多用户系统的容量及功率控制研究
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摘要
无线网络无论怎样发展,都不可能超越理论上的极限——网络在信息论意义下的容量。研究无线网络的容量问题可以使我们了解技术发展的潜力,发现容量的数学特性能启发我们找出趋近容量的必要条件和充分条件,为实际技术的设计指出探索的方向。
虽然香农公式早已给出了点到点通信的容量公式,但扩展到多用户系统时还需要考虑许多新的问题,包括多用户调度及功率控制、用户间干扰、信道边信息反馈设计等等。同时,关于容量的度量也从单一的标量扩展出了容量域、和容量这样一些新的概念。本文主要研究多用户系统的和容量及功率控制问题,包括蜂窝系统的下行和上行两种场景。主要工作如下：
(一)对于单小区下行多用户场景,研究了量化信道信息条件下的系统和容量问题。论文首先对单小区多用户系统的下行进行建模,然后结合Max C/I调度策略研究了量化信道信息条件下的系统和容量,针对有无功率控制、是否给定量化边界等情形对最优解进行了理论推导,给出了最优的功率、速率及量化边界的联合设计方案。
(二)针对单小区上行多用户场景,研究了能使系统和速率最大的功率控制问题。首先研究了可以达到系统容量的最优的功率控制策略,证明了在用户的峰值功率限制下可以达到系统容量的最优的功率控制为二值功控,即所有被调度的用户都以峰值功率发送；根据这性质,论文进一步推导出了最优的功率控制向量的形式及最优的功率控制为时分控制的充分条件；在此基础上,论文给出了最优的功率控制的求解算法,并提出了一个低复杂度的次优算法。
(三)针对单小区上行多用户场景,分别研究了服务质量约束条件和用户差异化约束条件下的系统和容量及最优的功率分配问题,推导了功率分配最优解的数学性质,然后根据这些数学性质分别给出了服务质量约束条件以及用户差异化情景下的最优功率分配。
(四)研究了多小区多用户场景下的系统容量及功率控制问题。首先讨论了使多小区多用户系统上行和速率最大的最优的功率控制,基于最优解的数学性质,给出了次优的功率控制及和容量的求解算法,然后对多小区多用户系统的下行容量进行了建模和分析。论文在上行的研究模型包含了采用了连续干扰删除技术的场景,针对在多小区上行系统中二值功率控制可以用来近似最优的功率控制的场景,论文提出了一些次优功率控制算法以及考虑了用户公平性的算法。
No mater how fast the evolution speed of the wireless network is, the rate of the wireless network can not transcend the theoretical limits-system capacity of the network under the perspect of information. Study the network theorical capacity can help us to know the developing goal of possible techniques and to explore the potential of the current networks. Besides, study the mathematic characters of system capacity can inspire us to find the neccesary condition and sufficient condition to reach the capacity, which indicates the directors for the design of the practical techniques.
The information capacity for point to point communications was originally arised by Shannon. When extend the Shannon formula to multiuser systems, many problems have to be considered, e.g. multiuser schedule, power control, interferences among users and channel side information feedback designs. At the same time, the measurement of capacity is changed from a single scalar to many new concepts such as capacity region and sum capacity. This paper is focus on sum capacity and power control of multiuser systems. Both downlink and uplink are considered:
(1) For the downlink of single cell multiuser systems, sum capacity with quantized channel side information is studied. The system capacity with quantized channel side information under Max C/I scheduler is studied. The optimal solutions for the scenarios with/without power control, with/without fixed quantization boundaries are derived, and the optimal joint design of power, rate and quantization boundaries are provided.
(2) For the uplink of single cell multiuser systems, the optimal power control for sum rate maximization is studied. It is proved that under the users' peak power constrains, binary power control is optimal, i.e. all scheduled users should transmit with peak power. Based on this property, the structure of the optimal power control is derived, the sufficient condition for time divison scheduler to be optimal scheduler is provided. With these conclusions, the optimal power control algorithm and a low complexity suboptimal algorithm are proposed.
(3) For the uplink of single cell multiuser systems, sum capacity and its optimal power allocation for users with Quality of Service(QoS) requirement and users with experience differentiations are studied respecitively. Mathemetic properties of the optimal power allocation are derived. Based on these properties, the power control for users with QoS constraints and users with different experience are provided respectively.
(4) For multicell multiuser systems, sun capacity and its optimal power control are studied. The optimal power control for uplink systems are analysised fisrtly, based on the properties of the optimal power control, some suboptimal algorithms are provided. Then we discuss the sum capacity of the downlink systems. The system model of uplink includes the cases of base stations with/without successive interference cancelation(SIC) technique. For the scenarios that binary power control can achieve similar performance as the optimal power control, many suboptimal algorithms as well as a fairness algorithm are proposed.
