Protocols For Dynamic Spectrum Access

Transcription

1 Clemson University TigerPrints All Dissertations Dissertations 5-8 Protocols For Dynamic Spectrum Access Thomas Royster Clemson University, Follow this and additional works at: Part of the Electrical and Computer Engineering Commons Recommended Citation Royster, Thomas, "Protocols For Dynamic Spectrum Access" (8). All Dissertations This Dissertation is brought to you for free and open access by the Dissertations at TigerPrints. It has been accepted for inclusion in All Dissertations by an authorized administrator of TigerPrints. For more information, please contact

2 PROTOCOLS FOR DYNAMIC SPECTRUM ACCESS A Dissertation Presented to the Graduate School of Clemson University In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Electrical Engineering by Thomas C. Royster IV May 8 Accepted by: Dr. Michael B. Pursley, Committee Chair Dr. Joel V. Brawley Dr. Daniel L. Noneaker Dr. Harlan B. Russell

3 ABSTRACT Protocols for modulation selection, initial transmitter power adjustment, modulation and coding adaptation, and transmitter power adaptation are presented. Most adaptive protocols in the literature are for full-duplex communication and they require channel estimation (e.g., using training symbols); however, our protocols are for half-duplex packet radios and they do not require estimation of the channel for adaptation. Instead, our protocols are driven by statistics that can be derived from the receiver s demodulator or decoder. We present the protocols in the context of their application to dynamic spectrum access networks. Our protocols are designed for adaptive radios, of which software-defined radios and cognitive radios are special cases. We describe and evaluate techniques that enable cognitive radios to adjust the decision thresholds of an adaptive transmission protocol based on past results. Finally, we describe statistics from our adaptive transmission protocol that can be used to provide information to higher-layer protocols and cognitive processes.

4 DEDICATION This dissertation is dedicated to my wife, Betsy.

5 ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Michael B. Pursley, for his assistance in preparing this dissertation. I am forever indebted to him for all the guidance and encouragement he has given me throughout my graduate education. I wish to thank Mrs. Pursley as well for many years of hospitality. I would like to thank Dr. Joel V. Brawley, Dr. Daniel L. Noneaker, and Dr. Harlan B. Russell for serving on my committee. I am also grateful for having the opportunity to take classes from each of them during my time in Clemson. Finally, I thank my friends and family for their love and constant support.

6 TABLE OF CONTENTS Page TITLE PAGE i ABSTRACT ii DEDICATION iii ACKNOWLEDGMENTS iv LIST OF TABLES x LIST OF FIGURES xii CHAPTER 1. INTRODUCTION SYSTEM AND CHANNEL MODELS RECEIVER STATISTICS Error Count Iteration Count Demodulator Statistics GENERAL ADAPTIVE PROTOCOLS Observation Spaces Selection Spaces Adaptive Protocols MODULATION SELECTION PROTOCOL

7 Table of Contents (Continued) Page 6. INITIAL POWER ADJUSTMENT Power Adjustment Protocol Description Robust Initial Power Adjustment ADAPTIVE CODING Performance Results for Static Channels Performance Results for Time-Varying Channels ADAPTIVE MODULATION AND CODING Performance Results Other Models for Time Variations of the Channel ADAPTATION OF TRANSMITTER POWER Protocol Description Performance Results THRESHOLD LEARNING Packet-By-Packet Session-By-Session SESSION STATISTICS CONCLUSION APPENDICES A. LIST OF SYMBOLS B. CAPACITY B.1 Notation B.1.1 Definitions B.1. Density and Mass Functions vi

8 Table of Contents (Continued) Page B.1.3 Expected Values B.1.4 Multiple Symbols Per Dwell Interval or Block... 9 B.1.5 Capacity B. Basic Density Functions B..1 N-Orthogonal (Coherent); Block Interference; Rician Fading B.. N-Biorthogonal (Coherent); Block Interference; Rician Fading B..3 N-Orthogonal (Noncoherent); Block Interference; Rician Fading B..4 N-Orthogonal (Coherent); Block Interference; Rician Fading; BICM B..5 N-Biorthogonal (Coherent); Block Interference; Rician Fading; BICM B..6 N-Orthogonal (Noncoherent); Block Interference; Rician Fading; BICM B.3 General Expressions for Monte Carlo Evaluations B.3.1 Density Functions B.3. Density Functions Specialized to Binary Codes.. 13 B.4 Special Case: AWGN-only Channel B.4.1 N-Orthogonal, Coherent B.4. N-Biorthogonal B.4.3 N-Orthogonal, Noncoherent B.4.4 N-Orthogonal, Coherent, BICM B.4.5 N-Biorthogonal, BICM B.4.6 N-Orthogonal, Noncoherent, BICM B.4.7 Summary B.5 Special Case: AWGN and Block Rician Fading B.5.1 N-Orthogonal, Coherent, Fading Amplitude Unknown B.5. N-Orthogonal, Coherent, Fading Amplitude Known B.5.3 N-Biorthogonal, Coherent, Fading Amplitude Unknown B.5.4 N-Biorthogonal, Coherent, Fading Amplitude Known B.5.5 N-Orthogonal, Noncoherent, Fading Amplitude Unknown vii

