Improved channel estimation schemes for DS CDMA RAKE receiver with the use of multiuser interference canceller

IMPROVED CHANNEL ESTIMATION SCHEMES FOR DS-CDMA RAKE RECEIVER WITH THE USE OF MULTIUSER INTERFERENCE CANCELLER TIE LOK TIING NATIONAL UNIVERSITY OF SINGAPORE 2004 IMPROVED CHANNEL ESTIMATION SCHEMES FOR DS-CDMA RAKE RECEIVER WITH THE USE OF MULTIUSER INTERFERENCE CANCELLER TIE LOK TIING (B. Eng. (Hons.), National University of Singapore) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2004 i Acknowledgement I would like to take this opportunity to thank my first supervisor, Dr. Chew Yong Huat, from Institute for Infocomm Research, for his constant support, encouragement and guidance, throughout my research years. I also thank my second supervisor, Dr. Nallanathan Arumugam, from Department of Electrical and Computer Engineering, National University of Singapore, for being a constant source of ideas and guidance, and for helping me believe in my work. I also wish to stretch my gratitude to my colleagues from Institute for Infocomm Research, especially Hu Xiao Yu, Lim Wei Chee, Yang Yang, Long Hai and Ng Woon Wei, for helping me to organize my thoughts and their valuable times spent on discussion. I should also mention that my scholarship of my graduate study in National University of Singapore was supported by Institute for Infocomm Research. ii Contents Acknowledgement i Contents ii Summary v List of Figures vii Abbreviations x List of Symbols Chapter 1. Introduction xi 1 1.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Research Motivations and Contributions . . . . . . . . . . . . . . 6 1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Chapter 2. Mobile Radio Channels 2.1 2.2 2.3 Propagation Channel . . . . . . . . . . . . . . . . . . . . . . . . . 9 9 2.1.1 Flat and Frequency-selective Fading . . . . . . . . . . . . . 15 2.1.2 Fast and Slow Fading . . . . . . . . . . . . . . . . . . . . . 16 Rayleigh Fading Generator . . . . . . . . . . . . . . . . . . . . . . 16 2.2.1 Mathematical Reference Model . . . . . . . . . . . . . . . 17 2.2.2 Clarke’s Model . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2.3 Jakes’ Model Generator . . . . . . . . . . . . . . . . . . . 18 DS-CDMA System and Channel Model . . . . . . . . . . . . . . . 20 Contents iii 2.3.1 Continuous time received signal . . . . . . . . . . . . . . . 21 2.3.2 Discrete time received signal . . . . . . . . . . . . . . . . . 22 Chapter 3. CDMA Systems Background 3.1 27 Cellular CDMA Systems . . . . . . . . . . . . . . . . . . . . . . . 27 3.1.1 Short Sequence Systems . . . . . . . . . . . . . . . . . . . 28 3.1.2 Uplink Transceiver Structures . . . . . . . . . . . . . . . . 29 3.2 RAKE receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3 Parallel Interference Cancellation . . . . . . . . . . . . . . . . . . 35 3.4 Implementation of Parameter Estimates in RAKE Receiver . . . . 37 3.4.1 Conventional single-user detection . . . . . . . . . . . . . . 37 3.4.2 Multiuser and multipath interference cancellation . . . . . 43 Chapter 4. Training-based Decoupled Maximum Likelihood Channel Estimation 46 4.1 The DEML Channel Estimation Method . . . . . . . . . . . . . . 47 4.2 Recursive Method and Computational Complexity . . . . . . . . . 52 4.3 Influence of Pilot Symbol Length . . . . . . . . . . . . . . . . . . 54 4.3.1 Analytical Results on Pilot Length . . . . . . . . . . . . . 56 4.3.2 Simulation Results on Pilot Length . . . . . . . . . . . . . 60 Simulation Results for Estimator . . . . . . . . . . . . . . . . . . 64 4.4.1 Simulation Parameters . . . . . . . . . . . . . . . . . . . . 64 4.4.2 Probability of Correct Acquisition against M . . . . . . . . 64 4.4.3 BER Performance against SNR . . . . . . . . . . . . . . . 66 4.4.4 BER Performance against Number of Users, K . . . . . . 68 4.4.5 Tracking Performance . . . . . . . . . . . . . . . . . . . . 68 4.4.6 BER Performance with Different Number of Paths . . . . . 70 4.4 Chapter 5. PIC-based DEML Channel Estimation 5.1 PIC-based Channel Estimation Model . . . . . . . . . . . . . . . . 72 75 Contents iv 5.2 Statistical Accuracy of the Estimator . . . . . . . . . . . . . . . . 76 5.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.3.1 MSE against SNR . . . . . . . . . . . . . . . . . . . . . . . 79 5.3.2 BER Performance against SNR . . . . . . . . . . . . . . . 81 5.3.3 BER Performance against Number of Users, K . . . . . . 81 5.3.4 BER Performance with Different Number of Paths . . . . . 