虽然香农公式早已给出了点到点通信的容量公式,但扩展到多用户系统时还需要考虑许多新的问题,包括多用户调度及功率控制、用户间干扰、信道边信息反馈设计等等。同时,关于容量的度量也从单一的标量扩展出了容量域、和容量这样一些新的概念。本文主要研究多用户系统的和容量及功率控制问题,包括蜂窝系统的下行和上行两种场景。主要工作如下：
(一)对于单小区下行多用户场景,研究了量化信道信息条件下的系统和容量问题。论文首先对单小区多用户系统的下行进行建模,然后结合Max C/I调度策略研究了量化信道信息条件下的系统和容量,针对有无功率控制、是否给定量化边界等情形对最优解进行了理论推导,给出了最优的功率、速率及量化边界的联合设计方案。
(二)针对单小区上行多用户场景,研究了能使系统和速率最大的功率控制问题。首先研究了可以达到系统容量的最优的功率控制策略,证明了在用户的峰值功率限制下可以达到系统容量的最优的功率控制为二值功控,即所有被调度的用户都以峰值功率发送；根据这性质,论文进一步推导出了最优的功率控制向量的形式及最优的功率控制为时分控制的充分条件；在此基础上,论文给出了最优的功率控制的求解算法,并提出了一个低复杂度的次优算法。
(三)针对单小区上行多用户场景,分别研究了服务质量约束条件和用户差异化约束条件下的系统和容量及最优的功率分配问题,推导了功率分配最优解的数学性质,然后根据这些数学性质分别给出了服务质量约束条件以及用户差异化情景下的最优功率分配。
(四)研究了多小区多用户场景下的系统容量及功率控制问题。首先讨论了使多小区多用户系统上行和速率最大的最优的功率控制,基于最优解的数学性质,给出了次优的功率控制及和容量的求解算法,然后对多小区多用户系统的下行容量进行了建模和分析。论文在上行的研究模型包含了采用了连续干扰删除技术的场景,针对在多小区上行系统中二值功率控制可以用来近似最优的功率控制的场景,论文提出了一些次优功率控制算法以及考虑了用户公平性的算法。
No mater how fast the evolution speed of the wireless network is, the rate of the wireless network can not transcend the theoretical limits-system capacity of the network under the perspect of information. Study the network theorical capacity can help us to know the developing goal of possible techniques and to explore the potential of the current networks. Besides, study the mathematic characters of system capacity can inspire us to find the neccesary condition and sufficient condition to reach the capacity, which indicates the directors for the design of the practical techniques.
The information capacity for point to point communications was originally arised by Shannon. When extend the Shannon formula to multiuser systems, many problems have to be considered, e.g. multiuser schedule, power control, interferences among users and channel side information feedback designs. At the same time, the measurement of capacity is changed from a single scalar to many new concepts such as capacity region and sum capacity. This paper is focus on sum capacity and power control of multiuser systems. Both downlink and uplink are considered:
(1) For the downlink of single cell multiuser systems, sum capacity with quantized channel side information is studied. The system capacity with quantized channel side information under Max C/I scheduler is studied. The optimal solutions for the scenarios with/without power control, with/without fixed quantization boundaries are derived, and the optimal joint design of power, rate and quantization boundaries are provided.
(2) For the uplink of single cell multiuser systems, the optimal power control for sum rate maximization is studied. It is proved that under the users' peak power constrains, binary power control is optimal, i.e. all scheduled users should transmit with peak power. Based on this property, the structure of the optimal power control is derived, the sufficient condition for time divison scheduler to be optimal scheduler is provided. With these conclusions, the optimal power control algorithm and a low complexity suboptimal algorithm are proposed.
(3) For the uplink of single cell multiuser systems, sum capacity and its optimal power allocation for users with Quality of Service(QoS) requirement and users with experience differentiations are studied respecitively. Mathemetic properties of the optimal power allocation are derived. Based on these properties, the power control for users with QoS constraints and users with different experience are provided respectively.
(4) For multicell multiuser systems, sun capacity and its optimal power control are studied. The optimal power control for uplink systems are analysised fisrtly, based on the properties of the optimal power control, some suboptimal algorithms are provided. Then we discuss the sum capacity of the downlink systems. The system model of uplink includes the cases of base stations with/without successive interference cancelation(SIC) technique. For the scenarios that binary power control can achieve similar performance as the optimal power control, many suboptimal algorithms as well as a fairness algorithm are proposed.
引文
[1]May M, Ilnseher T, Wehn N, et al. A 150Mbit/s 3GPP LTE turbo code decoder[C]. In:Conference on Design, Automation and Test in Europe, European Design and Automation Association,2010:1420-1425.
[2]Kudekar S, Richardson T J, Urbanke R L. Threshold saturation via spatial coupling:Why convolutional LDPC ensembles perform so well over the BEC[J]. IEEE Transactions on Information Theory, vol.57, no.2,2011:803-834.
[3]Hara S, Prasad R. Overview of multicarrier CDMA[J]. IEEE Communications Magazine, vol.35, no.12,1997:126-133.
[4]Sampath H, Talwar S, Tellado J, A fourth-generation MIMO-OFDM broadband wireless system:design, performance, and field trial results[J], IEEE Communications Magazine, vol.40, no.9,2002:143-149.
[5]Li Q, Li G, Lee W, et al. MIMO techniques in WiMAX and LTE:a feature overview[J]. IEEE Communications Magazine, vol.48, no.5,2010:86-92.
[6]Astely D, Dahlman E, Furuskar A, et al. LTE:the evolution of mobile broadband[J]. IEEE Communications Magazine, vol.47, no.4, Apr.2009:44-51.
[7]Shen Z, Papasakellariou A, Montojo J, et al. Overview of 3GPP LTE-advanced carrier aggregation for 4G wireless communications[J]. IEEE Communications Magazine, vol.50, no.2, Feb.2012:122-130.
[8]Claude E. Shannon, A Mathematical Theory of Communication[J]. The Bell System Technical Journal, vol.27,1948:379-423,623-656.
[9]Andrea Goldsmith著,杨鸿文,李卫东,郭文彬等译,《无线通信》,人民邮电出版社,2007.
[10]Nechiporenko T, Phan K T, Tellambura C, et al. On the capacity of Rayleigh fading cooperative systems under adaptive transmission [J]. IEEE Transactions on Wireless Communications, vol.8, no.4, Apr.2009:1626-1631.
[11]Ong L T, Shikh-Bahaei M, Chambers J A. Variable rate and variable power MQAM system based on Bayesian bit error rate and channel estimation techniques[J]. IEEE Transactions on Communications, vol.56, no.2, Feb.2008: 177-182.
