19 Joint Channel and Power Allocation in OFDMA System Conclusions APD can achieve almost as good performance as WSRmax and exhaustive search and it converges very fast in our simulations Both considering the power constraints and individual user data rate constraints can achieve higher user satisfactory

20 Joint Channel and Power Allocation in OFDMA System References 1. Zhiwei. Mao and X. Wang, Branch-and-bound approach to ofdma radio resource allocation, IEEE VTC 2006-Fall, pp. 1 5, May W. Rhee and M. Cioffi, Increase in capacity of multiuser ofdm system using dynamic subchannel allocation, IEEE VTC 2000-Spring Tokyo, vol. 2, pp , May J. Tellado and M. Cioffi L. M. C. Hoo, B. Halder, Multi user transmit optimization for multiuser broadcast channels: Asymptotic fdma capacity region and algorithms, IEEE Trans. Comm., vol. 52, no. 6, pp , Jun G. Li and H. Liu, On the optimality of the ofdma systems, IEEE Commun. Lett., vol. 9, no. 5, pp , May J. Jang and K. B. Lee, Transmit power adaptation for multiuser ofdm systems, IEEE Trans. Comm., vol. 21, no. 2, pp , Feb M. Mohseni and M. Cioffi K. Seong, Optimal resource allocation for ofdma downlink systems, ISIT. Seattle, USA, pp , Jul K. B. Letaief C. Y. Wong, R. S. Cheng and R. D. Murch, Multiuser ofdm with adaptive subcarrier, bit, and power allocation, IEEE J. Select. Areas Commun, vol. 17, no. 10, pp , Oct Guodong Zhang, Subcarrier and bit allocation for real-time services in multiuser ofdm systems, IEEE ICC 06., vol. 5, pp , June D. P. Palomar and M. Chiang, Alternative distributes algorithms for network utility maximization: Framework and applications, IEEE Trans. Automatic Control., vol. 52, no. 12, pp , Dec S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, UK, D. P. Bertsekas, NETWORK OPTIMIZATION CONTINUOUS AND DISCRETE MODELS, Belmont, MA, USA: Athens Scientific, R. T. Rockafellar, Convex Analysis, NJ: Prinston University Press, Princeton, Z. Shen, J. G. Andrews and B. L. Evans, Adaptive Resource Allocation in Multiuser OFDM Systems With Proportional Rate Constraints, IEEE Trans. Wireless. Comm., vol. 4, no. 6, pp , Nov

21 Resource Allocation in Multi-user MIMO Background 1995 & 1996, [1,2] reported the extra spatial diversity can be obtained in single user MIMO system & 1999, [3,4] provided the theoretic capacity region of MIMO MAC Convex problem 2001, [5] proposed an iterative algorithm to calculate the MIMO MAC sum capacity 2003, [6] presented the MIMO BC capacity region Based on Dirty Paper Coding (DPC) Non-convex 2003 & 2004, [7,8] established the duality between the MIMO BC (DPC) and MIMO MAC capacity regions [7] also proposed a similar iterative algorithm as [5] to calculate MIMO BC sum capacity 2005 & 2006, [9,10,11] proved ZFBF holding the same optimality as DPC in MIMO BC If the number of candidate users is large enough, e.g. 200 or more Propose two semi-orthogonal opportunistic user scheduling algorithm Never consider receiver cooperation 2002 & 2004, [12-15] proposed generalized ZFBF with receiver cooperation Some users may have multiple receive antennas Block diagonalization on the channel matrix Have the so-called dimensionality problem 2003, [16,17] suggested combining users post-processing at the receiver side with their real channel The dimensionality problem can be avoid No efficient way to find the optimal

22 Resource Allocation in Multi-user MIMO MIMO Broadcast System Base station User 1 s data stream M User K s data stream M Preprocessing Postprocessing M User 1 M M Postprocessing User K

23 Resource Allocation in Multi-user MIMO Generalized Zero Force (GZF) Approach The performance of GZF depends on User Scheduling Precoder Selection Power Allocation