85 Chapter 6. Conclusions 86 List of Publications 88 Bibliography 89 v Summary Direct-sequence code division multiple access (DS-CDMA) is a promising technology for future mobile communications. However for high bit rate transmission, several transmission problems including channel fading due to multipath propagation, Doppler effect and multiuser interference exist. The presence of these impairments give rise to the need for estimating the channel gain coefficients and its accuracy thus restricting the performance of RAKE receiver, which is usually used as the basic building block for more complex receiver structures to overcome inter-symbol interference (ISI). Furthermore, precise knowledge of propagation delays is required for accurate code despreading in RAKE receiver. These parameters need to be estimated in practice and will, therefore, be subject to estimation errors. The speed of estimation process is another concern which leads to the design of low complexity and high efficient algorithm in this thesis. The two corresponding tasks, delay and channel gain coefficients estimation for RAKE receiver, are the focus of this thesis. A decoupled maximum likelihood (DEML) channel estimation scheme using recursive matrix computation is proposed for asynchronous DS-CDMA communication systems. The DEML esti- Summary vi mation is obtained using training sequence. In the DEML algorithm, a recursive method is used to find the estimator so as to spread the computational time over each processing window. Next, the proposed recursive technique is extended to track moderate time-varying fading channel using decision feedback. Also, the RAKE receiver structure that employs parallel interference cancellation (PIC) both for detection and channel parameters estimation for Rayleigh frequency selective fading environments is proposed. The estimator unit starts with a training mode then reverts to a decision-directed mode. In the training mode, the initial values of multipath delays and channel gain coefficients of all users are estimated. These initial parameters are used for parallel multiuser interference cancellation. Once the interference is cancelled, the signal is fed to the estimator for fine estimation of delays and channel gain coefficients of all users. These more accurate estimates are used for detecting the next symbol interval. This process continues in the decision-directed mode. Simulations of BER performance using the proposed receiver architecture and algorithm in the uplink shows noticeable performance improvement compared to that of channel estimation using conventional PIC receiver structure under multipath fading condition. This is proved theoretically. Lastly, the thesis is concluded with summary of works and contributions. vii List of Figures 1.1 A wireless transmission system . . . . . . . . . . . . . . . . . . . . 3 1.2 Asynchronous nature of uplink transmission together with multipaths 4 2.1 Rayleigh fading magnitude profile for fd T = 0.001 . . . . . . . . . 11 2.2 Rayleigh fading phase profile for fd T = 0.001 . . . . . . . . . . . . 12 2.3 Doppler shift caused by a moving vehicle . . . . . . . . . . . . . . 14 2.4 Frequency domain implementation of Clarke’s model simulator at baseband. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 19 Contributions of the spreading sequence and transmitted bits of respective users and path to the received signal, assuming constant channel parameters of 1 and no noise situation. . . . . . . . . . . 2.6 23 The fundamental structure of the matrix S for multipath CDMA with K = 3, L = 2, N = 8, M = 2. The delays for the three users are (0,5Tc ), (3,4Tc ) and (2,7Tc ) respectively. . . . . . . . . . . . . 25 3.1 Mobile user transmitter . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Base station receiver . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3 MRC-RAKE receiver structure for user k . . . . . . . . . . . . . . 34 3.4 Coherent detector for user k at finger m (CohDetk,m ) . . . . . . . 34 3.5 Fundamental PIC receiver structure . . . . . . . . . . . . . . . . . 36 3.6 MRC RAKE receiver . . . . . . . . . . . . . . . . . . . . . . . . . 38 List of Figures 3.7 viii RAKE with single stage PIC receiver structure for accurate decision feedback channel estimation . . . . . . . . . . . . . . . . . . 45 3.8 Path regenerative block for user k at path m (PRegk,m ) . . . . . . 45 4.1 Channel errors due to noise Jn and hysteresis Jd as a function of pilot symbol length, L . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Theoretical and numerical results of channel M SE against L for SN R = 0dB under various fade rates . . . . . . . . . . . . . . . . 4.3 69 Phase of channel tracking performance for K = 5, SN R = 10dB, N = 31, M = 2, fd T = 0.0001 . . . . . . . . . . . . . . . . . . . . . . . 4.9 68 Absolute value of channel tracking performance for K = 5, SN R = 10dB, N = 31, M = 2, fd T = 0.0001 . . . . . . . . . . . . . . . . . 