[12]Xiaofeng L, Hongwen Y, Wenbin G, et al. Capacity of fading channels with quantized channel side information[J]. IEICE transactions on communications, vol.89, no.2,2006:590-593.
[13]Akbudak T, Simsek M, Zhao B, et al. Symmetric Capacity of Multi-user MIMO Downlink Under Per-Base Station Power Constraints,2011 International ITG Workshop on Smart Antennas, WSA 2011.
[14]L ee J, Jindal N. Symmetric capacity of MIMO downlink channels[C]. In:2006 IEEE International Symposium on Information Theory, IEEE,2006:1031-1035.
[15]Weingarten H, Steinberg Y, Shamai S. The capacity region of the Gaussian multiple-input multiple-output broadcast channel [J]. IEEE Transactions on Information Theory, vol.52, no.9,2006:3936-3964.
[16]Boche H, Jorswieck E A. Sum capacity optimization of the MIMO Gaussian MAC[C]. In:The 5th International Symposium on Wireless Personal Multimedia Communications, IEEE,2002:130-134.
[17]Sigen Ye, Ruick S. Blum, Leonard J. Cimini, Adaptive modulation for variable-rate OFDM systems with imperfect channel information[C]. In:IEEE 55th Vehicular Technology Conference(VTC'02 spring),2002:767-771.
[18]Radaydeh R M, Alouini M S. Adaptive transmit selection with interference suppression[C]. In:2010 5th IEEE International Symposium on Wireless Pervasive Computing (ISWPC), IEEE,2010:33-38.
[19]Ulukus S, Yates RD, Adaptive power control and MMSE interference suppression[J], Wireless Networks, vol.4, no.6,1998:489-496.
[20]Weingarten H, Liu T, Shamai S, et al. The capacity region of the degraded multiple-input multiple-output compound broadcast channel [J]. IEEE Transactions on Information Theory, vol.55, no.11,2009:5011-5023.
[21]Brehmer J, Molin A, Tejera P, et al. A low complexity approximation of the MIMO broadcast channel capacity region[C]. In:IEEE International Conference on Communications, ICC'06, IEEE,Jun.2006:3111-3116.
[22]Sankaranarayanan L, Kramer G, Mandayam N B. Hierarchical sensor networks: capacity bounds and cooperative strategies using the multiple-access relay channel model[C]. In:2004 First Annual IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks, IEEE SECON 2004, IEEE,2004:191-199.
[23]Gupta P, Kumar PR, The capacity of wireless networks[J]. IEEE Transactions on Information Theory[J], vol.46, no.2,2002:388-404.
[24]Kiani S G, Gesbert D. Optimal and distributed scheduling for multicell capacity maximization[J]. IEEE Transactions on Wireless Communications, vol.7, no.1, 2008:288-297.
[25]Huang J, Subramanian V G, Agrawal R, et al. Downlink scheduling and resource allocation for OFDM systems[J]. IEEE Transactions on Wireless Communications, vol.8, no.1,2009:288-296.
[26]Liu X, Yang H. Sum capacity of the reverse link for multi-cell multi-user cellular systems[J]. IEEE Communications Letters, vol.12, no.11,2008: 834-836.
[27]Chandrasekhar V, Shen Z. Optimal uplink power control in two-cell systems with rise-over-thermal constraints [J]. IEEE Communications Letters, vol.12, no.3, 2008:173-175.
[28]Liu E, Leung K. Expected throughput of the proportional fair scheduling over Rayleigh fading channels[J]. IEEE Communications Letters, vol.14, no.6, Jun. 2010:515-517.
[29]Huang J, Subramanian V G, Agrawal R, et al. Downlink scheduling and resource allocation for OFDM systems[J]. IEEE Transactions on Wireless Communications, vol.8, no.1,2009:288-296.
[30]3GPP TS 36.213-b10, Evolved Universal Terrestrial Radio Access (E-UTRA) Physical layer procedures, March 2013.
[31]Mochaourab R, Jorswieck EA, Optimal beamforming in interference networks with perfect local channel information[J], IEEE Transactions on Signal Processing, vol.59, no.3, Mar.2011:1128-1141.
[32]Srinivasa S, Ali Jafar S. Vector channel capacity with quantized feedback[C]. In: 2005 IEEE International Conference on Communications, ICC 2005, IEEE,2005: 2674-2678.
[33]Rajanna A, Jindal N. Multiuser Diversity in Downlink Channels:When Does the Feedback Cost Outweigh the Spectral Efficiency Benefit?[J], IEEE Transactions on Wireless Communications, vol.11, no.1,2012:408-418.
[34]Kim T, Lim J. Capacity Analysis and Feedback Threshold Optimization in Fair Multiuser Diversity System[J], IEEE Transactions on Vehicular Technology, vol. 61, no.9, Nov.2012:4189-4194.
[35]刘晓峰,量化反馈下的信道容量及多小区上行容量研究[学位论文],北京,北京邮电大学,2009.
[36]Ge sbert D, Kountouris M. Resource allocation in multicell wireless networks: Some capacity scaling laws[C]. In:5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks and Workshops, 2007. IEEE,2007:1-7.
[37]Deepthy G S, Susan R J. Analysis of Successive Interference Cancellation in CDMA Systems[C]. In:2012 Second International Conference on Advanced Computing & Communication Technologies (ACCT), IEEE,2012:481-485.
[38]Jemin L, Andrews J G, Daesik H.The Effect of Interference Cancellation on Spectrum-Sharing Transmission Capacity[C]. In:2011 IEEE International Conference on Communications (ICC),2011:1-5.
[39]Ekrem E, Ulukus S. Capacity Region of Gaussian MIMO Broadcast Channels with common and condifential messages [J], IEEE Transactions on Information Theory, vol.58, no.9,2012:5669-5680.
