POWER CONTROL AND RESOURCE ALLOCATION FOR DELAY-CONSTRAINED COMMUNICATIONS

Transcription

1 POWER CONTROL AND RESOURCE ALLOCATION FOR DELAY-CONSTRAINED COMMUNICATIONS By XIAOCHEN LI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA

2 c 2009 Xiaochen Li 2

3 To my beloved parents and dear husband 3

4 ACKNOWLEDGMENTS First of all, my special gratitude goes to my advisor, Professor Dapeng Oliver Wu, for his great inspiration and excellent guidance throughout this dissertation and my Ph.D. education at UFL. His enthusiasm and deep thoughts spark my interest in academic research. I am grateful to him for his insightful guidance and strict training on creative thinking, rigorous analyzing, and effective writing skills. My deeply appreciation goes to my committee members: Professor Liuqing Yang, Janise McNair and Shigang Chen, for their interest in my work and the valuable feedbacks on my research. I would like to thank Professor Jianbo Gao. I have learnt a lot from his signal processing classes and elaborately designed course projects. I would like to thank Professor P. Oscar Boykin for many useful discussions about the queueing theory. I would like to thank my Master advisor Professor Bingli Jiao, he guided me into the world of wireless communications. I would like to thank my lab-mates in the Multimedia Communications and Networking Laboratory (MCN) here in UF. I am fortunate to be a member of this friendly and family-like group. I would like to thank Xihua Dong, for the helpful discussions on the research and cooperation of many papers; Bing Han, Wenxing Ye, Jun Xu, Zhifeng Chen, Taoran Lu, Yiran Li, Yunzhao Li, and my senior lab-mate Dr. Jieyan Fan, for their constant supports and sincere friendship, and I cherish every minute we have spent together; Shanshan Ren, Ziyi Wang and Lin Zhang, for hosting the parties and adding the element of fun to my Ph.D. life. I have spent wonderful four years in Gainesville. Without them, it is not even possible. I would also like to thank Zongrui Ding, Lei Yang, Qian Chen, Jiangping Wang, Yakun Hu, Qin Chen, Qing Wang, Youngho Jo and Chris Paulson. Wish you all have success in your Ph.D. studies. I would like to thank my parents for the endless love and constant support they ve provided during my whole life. Thanks for the encouragement for every tiny progress that I have ever made. Without them, I would have never been able to accomplish what 4

5 I had today. Last but not the least I would like to thank my husband, Dr. Hongbing Cheng, for his deep love, understanding and support, both academically and morally. His encouragement is my best stimulus. 5

6 TABLE OF CONTENTS page ACKNOWLEDGMENTS LIST OF TABLES LIST OF FIGURES ABSTRACT CHAPTER 1 INTRODUCTION Wireless Fading Channels Related Works on Delay-Constrained Communications Physical Layer Model Link-PHY layer Model Outline of the Dissertation HIERARCHICAL QUEUE-LENGTH-AWARE POWER CONTROL System Description Structure of Data Source and Transmitter Markov Chain Model Hierarchical Queue-Length-Aware Power Control Scheme Hierarchical Queue-Length-Aware Power Control Scheme Steady State Queue Length Distribution Average Power Effective Capacity with Power Control Peak Power Constraint Simulation Results Steady State Queue Length Distribution Effective Capacity Power Gain in 3G Environment HQLA with Adaptive Modulation Peak Power Constraint Steady State Analysis for Variable-Rate Arrival Process and Correlated Channel Correlated channel Variable-Rate Arrival Process Summary QOS-DRIVEN POWER ALLOCATION FOR MULTI-CHANNEL COMMUNICATIONS UNDER OUTDATED CHANNEL SIDE INFORMATION Introduction

7 3.2 System Model Optimal Power Allocation Scheme Suboptimal Power Allocation Scheme Simulation Results Summary JOINT POWER AND CHANNEL ALLOCATION IN WIRELESS NETWORKS Introduction Reference Channel Approach System Description Simulation Results Simulation Setting Performance Evaluation Summary JOINT QUEUE-LENGTH-AWARE POWER CONTROL System Model Separate QLA Power Control Joint QLA Power Control Structure Of The Optimal Power Control Scheme Convexity of the Objective Function Solution for the Constraint-Relaxed Optimization Problem Only One Negative Column in ˆp i,j Arbitrary Number of Negative Columns in ˆp i,j Structure of the Optimal Power Control Scheme Simulation Results SQLA Power Control JQLA Power Control Summary POWER CONTROL WITH ADAPTIVE MODULATION Adaptive Modulation Overview Adaptive Modulation in Cross Layer Design JQLA with Adaptive Modulation Simulation Results Summary CONCLUSIONS APPENDIX A PROOFS A.1 Proof of Lemma A.2 Proof of Lemma

8 A.3 Proof of Lemma A.4 Proof of Lemma A.5 Proof of Lemma A.6 Proof of Lemma A.7 Proof of Lemma A.8 Proof of Lemma A.9 Proof of Lemma A.10 Proof of Lemma REFERENCES BIOGRAPHICAL SKETCH