4.8 67 BER performance against K for SN R = 10dB, N = 31, M = 2, fd T = 0.0001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 65 BER performance against SN R for K = 5, N = 31, M = 2, fd T = 0.0001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 62 Probability of correct delay acquisition for DEML estimator against L for K = 5, SN R = 10dB, N = 31, M = 2, fd T = 0.0001 . . . . . 4.5 61 Theoretical and numerical results of channel M SE against L for fd T = 0.001 under various SN R conditions . . . . . . . . . . . . . 4.4 55 69 BER performance against SN R for K = 5, N = 31, M = 2, fd T = 0.0001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.1 Proposed channel estimation receiver structure 74 5.2 Channel MSE performance against SNR for K = 5, N = 31, M = . . . . . . . . . . 4, fd T = 0.001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 List of Figures 5.3 ix BER performance against SNR for K = 5, N = 31, M = 4 under different Doppler rates (fd = 0Hz and 10Hz) implemented using different receiver structures . . . . . . . . . . . . . . . . . . . . . . 5.4 82 BER performance against K for SN R = 5dB, N = 31, M = 4 under different Doppler rates (fd = 0Hz and 10Hz) implemented using different receiver structures . . . . . . . . . . . . . . . . . . 5.5 83 BER performance against SNR for K = 5, N = 31, fd T = 0.0001 under various multipath lengths (M = 1, 2, 3 and 4) condition. . . 84 x Abbreviations DS-CDMA: TDMA: FDMA: D-CDMA: R-CDMA: PCS: LPI: BPSK: QPSK: OQPSK: MAI: MUD: BER: MSE: SNR: PIC: SIC: DEML: PSD: D/A: MRC: LOS: AWGN: ICI: ISI: Direct-Sequence Code Division Multiple Access Time Division Multiple Access Frequency Division Multiple Access Deterministic CDMA Random CDMA Personal Communications System Low Probability of Intercept Binary Phase Shift Keying Quadrature Phase Shift Keying Offset QPSK Multiple Access Interference Multi-user Detector Bit Error Rate Mean Square Error Signal to Noise Ratio Parallel Interference Cancellation Successive Interference Cancellation Decoupled Maximum Likelihood Power Spectral Density Digital to Analog Converter Maximal Ratio Combining Line of Sight Additive White Gaussian Noise Inter-chip Interference Inter-symbol Interference xi List of Symbols fd : fm : fc : v: T: Tc : K: L: Lopt : N: M: τk,m : τˆk,m : ck,m : cˆk,m : f (·): p(·|·): στ : σ: ρ(·): Tm : Bc : B: Tcoh : λ: bk (i): sk (i): ak (i): Doppler frequency maximum Doppler frequency carrier frequency velocity of mobile symbol period chip period number of users pilot symbol length optimum pilot symbol length spreading sequence length number of multipaths or fingers actual delay for user k with path m estimated delay for user k with path m actual channel gain for user k with path m estimated channel gain for user k with path m probability density function conditional probability density function root mean square delay spread variance of Rayleigh envelop channel autocorrelation function maximum delay spread coherent bandwidth signal bandwidth coherent time signal wavelength k th user’s symbol data at ith interval k th user’s spreading waveform k th user’s data symbol waveform List of Symbols g(t): sk (n): r(t): (q) rk (t): hk (t): n(t): R(t): zk (t): yk (t): ˆbk (i): (q) xk,m (t): S: ˜ S: ¯ S: sk (·): ˜sk (·): Ci : A: b: n: r: T (·) : (·)H : (·)∗ : | · |: tr(·): th arg[m max(·)]: Rn : Rrr (L): Rrb (L): Rbb (L): Rbb ¯ (L): Eb : E: N0 : xii chip pulse waveform k th user’s spreading waveform received signal waveform k th user’s received signal at stage q of PIC detector k th user’s channel response AWGN noise pulse autocorrelation function matched filter output soft decision data hard decision data regenerated signal for user k and path m at stage q of PIC detector spreading matrix normalized spreading matrix previous spreading matrix k th user’s spreading vector k th user’s normalized spreading vector ith interval channel coefficient matrix matrix with S and Ci multiplied together data vector noise vector received signal vector transpose Hermitian transpose complex conjugate determinant operator trace operator argument contributes to the mth largest cost function covariance matrix of noise correlation matrix for received signal correlation matrix between received signal and data correlation matrix for data correlation matrix between previous data and current data energy of a bit statistical expectation spectral energy of noise 1 Chapter 1 Introduction Code-division multiple access (CDMA) is a form of spread-spectrum, a family of digital communication techniques that have been used in military applications for many years. The core principle of spread spectrum is the use of noise-like carrier waves, and, as the name implies, bandwidths much wider than that required for simple point-to-point communication at the same data rate. Originally there were two motivations: either to resist enemy efforts to jam the communications (anti-jam), or to hide the fact that communication was even taking