9 Table of Contents (Continued) Page B.5.6 N-Orthogonal, Noncoherent, Fading Amplitude Known B.5.7 N-orthogonal, Coherent, BICM, Fading Amplitude Unknown B.5.8 N-orthogonal, Coherent, BICM, Fading Amplitude Known B.5.9 N-Biorthogonal, Coherent, BICM, Fading Amplitude Unknown B.5.1 N-Biorthogonal, Coherent, BICM, Fading Amplitude Known B.5.11 N-Orthogonal, Noncoherent, Binary Codes, Fading Amplitude Unknown B.5.1 N-Orthogonal, Noncoherent, Binary Codes, Fading Amplitude Known (N-ONC) B.6 Special Case: AWGN and Gaussian Block Interference B.6.1 N-Orthogonal Coherent, No CSI B.6. N-Orthogonal Coherent, CSI B.6.3 N-Biorthogonal Coherent, No CSI B.6.4 N-Biorthogonal Coherent, CSI B.6.5 N-Orthogonal Noncoherent, No CSI B.6.6 N-Orthogonal Noncoherent, CSI B.6.7 N-Orthogonal Coherent, BICM, No CSI B.6.8 N-Orthogonal Coherent, BICM, CSI B.6.9 N-Biorthogonal Coherent, BICM, No CSI B.6.1 N-Biorthogonal Coherent, BICM, CSI B.6.11 N-Orthogonal Noncoherent, BICM, No CSI B.6.1 N-Orthogonal Noncoherent, BICM, CSI B.7 Special Case: AWGN and Block Interference and Block Fading B.7.1 N-Orthogonal Coherent, No CSI, Fading Unknown 134 B.7. N-Orthogonal Coherent, No CSI, Fading Known. 134 B.7.3 N-Orthogonal Coherent, CSI, Fading Unknown B.7.4 N-Orthogonal Coherent, CSI, Fading Known B.7.5 N-Orthogonal Coherent, No CSI, Fading Unknown, BICM B.7.6 N-Orthogonal Coherent, No CSI, Fading Known, BICM viii

10 Table of Contents (Continued) Page B.7.7 N-Orthogonal Coherent, CSI, Fading Unknown, BICM B.7.8 N-Orthogonal Coherent, CSI, Fading Known, BICM B.7.9 N-Biorthogonal Coherent, No CSI, Fading Unknown B.7.1 N-Biorthogonal Coherent, No CSI, Fading Known B.7.11 N-Biorthogonal Coherent, CSI, Fading Unknown 14 B.7.1 N-Biorthogonal Coherent, CSI, Fading Known B.7.13 N-Biorthogonal Coherent, No CSI, Fading Unknown, BICM B.7.14 N-Biorthogonal Coherent, No CSI, Fading Known, BICM B.7.15 N-Biorthogonal Coherent, CSI, Fading Unknown, BICM B.7.16 N-Biorthogonal Coherent, CSI, Fading Known, BICM B.7.17 N-Orthogonal Noncoherent, No CSI, Fading Unknown B.7.18 N-Orthogonal Noncoherent, No CSI, Fading Known B.7.19 N-Orthogonal Noncoherent, CSI, Fading Unknown 146 B.7. N-Orthogonal Noncoherent, CSI, Fading Known. 147 B.7.1 N-Orthogonal Noncoherent, No CSI, Fading Unknown, BICM B.7. N-Orthogonal Noncoherent, No CSI, Fading Known, BICM B.7.3 N-Orthogonal Noncoherent, CSI, Fading Unknown, BICM B.7.4 N-Orthogonal Noncoherent, CSI, Fading Known, BICM C. CAPACITY-ACHIEVING CODES AND IDEAL PRO- TOCOLS C.1 Capacity-Achieving Codes C. Protocols with Perfect Channel State Information ix

11 LIST OF TABLES Table Page 6.1 Endpoints for partitioning the observation space for the initial power adjustment protocol Results of the initial power adjustment protocols for the first channel type (Target + Uniform [1, +1]). The power for each of the 1, sessions was adjusted to a level between P min + 1 and P min + by the protocol Results of the initial power adjustment protocols for the second channel type (Target + Uniform [15, +15]). The power for each of the 1, sessions was adjusted to a level between P min + 1 and P min + by the protocol CENR requirements for a 1 packet error probability for ten code-modulation combinations The values of µ 1 µ 38 for the robust initial power adjustment protocol Partitions of the observation space for 64-biorthogonal modulation Partitions of the observation space for 3-biorthogonal modulation Partitions of the observation space for 16-biorthogonal modulation Partitions of the observation space for 8-biorthogonal modulation Capacity and performance in terms of CENR for ten combinations of turbo product codes and modulation formats Partitions of the observation space for the adaptive modulation and coding protocol

12 List of Tables (Continued) Table Page 1.1 Packet error probability and session duration for Systems I and II (averaged over 1 sessions, 56KB of data per session) xi