9 Table LIST OF TABLES page 2-1 Parameters for 3G environment simulation Parameters for 3G environment simulation with adaptive modulation Comparison of computational complexity Configuration of f(g) Constructing p i,j from ˆp i,j Constructing yj from ŷ j Simulation parameters for SQLA Simulation results Simulation parameters for JQLA Simulation results for JQLA

10 Figure LIST OF FIGURES page 1-1 Type of fading channels Physical layer and link-phy layer system models Structure of data source and transmitter Update of the queue length Markov property of the queue length Hierarchical queue-length-aware power control scheme Hierarchical queue-length-aware power control scheme with peak power constraint Probability mass function of HQLA/CONST Probability mass function of HQLA/TDWF Delay bound violation probability of HQLA/TDWF Effective capacity of HQLA/CONST Effective capacity of HQLA/TDWF Effective capacity of HQLA/OPT Power gain of HQLA/CONST over CONST PC Power gain of HQLA/TDWF over TDWF PC Power gain of HQLA/TCI over TCI PC Power gain of HQLA/TCI over TCI PC with adaptive modulation, voice data D max vs. average power with fixed µ and ɛ Delay bound violation probability at 20mph Delay bound violation probability at 80mph An example of variable-rate arrival process Queue length distribution of TCI PC with variable-rate arrival process Queue length violation probability of TCI PC with variable-rate arrival process System diagram Effect of CSI delay on the effective capacity

11 3-3 Ratio of effective capacity achieved by the suboptimal solution to the optimal solution QoS provisioning architecture in a base station Queueing model used for multiple fading channels Performance gain L c (K, N) vs. average SNR Performance gain L p (K, N) vs. average SNR Performance gain L e (K, N) vs. average SNR System model Diagram of states update Example of P q (g), q = 0, µ = An example of fading regions of the optimal power control scheme when all ˆp i,j An example of fading regions of the optimal power control scheme when some of the ˆp i,j < SQLA, µ = 25, M = SQLA, µ = 5, M = TCI and TDWF power control JQLA power control, µ = 25, M = JQLA power control, µ = 10, M = JQLA power control, µ = 5, M = Packet drop probability v.s. average power. µ = 25, M = Packet drop probability v.s. average power. µ = 10, M = Packet drop probability vs. average power. µ = 5, M = A (K) and its curve fitting Constant power control, M = 10, µ = 5, P ER = TDWF power control, M = 10, µ = 5, P ER = PDR vs. PER. µ = 1, M = PDR vs. PLR. µ = 1, M =

12 6-6 PDR vs. PER. µ = 5, M = PDR vs. PER. µ = 5, M =

13 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy POWER CONTROL AND RESOURCE ALLOCATION FOR DELAY-CONSTRAINED COMMUNICATIONS Chair: Dapeng Oliver Wu Major: Electrical and Computer Engineering By Xiaochen Li August 2009 Real-time applications such as streaming multimedia will be supported in the next generation wireless networks. Services required by these applications are different from file transfer services in that they expect low transmission delay, i.e., delay-constrained communications. Providing quality of service (QoS) guarantees to multimedia applications poses a significant challenge for the design of wireless networks. This dissertation focuses on the power and resource allocation schemes for delay-constrained communications, with statistical QoS requirements characterized by the triplet of data rate, delay bound, and delay bound violation probability. We study the optimal power control and resource allocation schemes to provide statistical QoS guarantees, which are more challenging than providing average delay guarantees, since statistical QoS imposes constraints on the distribution of transmission delay. In the first part of the dissertation, we study the throughput maximization problem subject to the delay bound violation probability and average power constraint, for a single-user, single-channel system. The buffer size is assumed to be infinite and the delay bound is relatively large. This problem is actually the effective capacity maximization problem, which is defined as the maximum data rate a system can sustain under the statistical QoS constraint, in large delay regime. We propose a simple cross-layer suboptimal power control scheme which significantly increases the effective capacity comparing to the optimal channel-gain-based power control scheme. We also 13

14 investigate the impact of delayed channel state information on the performance of power control schemes. Finally, we study the joint power and channel allocation scheduler for a multi-user, multi-channel system, based on the effective capacity and reference channel approach. The scheduling algorithm explicitly guarantees users statistical QoS requirements while minimizing the resource usage. In the second part of the dissertation, we study the dual problem, minimizing the delay bound violation probability, subject to an average power constraint and throughput constraint. The transmission buffer size is assumed to be finite (small delay regime). Therefore the delay bound violation probability translates to buffer fullness probability, or packet drop probability. The queuing behavior with a finite size buffer is quite different from that of an infinite size buffer. We analyze the fundamental limit of power control performances over continuous wireless channels for finite size buffer models. Dynamic programming techniques, which are used to address the control of queueing systems under discrete channel models, will result performance degradation due to quantization. Our method is to decompose the original optimization problem into three sub-problems, and sequentially solve the three sub-problems. We prove that the two problems have the same optimal solution. By solving the sub-problems, we provide structural information about the optimal solution. The optimal cross-layer power control scheme is combined with adaptive modulation technique in a variable-rate, variable-power system, where both packet drop probability and decoding error probability are considered. 14