[40]Yongzhe X, Costas N G Some Results on the Sum-Rate Capacity of MIMO Fading Broadcast Channels [J]. IEEE Transactions on Wireless Communications, vol.5, no.2,2006:377-383.
[41]Zhang R, Cui S, Liang Y C. On ergodic sum capacity of fading cognitive multiple-access and broadcast channels[J]. IEEE Transactions on Information Theory, vol.55, no.11,2009:5161-5178.
[42]Inaltekin H, Hanly S. Optimality of binary power-control in a single cell via majorization[C]. In:2011 IEEE International Symposium on Information Theory Proceedings (ISIT). IEEE,2011:2891-2895.
[43]Hosein P. Optimality conditions for throughput maximization on the reverse link of a CDMA network[C]. In:2004 IEEE Eighth International Symposium on Spread Spectrum Techniques and Applications, IEEE,2004:764-768.
[1]Huang Y, Mao S, Li Y. Downlink power allocation for stored variable-bit-rate videos[M], Quality, Reliability, Security and Robustness in Heterogeneous Networks. Springer Berlin Heidelberg,2012:483-498.
[2]Firouzabadi S, Goldsmith A. Downlink performance and capacity of distributed antenna systems[J]. arXiv preprint arXiv:1109.2957,2011.
[3]Ji T, Zhou C, Zhou S, et al. Low complex user selection strategies for multi-user MIMO downlink scenario[C]. In:2007 IEEE Wireless Communications and Networking Conference, WCNC 2007,IEEE,2007:1532-1537.
[4]Xing Zhang, Wenbo Wang, Multiuser frequency-time domain radio resource allocation in downlink OFDM systems:Capacity analysis and scheduling methods[J], Computers & Electrical Engineering, vol.32,2006:118-134.
[5]Iosif O, Banica I. On the analysis of packet scheduling in downlink 3GPP LTE system [C]. In:The Fourth International Conference on Communication Theory, Reliability, and Quality of Service(CTRQ 2011),2011:99-102.
[6]Ikuno J C, Wrulich M, Rupp M. System level simulation of LTE networks[C]. In: 2010 IEEE 71st Vehicular Technology Conference (VTC 2010-Spring), IEEE, 2010:1-5.
[7]Kwan R, Leung C, Zhang J. Proportional fair multiuser scheduling in LTE[J]. IEEE Signal Processing Letters, vol.16, no.6,2009:461-464.
[8]Andrea Goldsmith著,杨鸿文,李卫东,郭文彬等译,《无线通信》,人民邮电出版社,2007.
[9]Xu W, Dong X, Lu W S. MIMO relaying broadcast channels with linear precoding and quantized channel state information feedback[J]. IEEE Transactions on Signal Processing, vol.58, no.10,2010:5233-5245.
[10]Rajanna A, Jindal N. Multiuser Diversity in Downlink Channels:When Does the Feedback Cost Outweigh the Spectral Efficiency Benefit?[J]. IEEE Transactions on Wireless Communications, vol.11, no.1,2012:408-418.
[11]Ban T W, Choi W, Jung B C, et al. Multi-user diversity in a spectrum sharing system[J]. IEEE Transactions on Wireless Communications, vol.8, no.1,2009: 102-106.
[12]Hwang C S, Seong K, Cioffi J. Throughput maximization by utilizing multi-user diversity in slow-fading random access channels[J]. IEEE Transactions on Wireless Communications, vol.7, no.7,2008:2526-2535.
[13]Knopp R, Humblet P A. Information capacity and power control in single-cell multiuser communications[C]. In:1995 IEEE International Conference on Communications, ICC'95, IEEE,1995:331-335.
[14]Xiaofeng L, Hongwen Y, Wenbin G, et al. Capacity of fading channels with quantized channel side information[J]. IEICE transactions on communications, vol.89, no.2,2006:590-593.
[15]3GPP2 C.S0024-A_Version 3.0-2006 CDMA2000 high rate packet data air interface specification Reversion A.,2006.
[1]Dahlman E, Parkvall S, Skold J.4G:LTE/LTE-Advanced for Mobile Broadband: LTE/LTE-Advanced for Mobile Broadband[M]. Academic Press,2011.
[2]G. Boudreau, John P C Panicker, Ning Guo, etc, Interference coordination and cancellation for 4G networks[J], IEEE Communications Magazine, vol.47, no.4, 2009:74-81.
[3]Sun Y, Jover R P, Wang X. Uplink interference mitigation for OFDMA femtocell networks[J]. IEEE Transactions on Wireless Communications, vol.11, no.2, 2012:614-625.
[4]Tolli A, Pennanen H, Komulainen P. Distributed coordinated multi-cell transmission based on dual decomposition[C]. In:2009 IEEE Global Telecommunications Conference(GLOBECOM 2009), IEEE,2009:1-6.
[5]Hosein P. Optimality conditions for throughput maximization on the reverse link of a CDMA network[C]. In:2004 IEEE Eighth International Symposium on Spread Spectrum Techniques and Applications, IEEE,2004:764-768.
[6]Gjendemsjo A, Gesbert D, Oien G E, et al. Optimal power allocation and scheduling for two-cell capacity maximization[C]. In:2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, IEEE,2006:1-6.
[7]Lopez-Perez D, Guvenc I, De La Roche G, et al. Enhanced intercell interference coordination challenges in heterogeneous networks[J]. IEEE Wireless Communications, vol.18, no.3,2011:22-30.
[8]Chandrasekhar V, Andrews J G, Muharemovic T, et al. Power control in two-tier femtocell networks [J]. IEEE Transactions on Wireless Communications, vol.8, no.8,2009:4316-4328.
[9]Oh S J, Soong A C K. QoS-Constrained information-theoretic sum capacity of reverse link CDMA. Systems[J]. IEEE Transactions on Wireless Communications, vol.5, no.1,2006:3-7.