24 Resource Allocation in Multi-user MIMO Precoder selection and power allocation In the conventional proposals, p SVD is used to find the precoder Consider the following sum capacity maximization

25 Resource Allocation in Multi-user MIMO Precoder selection and power allocation Summarization of the SVD based block diagonalization method

26 Resource Allocation in Multi-user MIMO User scheduling For ZF beamforming A successive projection based SUS (SUP-SUS), based on the Gram-Schmidt orthogonalization was proposed in [9] Maximum weighted clique (MWC) and greedy weighted clique (GWC), were further developed in [10] A full connected subgraph searching problem of a graph A sequential water-filling SUS (SWF-SUS) and its improved version were proposed in [18] and [19] Capacity based greedy algorithm A Frobenius norm-based SUS (FROBINV-SUS) was proposed in [20] Minimize the frobenius norm of the inverse of the composite channel matrix For GZF Treat different users receive antenna as an independent virtual users, SUS for ZFBF can be applied A lot of SVD-BD operations degrade the efficiency A capacity-based SUS (CAP-SUS) was proposed [21] Using SVD-BD to calculate the capacities of all candidate users A Frobenius norm-based SUS (FROB-SUS) was proposed in [21] Maximizing the frobenius norm of the composite channel matrix Some other improved SUS with receive antenna selections

27 Resource Allocation in Multi-user MIMO Precoder selection and power allocation We propose a precoder structure based on pseudo inverse method for GZF Prove the optimality Using our proposed pseudo inverse based precoder, the Using our proposed pseudo inverse based precoder, the generalized sequential waterfilling SUS is proposed for GZF Utilize the sequential calculation nature of pseudo inverse, the complexity can be reduced considerably

28 Resource Allocation in Multi-user MIMO With pseudo inverse precoder, the sum capacity optimization can be transformed into

29 Resource Allocation in Multi-user MIMO Complexity analysis 4 transmit antennas 2 users 2 receive antennas SVD-BD: 4282 flops PINV-BS: 1704 flops

30 Resource Allocation in Multi-user MIMO User scheduling

31 Resource Allocation in Multi-user MIMO User scheduling Similar as [21], Frobenius norm can be used as an approximation of the sum capacity for complexity reduction purpose GFROB2-SUS is proposed based on the Frobenius norm where maximizing the effective channel energy (MaxECE) and minimizing equivalent noise power (MinENP) criterions ions can be utilized

32 Resource Allocation in Multi-user MIMO Numerical results Sum capacity vs user numbers SNR P T /(N T N 0 ) The achieved sum ca apacity (bps/hz) CAP SUS FROB2 SUS GSWF SUS GFROB2 SUS MaxECE BFROB2 SUS MinENP SNR is 6 db SNR is 15 db SNR is 0 db The number of candidate users

33 Resource Allocation in Multi-user MIMO Numerical results Sum capacity vs SNR Average e sum capacity (bps/hz z) CAP SUS FROB2 SUS GSWF SUS GFROB2 SUS ECE GFROB2 SUS MinENP Average SNR (db) Average sum capacity (bsp/hz) CAP SUS FROB2 SUS GSWF SUS GFROB2 SUS MaxECE GFROB2 SUS MinENP Average sum capacity (bps/hz) CAP SUS FROB2 SUS GSWF SUS GFROB2 SUS MaxECE GFROB2 SUS MinENP Average SNR (db) Average SNR (db)

34 Resource Allocation in Multi-user MIMO Conclusions The optimal precoder of GZF has pseudo inverse based structure With pseudo inverse based precoder, the sum capacity maximizatin of GZF is transformed into an equivalent problem which can be solved by sequential waterfilling Require less complexity than the conventional SVD method Using the proposed precoder, opportunistic user scheduling and receive antenna can be done more efficiently