place, sometimes called low probability of intercept (LPI). The use of CDMA for civilian mobile radio applications is novel. It was proposed theoretically in the late 1940’s, but the practical application in the civilian marketplace did not take place until 40 years later. Commercial applications became possible because of two evolutionary developments. One was the availability of very low cost, high-density digital integrated circuits, which reduce the size, weight, and cost of the subscriber stations to an acceptably low level. The other 1.1 Problem Description 2 was the development of multiple access techniques that requires all user mobiles stations regulate their transmitter powers to the lowest to achieve adequate signal quality, thus helps to pro-long the battery’s life. In a CDMA system, since all users access the communication channel with a given bandwidth simultaneously, each mobile user is assigned a unique spreading sequence for distinguished modulation purpose. The well-known modulation scheme such as simple binary phase shift keying (BPSK) is often used for realtime systems or simulations and in our thesis as well. The basis for detection of the transmitted symbols of each user at the receiver is the low cross-correlation between the spreading sequences of various users and the peak auto-correlation property of each sequence. In wireless systems, two radio links are involved: the uplink from the mobile to the base station, and the downlink from the base station to the mobile. In this thesis, we study the channel parameter estimation problem, described later, primarily in the uplink, which is normally asynchronous. 1.1 Problem Description When a radio signal is transmitted through a wireless channel, it experiences various types of degradation (Fig. 1.1), which will be elaborated upon in greater detail in the next chapter. A great challenge is posed for the wireless channel in mobile radio when it is used as a medium for reliable high-speed communications. At the receiver end, a linear superposition of signal transmitted by all the users, 1.1 Problem Description c(t,W ) 3 W user 1 t 1 c(t,W ) W received signal user 2 2 detected bits t AWGN K c(t,W ) W user K t TRANSMITTERS CHANNEL RECEIVER Figure 1.1: A wireless transmission system attenuated by arbitrary factors and delayed by arbitrary amounts, is obtained. Moreover, due to scattering and reflections from various obstacles between the transmitter and receiver, replicas of same signal reach the receiver at different times, which often termed multipaths. The uplink is inherently asynchronous in nature, i.e. different signals arrive at the receiver base station with different relative time-offsets with respect to an arbitrary timing reference at the receiver. The asynchronity together with multiple propagation paths can be shown in Fig. 1.2. The received signal is first converted from passband to baseband, i.e. demodulated, digitized and then it is processed in baseband to detect and decode the information bits. The detection of a particular user’s transmitted bit at the receiver involves the correlation of the received waveform with a copy of the known corresponding spreading sequence. 1.1 Problem Description 4 arbitrary timing reference path 1 T W 1,1 user 1 path 2 W 1,2 T path M W 1,M T path 1 T W 2,1 user 2 path 2 T W 2,2 path M T W 3,M path 1 T W K ,1 user K path 2 T W K ,2 path M W K ,M T Figure 1.2: Asynchronous nature of uplink transmission together with multipaths 1.1 Problem Description 5 Accurate estimate of the user’s timing offset is necessary for accurate correlation. In addition to the delays of the different propagation paths of the different users, the detection schemes also require estimates for the complex coefficients of each path. All these parameters estimation constitute the channel estimation problem. Initial research on timing acquisition and channel coefficients estimation has been focused on jointly estimating the necessary parameters for all the user’s signals. While these techniques produce excellent results, they require a high computational cost to solve the multidimensional optimization problem for a large number of parameters and their user capacity is fairly restrictive. Therefore, in this thesis one of the algorithms which has been featured prominently in the literature [12], because of the various advantages in terms of performance and computational reduction, called decoupled maximum likelihood (DEML) is examined and used. This algorithm finds the maximum likelihood (ML) estimates of timing offsets of all possible users present in the communication channel, subsequently the channel coefficients of all users are computed based on these estimated timing offsets, thus the term decoupled. This algorithm, described in detail in the later chapters, deals with a variety of situations, such as multipath, multiple access, fading conditions. In addition, we have proposed a scheme that brings modification to the original estimation algorithm in order to achieve better bit-error-probability performance to the system. 