13 LIST OF FIGURES Figure Page 1.1 Our approach to adaptive protocols vs. the typical approach Spread-spectrum system model K-state Markov chain for modeling propagation losses Extraction of statistics for use in adaptive transmission Illustration of the concept of resource consumption Limits on the achievable normalized resource consumption Power adjustment protocol performance for 496-IQB Distribution of transmitter power after seven packet transmissions (496-IQB) Flow chart for the adaptive transmission protocol Performance of our adaptive coding protocol for 64-biorthogonal modulation Performance of our adaptive coding protocol for 3-biorthogonal modulation Performance of our adaptive coding protocol for 16-biorthogonal modulation Performance of our adaptive coding protocol for 8-biorthogonal modulation Performance of our adaptive coding protocol for 64-biorthogonal modulation on a channel with time-varying propagation losses (K = 6, = db, p =.1) Performance of our adaptive coding protocol for 3-biorthogonal modulation on a channel with time-varying propagation losses (K = 6, = db, p =.1)

14 List of Figures (Continued) Figure Page 7.8 Performance of our adaptive coding protocol for 16-biorthogonal modulation on a channel with time-varying propagation losses (K = 6, = db, p =.1) Performance of our adaptive coding protocol for 8-biorthogonal modulation on a channel with time-varying propagation losses (K = 6, = db, p =.1) Throughput for the fixed code-modulation combinations Throughput of the 1 selected code-modulation combinations and the upper envelope of 1 combinations with capacityachieving codes Performance of our protocols on a static channel Normalized throughput for the adaptive transmission protocol on a channel with a time-varying propagation loss modeled by a four-state Markov chain ( = 1 db, p =.1) Normalized throughput for the adaptive transmission protocol on a channel with a time-varying propagation loss modeled by a six-state Markov chain ( = 1 db, p =.1) Normalized throughput for the adaptive transmission protocol on a channel with a time-varying propagation loss modeled by a four-state Markov chain ( = db, p =.1) Normalized throughput for the adaptive transmission protocol on a channel with a time-varying propagation loss modeled by a six-state Markov chain ( = db, p =.1) Normalized throughput for the adaptive transmission protocol on a channel with a time-varying propagation loss modeled by a fifteen-state Markov chain ( =.5 db, p =.1) Performance results for a channel whose transitions can occur only between packet transmissions (error count protocol, K = 6, = db, p =.1) xiii

15 List of Figures (Continued) Figure Page 8.1 Performance results for a channel whose transitions can occur only between packet transmissions (PPSI protocol, K = 6, = db, p =.1) Performance results for a channel whose transitions can occur every 1 chip durations (error count protocol, K = 6, = db, p =.1) Performance results for a channel whose transitions can occur every chip durations (error count protocol, K = 6, = db, p =.1) Response of the adaptive protocol to changes in propagation loss Session duration for sending 5KB Performance results for systems with and without threshold learning protocols (error count threshold too large) Performance results for systems with and without threshold learning protocols (error count threshold too small) Frequency reassignment instead of power increase Resource consumption metric Normalized session time metric Average error count metric Session statistic metric: 1 i=1 (1i)N i, where code-modulation combination i was used N i times during the session xiv

16 CHAPTER 1 INTRODUCTION Many obstacles hinder reliable communication over wireless links, so engineers have typically included design margins in traditional communication systems. For example, several decibels (db) of excess transmitter power, a robust modulation format, and an error-control code with high redundancy increase the likelihood that packets will be received correctly, even in unfavorable conditions. However, when conditions are not at their worst, large design margins contribute to the waste of radio resources, such as energy and time, and network resources, such as spatial and frequency reuse. The number of wireless devices in use continues to increase, but spectrum is limited, and, by many accounts, used inefficiently (e.g., [1]). In fact, one of the conclusions of [1] is that improved spectrum access policies would largely alleviate the problems commonly blamed on spectrum scarcity. Dynamic spectrum access networks offer an advantage over traditional access policies because such networks permit radios to select from among a number of different bands. One example of a dynamic spectrum access network has predefined primary users and secondary users. As long as no primary users are operating, secondary users are allowed to use the spectrum. However, secondary users must vacate the spectrum if any primary users begin to use it. A more general example of a dynamic spectrum network is one that employs a spectrum assignment system (SAS) which may be centralized or distributed. The SAS is responsible for coordinating transmissions in the bandwidth it controls. Cognitive radios and cognitive networks [], [3] could perform the duties of an SAS; however, neither is required for dynamic spectrum access.

17 One goal of this research is to provide practical protocols for adaptation in halfduplex packet radios that are part of a dynamic spectrum access network. The radios need to have flexibility in terms of the spatial, spectrum, and temporal resources that their transmissions occupy so that the radios can adapt as some resources become scarcer and others become more plentiful. As such, the radios we consider have available several modulation formats, error control codes, and transmitter power settings. A protocol for modulation selection is responsible for choosing a combination of transmission parameters that balances the radio s goals of reliable communication and meeting quality-of-service priorities with constraints imposed by spectrum etiquette policies. A key aspect of the design of the adaptive transmission protocols is to determine a practical means to measure the transmitter s success and decide whether changes should be made in modulation, coding, or perhaps transmitter power while a session is taking place. To this end, we base our adaptation statistics on data that can be extracted from subsystems already present in many current receiver implementations. Because our radios are half-duplex, adaptation can take place only on a packet-bypacket basis. In this dissertation, we describe protocols for initial power adjustment, adaptive coding, adaptive modulation and coding, and adaptation of transmitter power. In contrast to designs that incorporate excess margins, these protocols strive for operation near the Shannon capacity limits. We compare the performance of our practical adaptive protocols with the performance of several different ideal protocols. One such ideal protocol has perfect knowledge of the channel state and employs capacity-achieving codes, so it always performs at the capacity limit. The performance of this protocol bounds the performance of any adaptive protocol, and we are able to demonstrate that our protocols perform almost as well. A common assumption in previous research on adaptive transmission is that the