15 CHAPTER 1 INTRODUCTION The growing demand on data services drives the evolution of wireless communication systems. The wireless communication technologies have been developed to a new stage that real-time applications, such as streaming multimedia, online games and remote medical monitoring and diagnosis, can be expected [1]. These real-time applications, or so called quality of service (QoS) guaranteed applications, are different from best-effort applications in that they are sensitive to transmission delay [2]. The realization of real-time applications relies on the adequate data rate provided by the physical layer technologies, as well as the elaborately designed protocols of the upper layers such that reserved throughputs, bounds on delays and loss rates are met. In the physical layer, by the use of broadband, multi-carrier modulation (MCM) such as orthogonal frequency-division multiplexing (OFDM) [3], multiple-input multiple-output (MIMO) [4] antennas, the data transmission rate will be as high as tens of megabits per second [5]. In the link layer, which utilizes the services provided by the physical layer directly, how to schedule the physical layer resources (power, bandwidth, code etc.) to provide satisfactory QoS guarantees becomes a big challenge [6]. Physical layer performances, e.g., capacity and error rate, are highly dependent on channel conditions. Wireless channels are shared media, which are vulnerable to interference and subject to time-, frequency- and location-dependent attenuations. Section 1.1 introduces the characteristics of wireless channels and the challenges they impose on the signaling design. We will restrict our attention to single input single output (SISO) flat slow fading channel, which is fundamental to the study of other complicated channel models. Delay-constrained communications have been widely studied in the past decade. Although all these works can be categorized as delay-constrained, the models of the system and the problem formulations are quite different. Section 1.2 reviews the major results on this topic. Section 1.3 outlines the dissertation. 15

16 1.1 Wireless Fading Channels The ultimate mission of a communication system is to reliably deliver information through lossy channels. Wireless fading channels, characterized by their time-varying nature, is more challenging than wired channels. The signals are severely attenuated by the wireless channel due to various factors. The signal bearing electromagnetic (EM) waves emitted from transmitter antenna(s) are subject to dissipation due to the propagation in the free space, which causes the strength of signal to decay proportionally to the distance traveled. Moreover the obstacles in between the transmitter antenna(s) and receiver antenna(s) cause reflection, scattering, diffraction and absorption of the EM waves. These obstacles include static objects such as hills, buildings or trees, and moving objects such as vehicles. The impact of these impediments to the EM wave is two-folded. First, there are creating multiple propagation paths from the transmitter to the receiver; different paths have different propagation delay. Second, the amplitude and phase of the EM wave of each path is attenuated severely. At the receiver side, the multipaths that experience similar delay (the delay difference is relatively small comparing to the inverse of the signal bandwidth) are unresolvable. These multipath components are constructively or destructively combined together and usually exhibit fast variations. The multipaths (or combined multipaths) which experience delay longer than the inverse of the signal bandwidth make the channel time dispersive. A single pulse transmitted from the transmitter will induce a sequence of pulses at the receiver. In the frequency domain, a time dispersive channel is characterized by its uneven frequency responses. There are deep fadings at some frequency locations, making the channel selective in the frequency domain. Coherent bandwidth is the statistical measure of a frequency selective channel; the frequency response of the channel is highly correlated within the coherent bandwidth. Despite the dispersive property in time domain, wireless channels are also dispersive in the frequency domain due to Doppler shift induced by the movement of the transmitter/receiver 16

17 Symbol duration Coherent bandwidth Flat slow fading Frequency selective slow fading Flat fast fading Frequency selective fast fading Coherent time Symbol duration Figure 1-1. Type of fading channels. antennas, and obstacles in between the propagation path. The dynamic environment accounts for the time-varying and unpredictable nature of wireless channels. Similar to the time dispersive property, the frequency dispersive channel is statistically measured by the coherent time, within which the channel has correlated fading. Depending on the relative value of the coherent time and the inverse of coherent bandwidth to the symbol duration, a wireless channel can be categorized as flat fast fading, flat slow fading, frequency selective fast fading and frequency selective slow fading. As illustrated in Fig. 1-1, a channel undergoes flat fading (resp., frequency selective fading) if the symbol duration is longer (resp., smaller) than the inverse coherent bandwidth, and undergoes slow fading (resp., fast fading) if the symbol duration is smaller (resp., larger) than the coherent time. We will study the QoS provisioning problem for flat slow fading channels. Although frequency selective channels are typical in broadband communication systems, the study on flat fading channels is more fundamental. The frequency selective channel can be viewed as multiple parallel narrowband sub-channels, and each of them undergoes a flat fading. This is exactly the idea behind OFDM systems, which have been adopted in various industry standards, e.g., IEEE a/g/n, LTE and WiMAX. Typically, the diversity inherent in multiple channels will substantially improve the QoS provisioning performance [7]. 17