1.2 Research Motivations and Contributions 1.2 6 Research Motivations and Contributions The performance of CDMA systems can be significantly degraded due to the presence of multiple access interference (MAI) as a result of that different users are typically asynchronous but the codes used to support asynchronous transmission are not truly orthogonal. Several optimal and sub-optimal multiuser detectors (MUD) [1, 2, 3] have been proposed to mitigate the MAI effectively. However, most researches are focused on sub-optimal MUD [8] algorithms due to their relatively low complexities. One of the sub-optimal MUD algorithms used is parallel interference cancellation (PIC) [9]. It provides not only accurate decision data detectional than conventional detector for decision-directed channel estimation, but also has shorter computational time for subtracting the replicas of interfering signals from the received signal in a parallel manner. As described in the previous section, another concern in a CDMA system is that the received signal usually consists of many replicas of transmitted signal and these replicas arrive at the receiver at different time instants. To exploit these replicas, RAKE receiver is still the receiver structure of choice for the first round of low-complexity receiver for broadband transmission. However, the performance of RAKE is very much dependent on the quality of its channel estimates. To attain more accurate channel estimation in the presence of MAI and multipath, many joint multiuser detection and parameter estimation techniques [10, 11] have been developed. These techniques produce excellent results but require large computational cost, because the channel parameters are estimated sequentially 1.3 Thesis Outline 7 instead of in parallel manner. The structure of RAKE receiver and existing channel estimation techniques will be further discussed in Section 3.2. In this thesis, we have devised a scheme that exploits the signals that are obtained after parallel interference (interference from undesired users and paths) cancellation. After the process of PIC, signals are fed back to the DEML channel estimator module for fine estimation of channels for next symbol interval. The major difference between the ordinary DEML scheme and the devised scheme is the input to the channel estimator. However, the later uses direct received signal as input in the decision-directed mode (to be discussed in detail in Chapter 5) as input. The proposed receiver structure is depicted in Fig. 5.1. Our computer simulations indicate that the proposed algorithm has performance signal-to-noise ratio (SNR) gain of 2 dB more than the existing methods of comparable complexities at bit-error-rate (BER) of 10−3 under the multipath (in this case, paths of 4 for all users is used) environment. SNR used here is defined as symbol energy to noise energy ratio and it is used for the rest of the thesis. 1.3 Thesis Outline The thesis is organized as follow: The introductory chapter has briefly addressed the problem definition for the thesis and the need for efficient solutions to channel estimation problem. The motivations and contributions of research have also been described. In the next chapter, the background knowledge for the subject material of 1.3 Thesis Outline 8 this thesis is presented. First we describe the fading propagation environment and the key considerations for a CDMA system. Followed by the development of the system and channel model used throughout the rest of the thesis. Chapter 3 gives the principles of the wireless CDMA transmitter and receiver. Furthermore, the RAKE receiver and the multiuser PIC are also discussed in this chapter. In the last section, the implementation of parameter estimates in RAKE receiver is addressed to see the impact of estimates on decision data. In Chapter 4, we present a ML-based channel estimation algorithm that has been developed in the multiuser and multipath environment. We also include the complexities considerations and the recursive method that reduces the computational time of estimation process. Chapter 5 presents the devised scheme on the performance improvement by using the PIC in channel estimation. At the end of chapter, the analysis and simulation is conducted to justify the results. Finally, the conclusions on the research are given in last chapter. 