18 Our Protocols Adapt TX Channel RX Estimate Adapt Typical Approach Figure 1.1: Our approach to adaptive protocols vs. the typical approach. radios have full-duplex transmission capability so that channel-state information can be sent on a feedback link at the same time that data transmission is taking place on the forward link. Many of the previously published adaptive transmission protocols rely on perfect channel-state information (e.g., [4] [6]). Other protocols use pilot or training symbols to permit the estimation of the channel state; for example, this approach is employed in [6] and in several IEEE standards. Many authors either assume the availability of perfect knowledge of the channel gain on the forward link or estimates of the channel gain that are sent to the transmitter on a feedback link, perhaps using a feedback model that incorporates estimation error and delay (see Chapter 9 of [7] and the references cited therein). In contrast, our adaptive transmission protocols do not require channel-state information to be supplied by an external source nor do they require estimation of the channel gain or the received power, insertion of pilot or training symbols, or full-duplex transmission. Figure 1.1 provides an illustration of the differences between our adaptive protocols and most adaptive protocols described in the literature. Our approach is based on our belief that an adaptive transmission protocol should rely on information from the demodulator and decoder to determine whether changes are needed in coding and 3

19 modulation and what the changes should be. Regardless of what is happening on the channel, more powerful modulation and coding are unnecessary if an acceptable error probability is provided at the decoder output. The statistics used by our protocols are easy to derive in the receiver s demodulator and decoder, they provide reliable assessments of the receiver s performance, and they can be communicated to the transmitter by sending only a few bits in each acknowledgment packet. Although halfduplex communication introduces some delay in receiving feedback, in the networks we consider, we believe that the main goal of adaptive transmission is to respond to slow variations in the channel. The conclusions in [8] support this belief. 4

20 CHAPTER SYSTEM AND CHANNEL MODELS We consider packet radio networks consisting of half-duplex adaptive radios. The parameters that can be adapted include modulation, coding, and transmitter power; however, it is possible that some radios can adapt only a subset of these parameters. The radios are also able to change center frequencies and bandwidths, which enables them to operate in different frequency bands. A session must be established whenever one radio, the source, wishes to send a sequence of packets to another radio, the destination. Other radios within range of the source are referred to as unintended receivers; these radios may erience interference from the source s transmissions. The system model is shown in Figure.1. We consider bit-interleaved coded modulation (BICM) [9] because of the flexibility it allows in choosing the modulation and error-control code. For example, with BICM, multiple modulation formats can be employed with the same binary code. As shown in the figure, a pseudorandom signature sequence can be applied to the data-modulated signal. Although this does not affect the performance on interference-free channels, the signature sequence helps to mitigate multiple-access and multipath interference, which enables the network to permit simultaneous transmissions over a common frequency band. Terminal i has n c,i available binary codes which form the set C i. Code C i,j C i has Binary Encoder Interleaver m-bit Words M-ary Modulator PN Sequence PN Sequence Channel Decoder Deinterleaver M-ary Demodulator Figure.1: Spread-spectrum system model.

21 rate r i,j, and we assume that r i,1 < r i, < < r i,nc,i. Terminal i also has n m,i available modulation formats which form the set M i. The jth modulation format of M i is denoted M i,j. In general, modulation format M j has parameters (M j, L j, m j, η j ), where M j is its alphabet size or cardinality, L j is the number of modulation chips per symbol, m j bits are represented by each symbol, and η j signature sequence chips are applied to each modulation chip. Non-spread direct sequence modulation is obtained if a signature sequence is used with η j = 1. The modulation symbol has energy E = A T, where A is the signal amplitude and T is the symbol duration. Format M j has M j modulation symbols, and each modulation symbol represents a unique sequence of m j = log (M j ) binary (code) symbols. The binary symbol energy is thus E s = E/m j. The energy per information bit is related to the binary symbol energy by E s = re b, where r is the rate of the error-control code. If the modulation format has L j modulation chips per symbol, then the energy per chip is given by E c = E/L j. Each modulation format can be employed with each error-control code, so terminal i has n c,i n m,i code-modulation combinations that it can use. In some situations, the protocol may employ only a subset of n i combinations, where n i n c,i n m,i. For simplicity, the subscript i denoting the terminal will not be included henceforth, and we will assume that if terminals i and j wish to communicate, then they have n available code-modulation combinations in common. The kth code-modulation combination is denoted by D k, 1 k n. Let R k be the information rate of D k, where the information rate is the number of information bits per signature sequence chip provided by a code-modulation combination. If D k consists of M l and C j, then R k = r jm l L l η l. The code-modulation combinations are indexed in order of increasing information 6