18 The interest in slow fading is motivated by the fact that most wireless communication systems are designed in a way such that the signaling rate is much faster than the change of propagation environment. The fading states can be estimated at the receiver by pilot aided transmissions [8]. In a pilot aided system, the pilot symbols are periodically multiplexed with the information bearing symbols and used to tracking the variation of the fading channel. Blind channel estimation, which do not need pilot symbols, is more bandwidth efficient than pilot aided schemes [9]. However the pilot aided schemes are favorable in industry due to its simplicity and accuracy in fading state estimation. They have been adopted in many mobile wireless standards, e.g., WiMAX [10] and LTE. For a WiMAX system operating at 2.5GHz, a vehicle moving on the highway at 70mph will experience a time-varying channel with coherent time approximately 1.6ms [11, page 204]. The symbol duration of WiMAX signal is 0.1ms, and the pilot symbols are inserted every two symbols, which is much smaller than the coherent time. The flat slow fading channel can be modeled by block-fading additive white Gaussian channel (BF-AWGN) [12], which belongs to a general class of block-interference channels introduced by McEliece and Stark [13]. In BF-AWGN model, the flat fading channel has bandwidth W Hz. The fading state is assumed to be fixed within one block of duration T b sec, and varies from one block to another. The fading process is represented by real sequence {g n }, g n 0, where n is the index for the block. Depending on the model of the fading process, the value of g n can be taken from a finite set or span over the whole non-negative real axis. The fading process may have memory, i.e., {g n } is not necessary to be independent, identically, distributed (i.i.d.). For example, the fading process can be modeled as a Markov chain. The distribution of g n+1 conditioned on the previous fading state g n is, in general, different for each g n. In the following, we will refer to g n as fading gain, fading state or channel gain interchangeably. Despite the fading process, the channel itself is memoryless. This is the direct consequence of flat fading assumption. The channel output only depends on the current 18

19 channel input, and is irrelevant to the previous channel inputs. By Nyquist sampling theorem, a real bandlimited waveform signal with bandwidth W Hz can be represented by N = 2W T b samples in one block. Denote x n = [x 1n, x 2n,..., x Nn ] T the real input of the n-th block, and y n = [y 1n, y 2n,..., y Nn ] T the channel output, y n = g n x n + w n, (1 1) where w n is the real Gaussian random vector with zero mean and diagonal covariance matrix σi. 1.2 Related Works on Delay-Constrained Communications The studies on delay constrained communication generally fall into two categories. The difference is whether or not a queue is included in the system. Fig. 1-2 illustrates the two delay-constrained system models. The first model is a pure physical layer model where queue (or buffer) is excluded. The transmission delay, i.e., coding delay, is strictly restricted within M blocks, and each block has N channel uses, as described in the previous section. Reliable transmission is achieved by encoding the information bits within M blocks to average out the Gaussian noise and fading effect. The second model is a link-phy layer model. The incoming packets are stored in the transmission buffer until they are served or dropped. Both the arrival process and fading process contribute to the dynamics of the system. Hence the link-phy layer model is more complicated to study. The transmission delay consists of two parts: one is the queuing delay in the buffer, and the other one is the coding delay in the physical layer. For both of the two models, the channel side information (CSI) is assumed to be perfectly known at the receiver side and the transmitter side. Hence the power or rate control can be performed to optimize the system performance. The fading process is assumed to be stationary and ergodic. 19

20 P( n) g( n ) w( n) A Data Source Transmitter Link Layer Tx Buffer Arrival Process Information Buffer Occupancy Information Physical Layer Coding and Modulation P( n) Rate and Power Control Channel g( n ) w( n) Receiver Demodulation and Decoding Channel Estimation B Channel State Information Feedback Figure 1-2. Physical layer and link-phy layer system models. A. Physical layer model; B. Link-PHY layer model. 20

21 1.2.1 Physical Layer Model Channel capacity is considered as the most important performance measure of a channel. It gives the ultimate limit on the error free data rate that one can expect from a channel. An elegant overview and a comprehensive list of references of on capacity of fading channels are provided in [14]. We briefly review the capacity notions of fading channels and the power control schemes that achieve the maximum capacities. Capacity Without Delay Constraints-Ergodic Capacity. Ergodic capacity is for the scenario M = and arbitrary N. Since we allow M to be arbitrary large, the capacity obtained here is delay free. It is shown in [13] that with perfect CSI, the capacity is independent of N. Under the average power constraint P 0, the capacity is C 1 = max E g [W log 2 (1 + gp (g))], (1 2) P (g) where the power control P (g) satisfies the average power constraint E g [P (g)] P 0. (1 3) The optimal P (g) that maximize (1 2) is time-domain water filling (TDWF) [15] 1 g P (g) = 0 1 g g g 0. (1 4) 0 g < g 0 Two coding schemes can be applied to achieve this capacity. One is the variable-rate, variable-power code. The whole codeword is multiplexed by codewords selected from different codebooks. Each codebook is particularly designed for a specific fading region with distinct rate and average power. The codeword selected from one codebook span over all the blocks that fall into the fading region of that codebook [15]. Since M =, any multiplexed codeword has infinite duration. Another coding scheme uses single codebook and can be characterized as constant rate, variable power. The rate of the code matches the ergodic capacity in (1 2) and has unity average power. The symbols of codeword 21