9 Chapter 2 Mobile Radio Channels 2.1 Propagation Channel A radio signal wave experiences various types of distortion when it is transmitted through a wireless channel. This process poses a great challenge for CDMA channel estimation in order to attain a reliable high-speed communications. The distortion comes from the physical structures or objects such as buildings, hills, ground, trees and moving pedestrians or vehicles, etc. The random and timevarying phenomena are formed as a result of signal reflections, diffractions and scattering that leads to multipath. Besides, the relative motion of mobile causes Doppler effect on allocated carrier frequency as the mobile terminal moves. Radio propagation models usually focus on predicting the average signal strength based upon the separation between the transmitter and the receiver, and also the rapid fluctuations in the instantaneous signal level that may be observed over short distances. The variation of the average signal strength over 2.1 Propagation Channel 10 large distances (typically several hundred of meters), is called the large-scale path loss. This type of fading is not considered in our research and thus is not covered in detail. The rapid fluctuation over short travel distance (typically a few wavelengths) is termed as small-scale fading. Typical profile of small-scale Rayleigh fading in terms of envelope and phase is depicted in Fig. 2.1 and Fig. 2.2. To characterize the small-scale spatial distribution of the received multipath signal amplitude, it is necessary to reasonably approximate the environment, based on the measurement made in the field. It has been found that in many situations, the Rayleigh distribution provides a good fit to the signal amplitude measurement when there is no line-of-sight (LOS) or dominant path [27, 6]. Here let us denote the received signal as s(t), which is a composite of all arriving waves. s(t) can be expressed as s(t) = x(t) cos(ωc t) − y(t) sin(ωc t) = Re [(x(t) + jy(t)) exp(jωc t)] = Re[r(t) exp(j(ωc t + φ))] where x(t) and y(t) are the in-phase and quadrature components. r(t) denotes the envelope of the complex signal s(t), and it is related with x(t) and y(t) by r(t) = x2 (t) + y 2 (t). If there are sufficient large number of waves arriving at the receiver, by the central limit theorem, the in-phase and quadrature components x(t) and y(t) are independent Gaussian processes with zero means and equal variance σ 2 . Thus 2.1 Propagation Channel 11 2 1.8 Rayleigh Fading Magnitude Profile 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 500 1000 1500 2000 Symbol Index 2500 3000 3500 4000 Figure 2.1: Rayleigh fading magnitude profile for fd T = 0.001 the probability density function (pdf) of x(t) and y(t) can be written as x2 2σ 2 2πσ 2 1 y2 f (y) = √ exp − 2 2σ 2πσ 2 f (x) = √ 1 exp − Then the pdf of the envelope r(t), is given by  r r2    2 exp − 2 σ 2σ f (r) =    0 (−∞ < x < ∞) (−∞ < y < ∞) (r ≥ 0) (2.1) (r < 0) in which 2σ 2 is the mean power of the multipath signal before envelope detection. Equation (2.1) is the Rayleigh density function. Since the thesis mainly focuses on mitigating the effects of small-scale fading by using some sophisticated and proposed signal processing techniques, it’s effects are hereby discussed in the remaining of this section. The small scale fading refers to rapid variations in the amplitude of the received signal in the wireless channel 2.1 Propagation Channel 12 4 3 Rayleigh Fading Phase Profile 2 1 0 −1 −2 −3 −4 0 500 1000 1500 2000 Symbol Index 2500 3000 3500 4000 Figure 2.2: Rayleigh fading phase profile for fd T = 0.001 over short distances or time intervals, as mentioned before, this rapid fluctuations are caused by a number of physical factors: Multipath propagation: very often there is no LOS path between transmitter and receiver under typical mobile channels for either indoors or outdoors communications. Received signal is the superposition of many independent plane-wave components of approximately equal power with random amplitudes and phases. The resultant signal shows constructive (large amplitude) and destructive (small amplitude) pattern and this pattern may vary over time which gives rise to the phenomenon of fading. The parameter of interest when dealing with multipath is the delay spread. The maximum delay spread, Tm is defined as the time delay during which the multipath energy falls to a pre-specified level below the maximum. However, with a large number of paths, root-mean-square (rms) delay 2.1 Propagation Channel 13 spread is more representative of the effect of delay spread on the performance of radio receivers, and can be used as one qualitative measure of the severity of multipath propagation. The rms delay spread of a profile, στ , is described as [4] (τ − τ¯)2 P (τ ) dτ , P (τ ) dτ στ = (2.2) where τ¯ is the mean excess delay of P (τ ) and can be computed by τ¯ = τ P (τ ) dτ . P (τ ) dτ (2.3) Usually στ can range from 1 to 20 µs in urban environments and