22 rate. In our investigations, we consider four binary product codes (n c = 4) and their respective turbo (iterative) decoders. Code C 1 consists of the product of two (16, 11) extended Hamming codes and one (8, 4) extended Hamming code, so its rate is r 1 =.36. Code C is a three-dimensional code derived from three (16, 11) extended Hamming codes, so r =.35. Code C 3 is a three-dimensional code whose constituent codes are two (3, 6) extended Hamming codes and a (4, 3) parity-check code, so r 3 =.495. Code C 4 is a two-dimensional code obtained from two (64, 57) extended Hamming codes, so r 4 =.793. These codes are particularly easy to use in adaptive coding because their encoders and decoders are available on a single chip [1]. The log-likelihood ratio (LLR) (e.g., [11],[1]) is used as the soft-decision metric, but we do not assume that the noise variance (or, equivalently, the signal-to-noise ratio) is known. Instead, the parameters in the LLR that depend on the signal-to-noise ratio are chosen to be constants that provide robust performance. The block length of C 1 is 48 bits and the block length of each of the remaining codes is 496 bits. The packet length is fixed at 496 bits, so there is one code word per packet when C, C 3, or C 4 is used and two code words per packet when C 1 is used. Each code word in the packet has to be decoded correctly for the packet to be correct. An S-random interleaver [13] is used to interleave each code block before modulation. Furthermore, if a packet contains N c code words, the packet layout is such that each set of N c consecutive modulation symbols in the packet contains one and only one modulation symbol derived from each code word. In effect, the modulation symbols from each code word are spread throughout the packet, which helps mitigate the effects of time-varying channel disturbances [14] [16]. The protocols that we present are applicable to many forms of modulation. For our numerical results, we consider coherent detection of quadrature amplitude mod- 7

23 p p p 1... K 1 p p p p 1 p 1 p Figure.: K-state Markov chain for modeling propagation losses. ulation (QAM), quadrature phase shift key (QPSK), and nonbinary coded modulation. Examples of nonbinary coded modulation include orthogonal and biorthogonal modulation derived from Hadamard matrices [17],[18]. If each row of an M M Hadamard matrix H M defines a sequence of polarities of M unit-amplitude pulses (known as modulation chips), then the result is an orthogonal signal set of size M. The union of this signal set and its complement (i.e., the signals derived from H M ) is a M-biorthogonal signal set. Furthermore, because QAM and QPSK utilize both the inphase branch and the quadrature branch, we also consider I-Q versions of biorthogonal signals. When M-biorthogonal modulation is independently used on each branch, we denote the resulting signal set M I-Q biorthogonal modulation (M -IQB). All channels under consideration are subject to additive white Gaussian noise (AWGN) with two-sided spectral density N /. We define the binary symbol energy to noise density ratio in db as SENR = 1 log 1 (E s /N ), the energy per information bit to noise density ratio in db as ENR = 1 log 1 (E b /N ), the energy per modulation chip to noise density ratio in db as CENR = 1 log 1 (E c /N ). To simplify the modeling and analyses of more complex channels, we employ a Markov chain for each time-varying parameter. Assume that the channel has N time-varying parameters and that the ith parameter is modeled by a K i -state Markov chain of the type shown in Figure. with transition probabilities p i (j k), 1 j K i, 1 k K i, where p i (j k) is the probability that the next state for the ith parameter will be j given that the previous state was k. Then, we can equivalently 8

24 describe the channel with a single K-state Markov chain, where K = N i=1 K i. Let s = (u 1, u,...,u N ) be the state vector, where u i is the state of the Markov chain for parameter i. Let U t i be a random variable representing the state of the Markov chain for parameter i at time t, so that S t = (U1, t U, t..., UN t ) is a random state of the composite Markov chain at time t. If U1 t, Ut,...,Ut N are conditionally mutually independent given U t1 1, U t1,...,u t1 N and if P(Ut i = u i S t1 = s) = P(U t i = u i U t1 i = v i ), and if S t is conditionally independent of S w : w t given S t1, then P S t = (u 1, u,..., u N ) S t1 = (v 1, v,..., v N ) = N p i (u i v i ) i=1 can be used to compute the transition probabilities of the composite Markov chain. 9

25 CHAPTER 3 RECEIVER STATISTICS Many existing adaptive transmission protocols require full-duplex communication and detailed channel-state information (CSI) [4] [8]. The corresponding subsystems add complexity and cost to both the transmitter and receiver. However, the intended application of our research is to half-duplex packet radio networks, in which information that the receiver wishes to convey to the transmitter is sent in acknowledgment packets, for example. To minimize overhead, one design goal for our protocols is that feedback be limited to a few bits. In this section we present low-complexity receiver statistics that can be extracted from computations already taking place in the receiver and require little or no additional hardware. 3.1 Error Count Because BICM is employed for all of the modulation and coding combinations considered herein, the output of the encoder and the input to the decoder are binary digits (though, the decoder inputs are scaled by soft-decision values). The error count for a received word is the number of hard decision bit errors between the encoder output and the decoder input. If the error count for the ith received word in the packet is c i, then the error count for the packet is N c c = c i, i=1 where N c is the number of codewords in the packet. In some decoders, the error count is readily available. As illustrated in Figure 3.1, regardless of the decoder, the error count can be determined by re-encoding the