22 transmitted in the n-th block are amplified by factor P (g n ) [16]. The constant-rate codeword spans over all the blocks, which leads to infinite coding delay. Capacity with Delay Constraints. For finite M, the codeword length is constrained in M blocks hence the coding delay is bounded by MT b sec. Different to ergodic capacity, the value of N impacts the capacity of the channel. As an upper bound, we assume N, i.e., the instantaneous channel capacity C 2 = W log 2 (1 + gp ), (1 5) is attainable for each block, where P is the power of the codeword. A Gaussian codebook with each symbol independently drawn from normal distribution N (0, 1) and scaled by P achieves C2 within each block. CSI is available to the transmitter in two ways, causal or acausal. In the causal case, the transmitter at the n-th block knows the fading gain of all the previous blocks and the current block. In the acausal case, fading gains of all M blocks are known to the transmitter at the beginning of the transmission. The acausal case is possible if the transmitter has access to multiple parallel channels and the fading gain of each channel is perfectly known [17] [18] [19]. We denote {P (n, g (c) )} the power control scheme for the n-th block, where g (c) denote the set {g 1,..., g c }. If CSI is causally known, c = n, while if CSI is acausally known, c = M. Similar to ergodic capacity, the expected capacity is defined as C 3 = max E[ {P (n,g (c) )} M W log 2 (1 + g n P (n, g (c) ))], (1 6) n=1 The optimal causal power control schemes subject to both short- and long-term average power constraints are given in [20]. Short-term power constraint imposes a upper bound on the total transmission power of each M blocks, while the long-term constraint only imposes the upper bound on the average. The optimization problem is solved by backward dynamic programming. The algorithm performs an exhaustive search. The optimal power 22

23 control for long-term average power constraint turns out to be TDWF as in (1 4). And it results higher capacity than optimal short-term power control since the constraint is less stringent. The optimal acausal power control scheme under the short-term power constraint is studied in [21]. To achieve expected capacity, we can concatenate the codeword that achieve the instantaneous capacity for each block. Each codeword spans one block and the transmission is variable-rate, variable-power. Motivated by the demand for constant-rate delay-limited applications such as VoIP [10], another delay-constrained capacity, outage capacity, was introduced [22], [23]. An information outage occurs if the instantaneous channel capacity is smaller than a target data rate R. Outage capacity is the maximum error-free data rate that a channel can support, provided that the information outage probability does not exceed a pre-defined threshold ɛ, C 4 = max {P (n,g (c) )} sup{r : Prob[ 1 M M W log 2 (1 + g n P (n, g (c) )) < R] ɛ}. (1 7) n=1 The optimal power allocation scheme for outage capacity is studied in [24] under acausal CSI assumption, subject to short- and long-term average power constraints. The problem is solved based on Lagrangian techniques. The optimal power allocation scheme is deterministic for continuous channel gain and probabilistic for discretized channel gain. In a special case M = 1, the optimal power control scheme is truncated channel inversion (TCI) 2 R/W 1 g P (g) = 0 g g 0, (1 8) 0 g < g 0 where R is determined by ɛ and g 0 is determined by the average power constraint. It is shown in [24] that the outage capacity can be achieved by using a single random Gaussian codebook. The constant-rate codeword spans over the M blocks. And the symbols of the codeword transmitted through the n-th block is scaled by P (n, g (M) ). 23

24 The optimal power control scheme with causal feedback is studied in [20] by dynamic programming approach. For long-term average power constraint, the causality of CSI substantially degrades the outage capacity at low outage probability ɛ. Similar to the acausal scenario, single random Gaussian codebook achieves the error-free outage capacity when N. The upper bound of random coding error probability is derived for finite N. The error probability approaches the outage probability as N for all rate smaller than the outage capacity. For a more stringent QoS requirement, no information outage is allowed, i.e., ɛ = 0. The outage capacity turns to be the delay-limited capacity introduced in [25] [26]. Delay limited capacity is the maximum error-free data rate that the channel can sustain regardless of the realization of the fading process. Hence without power control, delay capacity is actually the worst case channel capacity. If power control is available, for single channel case, the optimal strategy is total channel inversion P (g) = α g, (1 9) where α is obtained by the average power constraint E g ( α g ) = P 0. (1 10) And the delay-limited capacity is C 5 = W log 2 (1 + P 0 E g ( 1 (1 11) )). g If the channel can not be inverted with finite average power, e.g., Rayleigh fading channel, the delay limited capacity is zero. As in the outage capacity, the optimal power control scheme results constant-rate transmission over all M blocks. Hence a single codebook, variable-power coding scheme achieves the delay-limited capacity in the limiting case N. If the power control is considered as a part of the channel, the transmitter is actually dealing with an AWGN channel. When N is finite, the codeword spans M 24