[10]Razaviyayn M, Sanjabi M, Luo Z Q. Linear transceiver design for interference alignment:Complexity and computation[J]. IEEE Transactions on Information Theory, vol.58, no.5,2012:2896-2910..
[11]Cao M, Raghunathan V, Hanly S, et al. Power control and transmission scheduling for network utility maximization in wireless networks[C]. In:2007 46th IEEE Conference on Decision and Control, IEEE,2007:5215-5221.
[12]Yinyu Ye, Competitive Communication Spectrum Economy and Equilibrium, working paper, Stanford, USA,2007.
[13]Shi Q, Razaviyayn M, Luo Z Q, et al. An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel[J]. IEEE Transactions on Signal Processing, vol.59, no.9,2011:4331-4340.
[14]Joshi S K, Weeraddana P C, Codreanu M, et al. Weighted sum-rate maximization for MISO downlink cellular networks via branch and bound[J]. IEEE Transactions on Signal Processing, vol.60, no.4,2012:2090-2095.
[15]Kim S J, Giannakis G B. Optimal resource allocation for MIMO ad hoc cognitive radio networks[J]. IEEE Transactions on Information Theory, vol.57, no.5,2011: 3117-3131.
[1]SG Kiani, D Gesbert, Optimal and distributed scheduling for multicell capacity maximization[J], IEEE Transactions on Wireless Communications, vol.7, no.1, 2008:288-297.
[2]Bang CJ, Dohyung P, Shin WY, Opportunistic interference mitigation achieves optimal degrees-of-freedom in wireless multi-cell uplink networks, IEEE Transactions on Communications[J], vol.60, no.7,2012:1935-1944.
[3]H Zhang, H Dai, Cochannel interference mitigation and cooperative processing in downlink multicell multiuser MIMO networks[J], EURASIP Journal on Wireless Communications and Networking-Special issue on multiuser MIMO networks, vol.2,2004:222-235.
[4]Chatzinotas S, Imran M A, Hoshyar R, The multicell processing capacity of the cellular MIMO uplink channel under Correlated Fading[J], IEEE Communications letters, vol.12, no.11, Nov.2008:834-836,
[5]Chandrasekhar V, Shen Z, Optimal uplink power control in two-cell systems with Rise-over-Thermal constraints[J], IEEE Communications letters, vol.12, no.3, Mar.2008:173-175.
[6]Gjendemsj A, Gesbert D, Oien G E, et al. Binary power control for sum rate maximization over multiple interfering links[J]. IEEE Transactions on Wireless Communications, vol.7, no.8,2008:3164-3173.
[7]Liu X, Yang H. Sum capacity of the reverse link for multi-cell multi-user cellular systems[J]. IEEE Communications Letters, vol.12, no.11, Nov.2008:834-836.
[8]Metroplois N, Rosenbluth A, Equation of state calculations by fast computing machines[J]. Journal of Chemical Physics, vol.21, no.5,1953:1087-1092.
[9]Kirkpatrick S, Gelatt C D, Vechi Jr M P, Optimization by simulated annealing[J]. Science, vol.220,1983:671-680.
[10]Poongup Lee, Taeyoung Lee, Jangkeun Jeong, Jitae Shin, Interference management in LTE femtocell systems using Fractional Frequency Reuse[C]. In: 2010 The 12th International Conference on Advanced Communication Technology (ICACT), vol.2,2010:1047-1051.
[11]R. Madan, J. Borran,A. Sampath, et al. Cell association and interference coordination in heterogeneous LTE-A cellular networks[J], IEEE Journal on Selected Areas in Communications, vol.28, no.9,2010:1479-1489.
[12]Alade T, Zhu H, Wang J. Uplink co-channel interference analysis and cancellation in femtocell based distributed antenna system[C]. In:2010 IEEE International Conference on Communications (ICC), IEEE, May 2010:1-5.
[13]Balachandran K, Kang J H, Karakayali K, et al. NICE:A network interference cancellation engine for opportunistic uplink cooperation in wireless networks[J]. IEEE Transactions on Wireless Communications, vol.10, no.2, Feb.2011: 540-549.
[14]张新程,田韬,周晓津,文志成编著,LTE空中接口技术与性能。北京,人民邮电出版社,2009.
[15]Nie H, How J. Reverse link outage probability analysis for cellular CDMA systems employing successive interference cancellation[C]. In:4th Annual Communication Networks and Services Research Conference(CNSR 2006), IEEE,2006.
[16]Andrews J G, Meng T H. Optimum power control for successive interference cancellation with imperfect channel estimation[J]. IEEE Transactions on Wireless Communications, vol.2, no.2,2003:375-383.
[2]Kudekar S, Richardson T J, Urbanke R L. Threshold saturation via spatial coupling:Why convolutional LDPC ensembles perform so well over the BEC[J]. IEEE Transactions on Information Theory, vol.57, no.2,2011:803-834.
[3]Hara S, Prasad R. Overview of multicarrier CDMA[J]. IEEE Communications Magazine, vol.35, no.12,1997:126-133.
[4]Sampath H, Talwar S, Tellado J, A fourth-generation MIMO-OFDM broadband wireless system:design, performance, and field trial results[J], IEEE Communications Magazine, vol.40, no.9,2002:143-149.
[5]Li Q, Li G, Lee W, et al. MIMO techniques in WiMAX and LTE:a feature overview[J]. IEEE Communications Magazine, vol.48, no.5,2010:86-92.
[6]Astely D, Dahlman E, Furuskar A, et al. LTE:the evolution of mobile broadband[J]. IEEE Communications Magazine, vol.47, no.4, Apr.2009:44-51.