26 Hard Decisions Symbol Comparator Error Count Encoder Y(t) Demodulator Soft Decisions Iterative Soft-Decision Decoder Decoded Packet Iteration Count Compute Statistic Demodulator Statistic Figure 3.1: Extraction of statistics for use in adaptive transmission. decoder output and comparing the result with the hard decisions of the bits passed to the decoder. If the packet is decoded correctly and the packet length is sufficiently large, then the error count provides an accurate representation of the channel binary symbol error rate, which proves to be a useful statistic for the adaptive protocols we employ. 3. Iteration Count In an iterative decoder, such as the turbo decoder that we consider, more corruption on the channel generally means that more iterations are required to decode a received word if successful decoding is even possible. Based on this observation, we use the average number of iterations necessary to decode the received words that constitute the packet as an indication of channel quality. Specifically, if b j iterations are required to decode the jth received word of the packet, then the iteration count for the packet is b = 1 N c b j, N c j=1 where N c is the number of codewords in the packet. 11

27 3.3 Demodulator Statistics The choice of demodulator statistic depends on the modulation format and the desired complexity. For M-orthogonal modulation and M-biorthogonal modulation, the demodulator may consist of M correlators or matched filters. Regardless of the implementation, M decision statistics are produced for each received symbol. Let the largest magnitude among all decision statistics be Z and let the second largest magnitude be Z. The maximum-likelihood decision rule for coherent detection of orthogonal modulation is to select the symbol corresponding to the largest correlator output, so Z is presumed to be the signal output (i.e., if the decision is correct). It follows that Z gives an indication of the largest noise power. For the ith received symbol, the statistic w i = 1 Z /Z is computed. w i is based on Viterbi s ratio statistic [19]. Once the entire packet has been received, the value w = 1 N m N m w i i=1 is determined, where N m is the number of modulation symbols in the packet. w is known as the ratio statistic for the packet. For two-dimensional modulation formats, such as QPSK and QAM, the demodulator statistic is a distance statistic that is computed for each symbol. Let l j be the jth constellation point in an M-ary signal set. If the received point corresponding to modulation symbol i is s i, then define v i = min 1 j M s i l j, where a b is the Euclidean distance between a and b. After all N m modulation 1

28 symbols of the packet have been received, the distance statistic v = 1 N m N m v i i=1 is used as the demodulator statistic for the packet. The use of other demodulator statistics is certainly possible, but we have found that protocols employing the ratio statistic or the distance statistic perform very well. These statistics are especially accurate when the signal-to-noise ratio (SNR) is high. The ratio statistic does not depend on the received power and it is generally robust to interference and other disturbances. The distance metric is sensitive to received power levels and phase errors; however, in high SNR regions such sensitivity can often be mitigated. One attractive property of demodulator statistics is that they generally perform better than the error count or the iteration count when the channel quality is excellent. For example, the minimum error count is zero and the minimum iteration count is one. Once these values are reached, the channel can become arbitrarily better but neither statistic is sensitive to the change. Demodulator statistics typically do not saturate as quickly, if at all. 13

29 CHAPTER 4 GENERAL ADAPTIVE PROTOCOLS In their broadest sense, adaptive transmission protocols decide on a set of transmission parameters based on information they are given. First, adaptive transmission protocols must have something to adapt, such as code rate, modulation, or transmitter power. Then, the protocol must obtain information related to the effectiveness of the current set of parameters. The protocol then uses this information to decide what, if anything, should be changed to improve performance. Define the observation space I to be the set of possible inputs to the protocol, and define the selection space S to be the set of possible transmission parameters. Then, the adaptive protocol is a function f : I S, (4.1) where f is not necessarily one-to-one or onto. The operation of the adaptive protocol depends on both I and S, and the choices of I, S, and f affect the complexity and performance of the adaptive system. Many common devices can gather simple statistics from each packet reception, so the observation space can also be simple, whereas more complex devices may have very detailed channel-state information and thus a complex observation space. We wish to not only devise and evaluate simple adaptive systems, but we also wish to compare the performance of such systems with the performance of ideal systems. 4.1 Observation Spaces A protocol supplied with perfect previous state information (PPSI) is given i, 1 i K, the state of the channel when the last packet was received, as well as the

30 transition probabilities p(j i), 1 j K. Thus, I is the product of the set of all possible states and the set of all possible values of p(j i) for each j and i. A protocol with perfect next state information (PNSI) is supplied with j, 1 j K, the state of the channel for the next packet transmission, so I = 1,,..., K, the set of all possible states. If each state of the Markov chain represents the values of N parameters, then the observation space for PPSI and the observation space for PNSI are at least N- dimensional. In addition, because the exact value of each parameter is required, obtaining PPSI is very complex and obtaining PNSI is impossible. Nevertheless, we can define hypothetical protocols corresponding to each of these two observation spaces and study them analytically to provide performance bounds for practical systems. The receiver statistics in Chapter 3 produce observation spaces that are not only simpler than those for PPSI and PNSI, but whose statistics are also simpler to obtain. The error count observation space I is the set, 1,,..., N p of all possible binary symbol error totals, where N p is the number of binary symbols per packet. The adaptation statistic is the error count for the last packet. For an iterative decoder requiring at least A 1 iterations and at most A iterations, the iteration count observation space is the set I [A 1, A ], and the adaptation statistic is the average number of iterations per code block for a packet. The ratio statistic for biorthogonal signals has I = [, 1). The adaptation statistic for a packet is the average of the ratio statistics for all modulation symbols in the packet. The observation space for the distance statistic for QPSK and QAM is I = [, ). The distance statistic for a packet is the average of the distance statistics for all modulation symbols in the packet. 15