25 blocks and consists of NM symbols. The bound on the random coding error probability is studied in [27] [28] [29] [30]. For real-time applications that consist of both time-variant and time-invariant data streams, both expected QoS and outage capacity (delay-limited capacity as a special case) are not adequate to describe the capacity demands. A variable-rate transmission scheme is studied [31] which maximizes the expected capacity subject to an information outage probability (of a basic rate) constraint and a long-term average power constraint. The so obtained capacity is larger than outage capacity since the transmission rate is allowed to fluctuate. It is shown [31] that when M = 1, the optimal power control scheme is a combination (multiplexing) of water-filling and channel inversion, for continuous fading distributions. This work is extended to M > 1, acausal CSI scenario by the same authors [32]. The optimization problem is solved based on generalized Karush-Kuhn-Tucker conditions [33]. As in [24], the optimal power control scheme is deterministic for continuous fading distributions and probabilistic for discretized fading distributions Link-PHY layer Model The physical layer model of delay-constrained communication systems represents a set of communication problems where the transmission must be finished in a finite time duration. To achieve those delay-constrained capacities, powerful codes are needed which either span over all M blocks, or span one block but with different rates. For the first case, it is implicitly required that all the information are ready at the transmitter side at the beginning of the transmission. It is usually not a valid assumption for real-time applications whose data is generated on the fly. For the second case, the rate of data source must match the instantaneous capacity of the channel in each block, otherwise the capacity will not be achievable due to inadequate data at the transmitter side. For real-time applications such as video-chatting, the rate of source-data depends on the content of the pictures, which is independent to the instantaneous channel capacity. 25

26 Without loss of generality, it is still required that all the information are ready at the beginning of the transmission. Thus the physical layer model actually solves a set of delay-constrained problems: efficiently transmitting B information bits with average power P 0 within M blocks, and the B information bits are ready at the transmitter side at the beginning of the transmission. The capacity maximization problem in section maximizes B subject to constraint P 0. The dual problem, fixing B while minimizing P 0 is studied [34]. The physical layer model does not suitable for more complicated problems such as (we use term packet instead of bit in the rest of this chapter) B packets arrival at different time. Each packet has individual delay bound. These problems are common in packet switching networks. Essentially, the aforementioned difficulty stems from the fact that information-theoretical approaches only capture the variation of the channel but leave the variation of data source unconsidered. Therefore the link-phy layer model is needed to study both of the two factors [35]. Consider the link-phy layer model illustrated in Fig The buffer can accommodate K packets. We denote a(n), c(n) and s(n) the number of packets that arrive in the nth block, the maximum number of packets that can be transmitted in the nth block, and the actual number of packets that is transmitted in that block. Here we implicitly assume that s(n) c(n), hence c(n) represents the capability of service facilities. In each block, s(n) packets are encoded by one codeword that spans the whole block and transmitted. If we assume N is sufficiently large, c(n) is just the instantaneous channel capacity of that block, measured by the number of packets, and the transmission is error-free. The sequence {a(n)}, {s(n)} and {c(n)} are refereed to as arrival process, departure process, and service process, respectively. 26

27 The delay-constrained communication problems based on the link-phy layer model have been widely studied. With the knowledge of CSI at transmitter side, we can control the departure process {s(n)} to achieve certain performance optimization. Different assumptions about the arrival process, delay bound, buffer size, etc. lead to various system configurations and optimization problem formulations. In general, the object of the optimization involves one of the following Maximize throughput. Minimize energy/power. Minimize delay (average delay, delay bound violation probability, etc.) Minimize packet loss. When one is picked as the objective, the others become constraints to the system. Despite the number of packet size representation of process {a(n)}, {c(n)} and {s(n)}, there are other interpretations [36]. We will focus on the number of packet representation. It is shown in [37] that problems that based on different interpretations can be solved by a unified approach. Finite Arrival Process. Finite Arrival process assumption suits for the situation where all the packets are known to arrive within T blocks. The objective is to schedule transmission power and rate to deliver all the packets before their deadlines using minimum power or energy consumption. The buffer is assumed to be large enough to accommodate all the packets, i.e., no packets dropping is considered. The problem is commonly known as scheduling problem. El Gamal et al. [38] studied the case where all the packets have the same deadline, under AWGN channel. The optimal strategy is the lazy scheduling where the lowest rate that can meet the deadline are employed. This work is extended to the discrete-states BF-AWGN channel [34] with both causal and acausal CSI assumptions. The same deadline constraint is also extended to individual deadline constraint. Each packet is assumed to have the same life time l blocks. And the deadline of a packet is its arrival time plus the life time. The casual CSI problem is 27