[7]Shen Z, Papasakellariou A, Montojo J, et al. Overview of 3GPP LTE-advanced carrier aggregation for 4G wireless communications[J]. IEEE Communications Magazine, vol.50, no.2, Feb.2012:122-130.
[8]Claude E. Shannon, A Mathematical Theory of Communication[J]. The Bell System Technical Journal, vol.27,1948:379-423,623-656.
[9]Andrea Goldsmith著,杨鸿文,李卫东,郭文彬等译,《无线通信》,人民邮电出版社,2007.
[10]Nechiporenko T, Phan K T, Tellambura C, et al. On the capacity of Rayleigh fading cooperative systems under adaptive transmission [J]. IEEE Transactions on Wireless Communications, vol.8, no.4, Apr.2009:1626-1631.
[11]Ong L T, Shikh-Bahaei M, Chambers J A. Variable rate and variable power MQAM system based on Bayesian bit error rate and channel estimation techniques[J]. IEEE Transactions on Communications, vol.56, no.2, Feb.2008: 177-182.
[12]Xiaofeng L, Hongwen Y, Wenbin G, et al. Capacity of fading channels with quantized channel side information[J]. IEICE transactions on communications, vol.89, no.2,2006:590-593.
[13]Akbudak T, Simsek M, Zhao B, et al. Symmetric Capacity of Multi-user MIMO Downlink Under Per-Base Station Power Constraints,2011 International ITG Workshop on Smart Antennas, WSA 2011.
[14]L ee J, Jindal N. Symmetric capacity of MIMO downlink channels[C]. In:2006 IEEE International Symposium on Information Theory, IEEE,2006:1031-1035.
[15]Weingarten H, Steinberg Y, Shamai S. The capacity region of the Gaussian multiple-input multiple-output broadcast channel [J]. IEEE Transactions on Information Theory, vol.52, no.9,2006:3936-3964.
[16]Boche H, Jorswieck E A. Sum capacity optimization of the MIMO Gaussian MAC[C]. In:The 5th International Symposium on Wireless Personal Multimedia Communications, IEEE,2002:130-134.
[17]Sigen Ye, Ruick S. Blum, Leonard J. Cimini, Adaptive modulation for variable-rate OFDM systems with imperfect channel information[C]. In:IEEE 55th Vehicular Technology Conference(VTC'02 spring),2002:767-771.
[18]Radaydeh R M, Alouini M S. Adaptive transmit selection with interference suppression[C]. In:2010 5th IEEE International Symposium on Wireless Pervasive Computing (ISWPC), IEEE,2010:33-38.
[19]Ulukus S, Yates RD, Adaptive power control and MMSE interference suppression[J], Wireless Networks, vol.4, no.6,1998:489-496.
[20]Weingarten H, Liu T, Shamai S, et al. The capacity region of the degraded multiple-input multiple-output compound broadcast channel [J]. IEEE Transactions on Information Theory, vol.55, no.11,2009:5011-5023.
[21]Brehmer J, Molin A, Tejera P, et al. A low complexity approximation of the MIMO broadcast channel capacity region[C]. In:IEEE International Conference on Communications, ICC'06, IEEE,Jun.2006:3111-3116.
[22]Sankaranarayanan L, Kramer G, Mandayam N B. Hierarchical sensor networks: capacity bounds and cooperative strategies using the multiple-access relay channel model[C]. In:2004 First Annual IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks, IEEE SECON 2004, IEEE,2004:191-199.
[23]Gupta P, Kumar PR, The capacity of wireless networks[J]. IEEE Transactions on Information Theory[J], vol.46, no.2,2002:388-404.
[24]Kiani S G, Gesbert D. Optimal and distributed scheduling for multicell capacity maximization[J]. IEEE Transactions on Wireless Communications, vol.7, no.1, 2008:288-297.
[25]Huang J, Subramanian V G, Agrawal R, et al. Downlink scheduling and resource allocation for OFDM systems[J]. IEEE Transactions on Wireless Communications, vol.8, no.1,2009:288-296.
[26]Liu X, Yang H. Sum capacity of the reverse link for multi-cell multi-user cellular systems[J]. IEEE Communications Letters, vol.12, no.11,2008: 834-836.
[27]Chandrasekhar V, Shen Z. Optimal uplink power control in two-cell systems with rise-over-thermal constraints [J]. IEEE Communications Letters, vol.12, no.3, 2008:173-175.
[28]Liu E, Leung K. Expected throughput of the proportional fair scheduling over Rayleigh fading channels[J]. IEEE Communications Letters, vol.14, no.6, Jun. 2010:515-517.
[29]Huang J, Subramanian V G, Agrawal R, et al. Downlink scheduling and resource allocation for OFDM systems[J]. IEEE Transactions on Wireless Communications, vol.8, no.1,2009:288-296.
[30]3GPP TS 36.213-b10, Evolved Universal Terrestrial Radio Access (E-UTRA) Physical layer procedures, March 2013.
[31]Mochaourab R, Jorswieck EA, Optimal beamforming in interference networks with perfect local channel information[J], IEEE Transactions on Signal Processing, vol.59, no.3, Mar.2011:1128-1141.
[32]Srinivasa S, Ali Jafar S. Vector channel capacity with quantized feedback[C]. In: 2005 IEEE International Conference on Communications, ICC 2005, IEEE,2005: 2674-2678.
[33]Rajanna A, Jindal N. Multiuser Diversity in Downlink Channels:When Does the Feedback Cost Outweigh the Spectral Efficiency Benefit?[J], IEEE Transactions on Wireless Communications, vol.11, no.1,2012:408-418.
[34]Kim T, Lim J. Capacity Analysis and Feedback Threshold Optimization in Fair Multiuser Diversity System[J], IEEE Transactions on Vehicular Technology, vol. 61, no.9, Nov.2012:4189-4194.