31 4. Selection Spaces The selection space S is the set of choices of transmission parameters that are available to the adaptive protocol. For example, the systems we evaluate either employ four turbo product codes or the capacity-achieving codes of the same rates as the turbo product codes. We also investigate selection spaces with multiple modulation formats, which allows a larger dynamic range of bandwidth or throughput than adaptive coding alone. In particular, we present performance results for selection spaces with 16-QAM, QPSK, 64 -IQB, and M-biorthogonal modulation for different values of M. Finally, if the transmitter power can be adapted, the selection spaces contain the available power levels. If such selection spaces also include multiple error-control codes or modulation schemes, then there is great flexibility in defining the adaptive protocol. For example, in networks not limited by multiple-access interference, power increases may be the primary response to propagation losses. In interference-limited networks, power adaptation must be used sparingly, so adaptive modulation and coding is employed. 4.3 Adaptive Protocols Both I and S influence the definition and behavior of the adaptive protocol f. First, we consider protocols that can adapt only the code or both the code and modulation. We determine the ected normalized throughput of each code-modulation combination for each element in I. Then, if γ I is the adaptation statistic, the combination D i is chosen if it provides the maximum conditional ected normalized throughput given γ. For example, let s(j k) be the ected throughput for combination D j when the 16

32 channel is in state k. The average conditional ected throughput if D j is used for the next packet given the last state was state i is [] s(j i) = K s(j k)p(k i). k=1 Recall that the PPSI protocol is given the previous state i and p(j i), 1 j K, so the PPSI protocol chooses D ji if s(j i i) = max s(j i). (4.) 1 j n In other words, D ji is chosen if it is the combination that maximizes the ected throughput when conditioned on the value of the previous state. The throughput of each combination in each of the possible next states is taken into account in this protocol. The PNSI protocol is given k, the state of the channel when the next packet is to be transmitted, so this protocol chooses D jm if s(j m k) = max s(j k). (4.3) 1 j n This protocol simply chooses the code-modulation combination that provide the maximum ected throughput in the next state. The analytical ressions for the average throughput of the PPSI and PNSI protocols are given in Appendix C. The protocols that utilize a receiver statistic map I to S with interval tests. Given D k was used for the last packet, S k S is the set of possible code-modulation combinations that can be used for the next packet. Each ξ I for which D i provides the maximum ected normalized throughput of all D j S k is placed in interval I i. When the protocol is in operation, each time D k is used for the previous packet and the value of the receiver statistic falls in interval I i, then D i is chosen for the next packet. 17

33 For adaptive coding with four codes, we employ the PNSI protocol with selection spaces that include capacity-achieving codes of rates r 1, r, r 3, and r 4 to determine the maximum throughput of an adaptive protocol with any codes of these four rates. We also examine the performance of both the PNSI protocol and the PPSI protocol with selection spaces corresponding to the four turbo product codes to bound the performance of protocols using these codes. The receiver statistic protocols are employed with the four turbo product codes to illustrate the performance of adaptive systems with practical choices for I, S, and f. Now assume that D 1, D,...,D n, in order of increasing normalized information rate, are the only code-modulation combinations in S, but S also contains multiple transmitter power settings. For protocols that can adapt transmitter power, our convention is that power is allowed to be adapted only if D 1 or D n is employed; in particular, the power can only be increased if D 1 is in use and the power can only be decreased if D n is in use. If D 1 is not robust enough for reliable communication at the nominal power level, the power is increased. During the time that D 1 is used, the power can be adapted by the protocol as long as the power does not fall below the nominal level or does not exceed some predetermined maximum level. Instead of employing a power level below the nominal level, the protocol returns to adaptation of modulation and coding to increase the information rate. Similarly, if D n is being used and the protocol determines that the power is too high, the power can be adapted between some lower level and the nominal level. Thus, power adaptation relies not only on statistics from the observation space, but also on knowledge of the previous power adaptations. 18

34 CHAPTER 5 MODULATION SELECTION PROTOCOL Because the source and destination are part of a dynamic spectrum access network, they must choose or be assigned to an available frequency band that meets their communication requirements. They must select a combination of modulation and coding that is usable by both radios and satisfies all constraints imposed by the frequency band that was chosen. For example, the use of some modulation formats and code rates may require more bandwidth than is available at the chosen frequency if the session is to be completed within the allotted time. In [1] and [], we proposed a spectrum etiquette measure, the resource consumption, that can be used for the selection of the initial modulation and code for a new session. The intuitive idea behind our definition of resource consumption is illustrated in Figure 5.1. If the source s transmitted signal occupies a certain time (T ) and bandwidth (B), and if the power of the transmission prevents a certain number (N) of radios from using the spectrum, then the source consumes some of the network s resources. Our particular measure of resource consumption is obtained by considering the volume of the source s transmission in terms of time, bandwidth, and interference. Different modulation formats and different error-control codes require different combinations of resources, and the resource consumption is one way to conduct tradeoffs among the different choices. In [3], we showed that a normalized version of the resource consumption R is E b /N, so bounds on R can be determined from bounds on E b /N. Our goal is to minimize R, but the minimization is constrained by the fact that reliable communication must be possible. Thus, Shannon capacity limits in terms of E b /N can be employed as lower bounds on the normalized resource consumption. However, the