28 solved based on Lagrangian techniques and the acausal problem is solved by dynamic programming. In [39], the aforementioned optimization problem is generated to BT problem, i.e., transmitting B packets within time T, and each packet may have different arrival time and life time. Optimal solution is given for the case where all B packets arrive at the beginning and have the same deadline, over continuous-time discrete-state Markovian fading channel mode. Suboptimal solutions are given for arbitrary arrival processes and life time constraints. In [40] optimal solution for arbitrary BT problems is given for AWGN channel, and with acausal knowledge of arrival process. Strict average delay bound is considered in [41], where the scheduling algorithm guarantees that the average packet delay is smaller than a threshold. A near optimal strategy based on critical backlog policies is proposed for ON-OFF channel model (Gilbert-Elliott channel). By exploiting the scheduling algorithm, the queue length drifts around a target value, which is optimized to minimize the average power. Infinite Arrival Process. In many real-time applications such as video-chatting, the total number of packets to be transmitted or the deadline for which all the packets have to be delivered can not be obtained in advance. This motivated the study for the queueing system with infinite arrival process. The arrival process and service process are assumed to be ergodic and stationary. Berry et al. studied the optimal deterministic power control scheme for a queueing system with infinite buffer (no packet dropping) [37]. The power control policy determines the transmission power based on the system status which is defined as a triplet of number of arrival packets, fading gain and queue length of the current block. The fading process is modeled as a Markov chain. Two conflict objectives are considered, minimizing average transmission power and minimizing average delay. Intuitively, transmitting with a lower rate requires less power but increases the average delay and vice versa. Thus the two objectives can not be minimized simultaneously. This kind of problems is considered as 28

29 multiobjective optimization problem, and the solution is in the Pareto optimal sense. Denote {P, D } a Pareto optimal solution, where P and D are the average power and delay, respectively. Pareto optimal implies that no other power control scheme exists which can achieve an average power and delay pair {P, D} with both P < P and D < D. The problem of finding optimal deterministic power control policy is an average cost Markov decision problem which is solved by dynamic programming (which implicitly require finite state representation for both arrival and channel fading). The optimal power/delay curve is proved to be nonincreasing and convex. The average power/delay curve for a finite buffer with occupancy K packets is studied in [42], for AWGN channel. The power control schemes studied there belong to the class of zero-outage, probabilistic power control. Since the buffer size is finite, it is possible that arriving packets find a full buffer and some of the packets have to be dropped. The zero-outage property implies that all the packets will be delivered and none of them will be dropped due to finite buffer constraint (for AWGN channel this is achievable). Probabilistic power control is more general than deterministic power control. For a given system state, a probabilistic power control chooses one power level from multiple possible choices, according to a certain probability. For deterministic power control, there is only one power level associated with each system state. It is shown that deterministic power controls form the basis of probabilistic power controls, and the optimal deterministic power control form the boundary of achievable power/delay region. As in [37], the optimal deterministic power control is fund by dynamic programming. And the method is easily extended to finite-state Markovian BF-AWGN channel, or replace average delay constraint by a bounded delay constraint. Notice that in this case the state-space grows exponentially with the delay bound and usually prohibits its practice use. The concept of zero-outage power control is closely related to delay-limited capacity. And thus they suffer the same limitation from the variation of channel. If the channel can 29

30 not be inverted with a finite average power, the delay-limited capacity is zero. AWGN channel does not exhibit any variation and can be inverted with finite average power. Therefor the zero-outage power control always exists. For fading channels, e.g., finite state Markov channel (FSMC) or Rayleigh fading channel, if the channel gain is not bounded away from zero, the zero-outage power control does not exist and buffer overflow is inevitable. Be aware of the difficulty in providing zero-outage delay bound guarantee (also known as deterministic QoS guarantee), Wu and Negi studied statistical QoS provisioning problem in a fading channel environment [43] for large delay bound constraint. The buffer is assumed to be infinite and there is no packet dropping. Statistical QoS requirement is specified by the triplet of the source data-rate µ, the packet delay bound D max, and the delay bound violation probability ɛ (the outage probability). Satisfying the statistical QoS requirement implies that the delay bound violation probability is smaller than ɛ Prob[D( ) > D max ] ɛ, (1 12) where D( ) denotes the random variable of packet delay when queue enters the stable status. The maximum arrival data rate that a system can sustain under the statistical QoS constraint is derived in [44], termed as effective capacity α(u) = 1 u lim 1 P t log E[e u i=0 c(i) ]. (1 13) t t where u is the QoS exponent which relates the D max and ɛ. In fact, according to the large deviation theory, the probability of steady state queue length q( ) exceeding the threshold Q max satisfies [45] [46] Prob[ q( ) Q max ] e uq max, (1 14) 30