[35]刘晓峰,量化反馈下的信道容量及多小区上行容量研究[学位论文],北京,北京邮电大学,2009.
[36]Ge sbert D, Kountouris M. Resource allocation in multicell wireless networks: Some capacity scaling laws[C]. In:5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks and Workshops, 2007. IEEE,2007:1-7.
[37]Deepthy G S, Susan R J. Analysis of Successive Interference Cancellation in CDMA Systems[C]. In:2012 Second International Conference on Advanced Computing & Communication Technologies (ACCT), IEEE,2012:481-485.
[38]Jemin L, Andrews J G, Daesik H.The Effect of Interference Cancellation on Spectrum-Sharing Transmission Capacity[C]. In:2011 IEEE International Conference on Communications (ICC),2011:1-5.
[39]Ekrem E, Ulukus S. Capacity Region of Gaussian MIMO Broadcast Channels with common and condifential messages [J], IEEE Transactions on Information Theory, vol.58, no.9,2012:5669-5680.
[40]Yongzhe X, Costas N G Some Results on the Sum-Rate Capacity of MIMO Fading Broadcast Channels [J]. IEEE Transactions on Wireless Communications, vol.5, no.2,2006:377-383.
[41]Zhang R, Cui S, Liang Y C. On ergodic sum capacity of fading cognitive multiple-access and broadcast channels[J]. IEEE Transactions on Information Theory, vol.55, no.11,2009:5161-5178.
[42]Inaltekin H, Hanly S. Optimality of binary power-control in a single cell via majorization[C]. In:2011 IEEE International Symposium on Information Theory Proceedings (ISIT). IEEE,2011:2891-2895.
[43]Hosein P. Optimality conditions for throughput maximization on the reverse link of a CDMA network[C]. In:2004 IEEE Eighth International Symposium on Spread Spectrum Techniques and Applications, IEEE,2004:764-768.
[1]Huang Y, Mao S, Li Y. Downlink power allocation for stored variable-bit-rate videos[M], Quality, Reliability, Security and Robustness in Heterogeneous Networks. Springer Berlin Heidelberg,2012:483-498.
[2]Firouzabadi S, Goldsmith A. Downlink performance and capacity of distributed antenna systems[J]. arXiv preprint arXiv:1109.2957,2011.
[3]Ji T, Zhou C, Zhou S, et al. Low complex user selection strategies for multi-user MIMO downlink scenario[C]. In:2007 IEEE Wireless Communications and Networking Conference, WCNC 2007,IEEE,2007:1532-1537.
[4]Xing Zhang, Wenbo Wang, Multiuser frequency-time domain radio resource allocation in downlink OFDM systems:Capacity analysis and scheduling methods[J], Computers & Electrical Engineering, vol.32,2006:118-134.
[5]Iosif O, Banica I. On the analysis of packet scheduling in downlink 3GPP LTE system [C]. In:The Fourth International Conference on Communication Theory, Reliability, and Quality of Service(CTRQ 2011),2011:99-102.
[6]Ikuno J C, Wrulich M, Rupp M. System level simulation of LTE networks[C]. In: 2010 IEEE 71st Vehicular Technology Conference (VTC 2010-Spring), IEEE, 2010:1-5.
[7]Kwan R, Leung C, Zhang J. Proportional fair multiuser scheduling in LTE[J]. IEEE Signal Processing Letters, vol.16, no.6,2009:461-464.
[8]Andrea Goldsmith著,杨鸿文,李卫东,郭文彬等译,《无线通信》,人民邮电出版社,2007.
[9]Xu W, Dong X, Lu W S. MIMO relaying broadcast channels with linear precoding and quantized channel state information feedback[J]. IEEE Transactions on Signal Processing, vol.58, no.10,2010:5233-5245.
[10]Rajanna A, Jindal N. Multiuser Diversity in Downlink Channels:When Does the Feedback Cost Outweigh the Spectral Efficiency Benefit?[J]. IEEE Transactions on Wireless Communications, vol.11, no.1,2012:408-418.
[11]Ban T W, Choi W, Jung B C, et al. Multi-user diversity in a spectrum sharing system[J]. IEEE Transactions on Wireless Communications, vol.8, no.1,2009: 102-106.
[12]Hwang C S, Seong K, Cioffi J. Throughput maximization by utilizing multi-user diversity in slow-fading random access channels[J]. IEEE Transactions on Wireless Communications, vol.7, no.7,2008:2526-2535.
[13]Knopp R, Humblet P A. Information capacity and power control in single-cell multiuser communications[C]. In:1995 IEEE International Conference on Communications, ICC'95, IEEE,1995:331-335.
[14]Xiaofeng L, Hongwen Y, Wenbin G, et al. Capacity of fading channels with quantized channel side information[J]. IEICE transactions on communications, vol.89, no.2,2006:590-593.
[15]3GPP2 C.S0024-A_Version 3.0-2006 CDMA2000 high rate packet data air interface specification Reversion A.,2006.
[1]Dahlman E, Parkvall S, Skold J.4G:LTE/LTE-Advanced for Mobile Broadband: LTE/LTE-Advanced for Mobile Broadband[M]. Academic Press,2011.
[2]G. Boudreau, John P C Panicker, Ning Guo, etc, Interference coordination and cancellation for 4G networks[J], IEEE Communications Magazine, vol.47, no.4, 2009:74-81.
[3]Sun Y, Jover R P, Wang X. Uplink interference mitigation for OFDMA femtocell networks[J]. IEEE Transactions on Wireless Communications, vol.11, no.2, 2012:614-625.
[4]Tolli A, Pennanen H, Komulainen P. Distributed coordinated multi-cell transmission based on dual decomposition[C]. In:2009 IEEE Global Telecommunications Conference(GLOBECOM 2009), IEEE,2009:1-6.