35 Resource Allocation in Multi-user MIMO References [1] I. E. Telatar, "Capacity of multi-antenna Gaussian channels," Bell Labs Techical Memorandum, [2] G. J. Foschini, "Layered space-time architecture for wireless communication in fading environments when using multi-element antennas, " Bell Labs Techn. J., pp:41-59, Autumn [3] D. Tse and S. Hanly, "Multi-access fading channels: Part I: Polymatroid structure, optimal resource allocation and throughput capacities," IEEE Trans. on Info. Th., vol. 44, pp: , Nov [4] Wei Yu, Wonjong Rhee, Stephen Boyd, John M. Cioffi, "Iterative Water-filling for Gaussian Vector Multiple Access Channels," ISIT2001, Washington DC, June [5] Giuseppe Caire and Shlomo Shamai (Shitz), "On the Achievable Throughput of a Multi-antenna Gaussian Broadcast Channel," IEEE Trans. on Info. Th., vol. 49, No. 7, July [6] N. Jindal, S. Vishwanath, and A. Goldsmith, "On the duality of Gaussian channel and uplink-downlink duality," IEEE Trans. on Info. Th., Vol. 50, No. 5, pp: , May [7] P. Viswanath and D. N. Tse, "Sum capacity of the vector Gaussian channel and uplink-downlink duality," IEEE Trans. Info. Th., Vol. 49, No. 8, pp: , Aug [8] Wei Yu and J. Cioffi, "Sum capacity of Gaussian vector broadcast channels," IEEE Trans. Info. Th., Vol. 50, pp: , Sept [9] T. Yoo and A. Goldsmith, "Optimality of zero-forcing beamforming with multiuser diversity," in Proc. IEEE Int. Conf. Comm., pp: , May [10] T. Yoo and A. Goldsmith, "Sum-rate optimal multi-antenna downlink beamforming strategy based on clique search," in Proc. IEEE GLOBECOM, pp: , Nov [11] T. Yoo and A. Goldsmith, "On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming," IEEE J. Select. Areas Comm., Vol. 24, pp: , March [12] M. Rim, "Multi-user downlink beamforming with multiple transmit and receive antennas," Electronics Letters, Vol. 38, No. 25, pp: , [13] Q. H. Spencer, A. L. Swindlehurst and M. Haardt, "Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels, " IEEE Trans. Signal Processing, Vol. 52, No. 2, pp: , [14] Q. H. Spencer and M. Haardt, "Capacity and downlink transmission algorithms for a multi-user MIMO channel," in Proc. 36th Asilomar Conference on Signals, Systems and Computers, Vol. 2, pp: , Pacific Grove, Calif, USA, Nov [15] Lai-U Choi and Ross. D. Murch, "A transmit pre-processing technique for multi-user MIMO systems using a decomposition approach," IEEE Trans. on Wireless Commu., Vol. 3, No. 1, pp:20-24, Jan [16] B. Farhang-Boroujeny, Q. Spencer and A. Swindlehurst, "Layering techniques for space-time communication in multi-user networks," in IEEE 58th Vehicular Technology Conference, Vol. 2, pp: , 1343, Orlando Fla USA, Oct [17] Z. G. Pan, K. K. Wong and T. S. Ng, "MIMO antenna system for multi-user multi-stream orthogonal space division multiplexing," in Proc IEEE International Conf. on Commu., Vol. 5, pp: , Anchorage Alaska USA, May [18] Goran Dimic and Nicholas D. Sidiropoulos, On Downlink Beamforming With Greedy User Selection: Performance Analysis and a Simple New Algorithm, IEEE Trans. On Signal Processing, Vol. 53, No. 10, Oct [19] J. Wang, D. J. Love and M. D. Zoltowski, User selection for MIMO broadcast channel with sequential water-filling, in Allerton Conference on Communication, Control and Computing. [20] J. Wang, D. J. Love and M. D. Zoltowski, User selection for the MIMO broadcast channel with a fairness constraint, in ICASSP 2007 [21] Zukang Shen, Runhua Chen, Jeffrey G. Andrews, Robert W. Heath, Jr. and Brian L. Evans, "Low Complexity User Selection Algorithms for Multiuser MIMO Systems with Block Diagonalization," IEEE Trans. Signal Processing, Vol. 54, No. 9, pp: , Sept

36 Thanks! Questions?