31 for large Q max. If the arrival process has a constant rate µ, D( ) = q( )/µ, (1 14) can be rewritten as Prob[ D( ) D max ] e uµd max, (1 15) where D max = Q max /µ. From (1 15) and (1 12), let e uµd max = ɛ, the statistical QoS requirement can be satisfied. And u = log(ɛ)/d max µ. (1 16) If the arrival process has variable rate, the linear relationship between D max = Q max /µ does not hold and only queue length violation probability (1 14) can be guaranteed [47]. Effective capacity characterizes the statistical QoS provisioning capability in large delay bound regime. For small delay bound or finite buffer where packet drop due to full buffer may occur, the approximation derived from large deviation theory (1 14) and (1 15) do not hold. With infinite buffer size, the queue length q(n) updates as q(n + 1) = max(q(n) + a(n) c(n), 0). (1 17) In a finite buffer of size L, q(n + 1) = max(min(q(n) + a(n), L) c(n), 0). (1 18) The max min structure makes the queuing behavior complicated and the elegant exponential decay property of the tail distribution of packet length (and also the packet delay if the arrival is constant) vanishes. Providing explicit statistical QoS guarantees for a variable-rate arrival process and finite buffer size is not an easy task. People resort to another QoS measure, the packet loss probability. Packet loss includes the packets dropping at the transmitter because of a full buffer and erroneously decoding at the receiver due to noisy channel. Notice that many aforementioned works assume that N and the transmission is error free, or kept 31

32 a fixed packet error rate and neglect this effect. Notice that the packet loss probability translates to delay bound violation probability if the arrival rate is constant. QoS provisioning problem in terms of packet loss probability for a finite buffer is studied in [48] and the references therein. The optimal rate and power control scheme are obtained which minimize the packet dropping probability subject to a fixed packet error probability, or minimize the total packet loss probability. The channel model is still finite-state Markovian BF-AWGN. And the optimization problem is solved by dynamic programming, as in [37] and [42]. 1.3 Outline of the Dissertation The dissertation is organized as follows. Chapter 2 studies the queue-length-aware (QLA) power control (PC) scheme which maximizes the effective capacity subject to long-term average power constraint. The power control schemes that aim at optimizing physical-layer performance measures, adapt the transmission power to the channel gain; we call these channel-gain-based (CGB) PC, such as TDWF and TCI described in section It is shown that CGB-PC is not optimal in link-phy layer models where the queue is incorporated [37]. The optimal CGB-PC that maximizes the effective capacity is proposed in [49] and [7]. The structure of the optimal CGB-PC depends on the delay bound. At two extremes, i.e., delay bound approaches to infinite and zero, the optimal CGB-PC approaches TDWF and TCI, respectively. To further improve the performance, we propose the hierarchical queue-length-aware (HQLA) power control which is a simple scheme but substantially increase the effective capacity over the optimal CGB-PC scheme in moderate QoS requirements regime. Chapter 3 investigates the impact of imperfect CSI to the optimal power control scheme. The CSI is assumed to be perfectly estimated at the receiver side but delivered to the transmitter side after n blocks. The outdated CSI degrades the efficiency of the optimal power control scheme greatly since it relies on the accuracy of CSI. To address this problem, a two-step suboptimal power allocation scheme is proposed for a 32

33 single user multiple-channel system with statistical QoS requirements. In the first step, the total transmission power that can be used by one block is determined according to the summation of the channel gains of all the channels. In the second step, the total transmission power is allocated to all the channels. Compared to the optimal power allocation scheme designed for the perfect CSI assumption, the proposed power allocation scheme reduces the computation complexity significantly while achieves comparable performance. Chapter 4 addresses the problem of providing explicit statistical QoS guarantees for a multi-user, multi-channel system. The joint power and channel allocation algorithm is studied, and the QoS provisioning capability is ensured by exploiting effective capacity and reference channel approach. We assume the transmitter (the base-station) has the perfect CSI knowledge about the channels. At each transmission slot, a scheduler allots the transmission power and channel access to all the users based on a pre-determined reference channel. Three allocation schemes are proposed, which utilize both multiuser diversity and frequency diversity. The proposed schemes substantially reduce the resource usage while explicitly guaranteeing the users QoS requirements. Chapter 5 and Chapter 6 study optimal power control scheme that minimizes packet loss probability subject to long-term average power constraint. In chapter Chapter 5, we assume N and the packet loss probability reduces to packet drop probability. In Chapter 6, we consider a more practical scenario, i.e., N is finite and packet loss probability consists of both packet drop and packet error. This work is closely related to [48]. The difference is the channel model been used. In [48] and most related works, the BF-AWGN channel is modeled as FSMC. Thus the optimization problem can be formulated as a Markov decision problem and solved by dynamic programming. This approach is not suitable for solving continuous channel model problems such as Rayleigh fading channel, since the quantization of continuous channel results performance degradation and computational complexity grows exponentially as the number of channel 33