[5]Hosein P. Optimality conditions for throughput maximization on the reverse link of a CDMA network[C]. In:2004 IEEE Eighth International Symposium on Spread Spectrum Techniques and Applications, IEEE,2004:764-768.
[6]Gjendemsjo A, Gesbert D, Oien G E, et al. Optimal power allocation and scheduling for two-cell capacity maximization[C]. In:2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, IEEE,2006:1-6.
[7]Lopez-Perez D, Guvenc I, De La Roche G, et al. Enhanced intercell interference coordination challenges in heterogeneous networks[J]. IEEE Wireless Communications, vol.18, no.3,2011:22-30.
[8]Chandrasekhar V, Andrews J G, Muharemovic T, et al. Power control in two-tier femtocell networks [J]. IEEE Transactions on Wireless Communications, vol.8, no.8,2009:4316-4328.
[9]Oh S J, Soong A C K. QoS-Constrained information-theoretic sum capacity of reverse link CDMA. Systems[J]. IEEE Transactions on Wireless Communications, vol.5, no.1,2006:3-7.
[10]Razaviyayn M, Sanjabi M, Luo Z Q. Linear transceiver design for interference alignment:Complexity and computation[J]. IEEE Transactions on Information Theory, vol.58, no.5,2012:2896-2910..
[11]Cao M, Raghunathan V, Hanly S, et al. Power control and transmission scheduling for network utility maximization in wireless networks[C]. In:2007 46th IEEE Conference on Decision and Control, IEEE,2007:5215-5221.
[12]Yinyu Ye, Competitive Communication Spectrum Economy and Equilibrium, working paper, Stanford, USA,2007.
[13]Shi Q, Razaviyayn M, Luo Z Q, et al. An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel[J]. IEEE Transactions on Signal Processing, vol.59, no.9,2011:4331-4340.
[14]Joshi S K, Weeraddana P C, Codreanu M, et al. Weighted sum-rate maximization for MISO downlink cellular networks via branch and bound[J]. IEEE Transactions on Signal Processing, vol.60, no.4,2012:2090-2095.
[15]Kim S J, Giannakis G B. Optimal resource allocation for MIMO ad hoc cognitive radio networks[J]. IEEE Transactions on Information Theory, vol.57, no.5,2011: 3117-3131.
[1]SG Kiani, D Gesbert, Optimal and distributed scheduling for multicell capacity maximization[J], IEEE Transactions on Wireless Communications, vol.7, no.1, 2008:288-297.
[2]Bang CJ, Dohyung P, Shin WY, Opportunistic interference mitigation achieves optimal degrees-of-freedom in wireless multi-cell uplink networks, IEEE Transactions on Communications[J], vol.60, no.7,2012:1935-1944.
[3]H Zhang, H Dai, Cochannel interference mitigation and cooperative processing in downlink multicell multiuser MIMO networks[J], EURASIP Journal on Wireless Communications and Networking-Special issue on multiuser MIMO networks, vol.2,2004:222-235.
[4]Chatzinotas S, Imran M A, Hoshyar R, The multicell processing capacity of the cellular MIMO uplink channel under Correlated Fading[J], IEEE Communications letters, vol.12, no.11, Nov.2008:834-836,
[5]Chandrasekhar V, Shen Z, Optimal uplink power control in two-cell systems with Rise-over-Thermal constraints[J], IEEE Communications letters, vol.12, no.3, Mar.2008:173-175.
[6]Gjendemsj A, Gesbert D, Oien G E, et al. Binary power control for sum rate maximization over multiple interfering links[J]. IEEE Transactions on Wireless Communications, vol.7, no.8,2008:3164-3173.
[7]Liu X, Yang H. Sum capacity of the reverse link for multi-cell multi-user cellular systems[J]. IEEE Communications Letters, vol.12, no.11, Nov.2008:834-836.
[8]Metroplois N, Rosenbluth A, Equation of state calculations by fast computing machines[J]. Journal of Chemical Physics, vol.21, no.5,1953:1087-1092.
[9]Kirkpatrick S, Gelatt C D, Vechi Jr M P, Optimization by simulated annealing[J]. Science, vol.220,1983:671-680.
[10]Poongup Lee, Taeyoung Lee, Jangkeun Jeong, Jitae Shin, Interference management in LTE femtocell systems using Fractional Frequency Reuse[C]. In: 2010 The 12th International Conference on Advanced Communication Technology (ICACT), vol.2,2010:1047-1051.
[11]R. Madan, J. Borran,A. Sampath, et al. Cell association and interference coordination in heterogeneous LTE-A cellular networks[J], IEEE Journal on Selected Areas in Communications, vol.28, no.9,2010:1479-1489.
[12]Alade T, Zhu H, Wang J. Uplink co-channel interference analysis and cancellation in femtocell based distributed antenna system[C]. In:2010 IEEE International Conference on Communications (ICC), IEEE, May 2010:1-5.
[13]Balachandran K, Kang J H, Karakayali K, et al. NICE:A network interference cancellation engine for opportunistic uplink cooperation in wireless networks[J]. IEEE Transactions on Wireless Communications, vol.10, no.2, Feb.2011: 540-549.
[14]张新程,田韬,周晓津,文志成编著,LTE空中接口技术与性能。北京,人民邮电出版社,2009.
[15]Nie H, How J. Reverse link outage probability analysis for cellular CDMA systems employing successive interference cancellation[C]. In:4th Annual Communication Networks and Services Research Conference(CNSR 2006), IEEE,2006.
[16]Andrews J G, Meng T H. Optimum power control for successive interference cancellation with imperfect channel estimation[J]. IEEE Transactions on Wireless Communications, vol.2, no.2,2003:375-383.