35 T B N Figure 5.1: Illustration of the concept of resource consumption. capacity limits depend on the code rate and the modulation format, so we must determine the capacity as a function of the code rate for each modulation format in the set M j : 1 j n m. Let Λ be the minimum value of E b /N that permits reliable communication with binary codes of rate r and modulation format M. The capacity ressions in Appendix B can be used to find such capacity limits for orthogonal and biorthogonal modulation formats, of which BPSK, QPSK, and BFSK are special cases. Other potential limits on the session include power (peak or average), time (or rate), and maximum resource consumption. An illustration of these limits along with capacity bounds for several modulation formats is provided in Figure 5.. The actual numerical limits shown for maximum R (RC), rate, and power are chosen for illustrative purposes only. For modulation formats whose minimum ENR requirement is a strictly increasing function of the information rate (e.g., BPSK), R is minimized by operating at the capacity limit for the lowest possible information rate. However, R is not necessarily minimized at the lowest information rate for modulation formats without strictly increasing ENR requirements (e.g., 16-biorthogonal in Figure 5.).

36 bi 3-bi 16-bi 8-bi 4-bi (also BPSK) ENR (db) 6 4 RC Restriction (Eb/N < 4 db) Power Restriction (P/N < db) Rate Restriction (>.1) Information Rate Figure 5.: Limits on the achievable normalized resource consumption. A practical system will not be able to operate at the lower limits shown in Figure 5. because capacity-achieving codes do not exist. However, our turbo product codes perform approximately 1 db away from capacity for most of the modulation formats we consider. Another limitation of practical systems is that only a finite number of codes are available, so each continuous lower bound becomes a set of discrete points. Thus, for such systems, minimization of R takes place over a finite number of (information rate, ENR) pairs, but the concepts are the same as for a continuous range of pairs. 1

37 CHAPTER 6 INITIAL POWER ADJUSTMENT In dynamic spectrum networks, new communication sessions often begin in frequency bands for which little propagation information is known by the source or destination. For example, in urban environments, shadow losses can vary by db or more [4]. It is difficult to predict the propagation loss on a certain frequency band, as evidenced by the large variations in correction factors used with empirical formulas for outdoor propagation (e.g., [5] and [6]). Even if a frequency band is reused, the previous information is likely to be outdated quickly (e.g., due to mobility). Due to these uncertainties, the initial choice of transmitter power may be excessively high or low. Clearly, if the power is too low, the packet success probability will be insufficient for reliable communication. On the other hand, transmitting at a high power level for a long period of time has a potential to cause excessive interference to other terminals, and it will deplete the radio s energy resources. We employ an initial power adjustment protocol that uses feedback information from the destination to determine the transmitter power for the next packet. The goal is to iteratively set the power so it quickly converges to within a range that allows reliable communication with little excess power. Because an initial power adjustment protocol is intended to operate for only a few packets, we first consider their performance on static channels. On such channels, protocols that have access to perfect channel information would obviously be very accurate and converge quickly to the proper power level. Thus, we consider the more practical observation spaces corresponding to receiver statistics. Of the receiver statistics mentioned in Chapter 3, demodulator statistics give the most accurate indication that the power is too high or too low. In fact, as received power increases,

38 the error count eventually reaches zero and the iteration count may reach one, in which case, all we know from the error count and iteration count is that the power is higher than necessary. The ratio statistic for orthogonal and biorthogonal modulation and the distance statistic for two-dimensional modulation provide more detailed information about the power level. 6.1 Power Adjustment Protocol Description Our protocol employs simple interval tests to determine the necessary power adjustment. The range of possible values of the demodulator statistic is partitioned into intervals with endpoints µ 1, µ,..., µ N, and the minimum step size for transmitter power adjustments is β db. When the protocol begins, a counter, C s, is set to zero. This counter and a corresponding threshold S track the protocol and trigger the stopping condition. The protocol can also be terminated if the stopping condition is not reached after a specified number of packets have been transmitted. For the following description of the protocol, assume that the ected value of the statistic that the protocol uses during the initial power adjustment increases as the power increases. If the statistic decreases as the power increases, then all inequalities are reversed. Suppose that the value of the statistic from the last packet was γ. If the power has not yet been decreased and if γ < µ 1, then increase the power by some amount β 1 db. If µ i γ < µ i+1 for some i 1,,..., N 1, then decrease the power by iβ db. If γ > µ N, decrease the power by Nβ db. In the case that no acknowledgement packet is received, γ is not known. Based on the assumption that the power used for the previous packet was too low, the transmitter power is increased by β 1 db. If none of the previous conditions is met, then increment C s. If C s = S, then stop the 3