from ten to a few hundred ns in indoor environments. The rms delay spread στ is closely related to another measure of delay spread in the frequency domain, which is referred to as the coherence bandwidth. Coherent bandwidth, Bc , represents a frequency range over which frequency components have a strong potential for amplitude correlation. That is, a signal’s spectral components in that range are affected by the channel in a similar manner as, e.g., exhibiting strong fading or no fading. There is no exact relationship between Bc and στ , but in general the relation can be approximately expressed as [4] Bc ∼ 1 c στ (2.4) The constant c varies from 5 to 50 depending on how strict the coherence bandwidth is to be defined, for example, if the frequency correlation is defined above 0.9, c takes the value of 50. Doppler shift: the relative motion between the base station and mobile as well as the movements of surrounding objects results in random frequency modulation 2.1 Propagation Channel 14 S 'l Tc X Tc d v Y Figure 2.3: Doppler shift caused by a moving vehicle due to the Doppler shift of each multipath components. This can be illustrated in Fig. 2.3 with a mobile moving at a constant speed of v. The difference in path lengths travelled by wave from remote source S to the mobile at points X and Y is ∆l = d cos θ = v∆t cos θ , ∆t is the time required for the mobile to travel from X to Y, and θ is assumed to be the same at points X and Y since the source is very far away. The phase change in the received signal due to the difference in path lengths is ∆φ = β∆l = 2π∆l = 2πv∆t , where β = 2π . The apparent λ λ λ change in frequency shift is fd = v 1 ∆φ · = · cos θ . 2π ∆t λ (2.5) The Doppler shift will be positive or negative depending on the direction of relative motion between the mobile and the base station. The maximum Doppler 2.1 Propagation Channel 15 shift will occur when |cos θ | = 1. Define the maximum positive Doppler shift to be fm , so vfc c fm = (2.6) The Doppler spread or the spectral broadening is the parameter of interest. It is defined as the range of frequencies over which the received Doppler spectrum is non-zero and above a certain threshold. Another useful statistical measure for describing the time varying nature of the channel is the coherence time, Tcoh , which is defined as the time duration over which the channel impulse response is essentially invariant. The coherence time Tcoh is inversely proportional to the maximum Doppler shift fm . And as a rule of thumb for modern digital communications, it is approximately given by [4] Tcoh = 0.423 fm (2.7) The relationship between the signal parameter (symbol period) and the channel parameters (delay spread and Doppler spread) gives rise to different type of small-scale fading, which will be discussed in the next section. 2.1.1 Flat and Frequency-selective Fading If the mobile radio channel has a constant gain and linear phase response over the coherence bandwidth Bc , which is greater than the signal bandwidth Bs ≈ T1 , i.e. Bc > Bs , the received signal undergoes flat fading and in the opposite case, it is said to experience frequency selective fading [4]. In the flat fading case, the delay spread is much less than the symbol period 2.2 Rayleigh Fading Generator 16 and hence the spectral characteristics of the transmitted signal are preserved at the receiver. However the strength of the received signal varies with time. In frequency selective fading, the received signal includes multiple copies of the transmitted waveforms, attenuated and delayed in time, and hence it is distorted. A typical model for frequency selective fading channel is made up of a number of delta functions which independently faded according to Rayleigh model and have sufficient time delay between them to induce frequency selective fading. 2.1.2 Fast and Slow Fading Depending upon the relative rate of change of the transmitted signal and the channel characteristics as mentioned above, a channel may be fast fading or slow fading. In a fast fading channel, the channel impulse response varies rapidly within symbol period, i.e. the coherence time is much smaller than the symbol duration (Tcoh T ). In slow fading, the channel may be assumed to be static over several symbol periods. 2.2 Rayleigh Fading Generator Many different methods have been used for the modeling and simulate of mobile radio channel to reduce the cost of field trials. When performing simulation, more flexible methods are necessary to generate the Rayleigh fading effect. Among them, the well-known mathematical reference model proposed by Clarke [4] and it’s simplified simulation model proposed by Jakes [5, 6] have been widely 2.2 Rayleigh Fading Generator 17 used as Raleigh fading generator. 2.2.1 Mathematical Reference Model Consider a flat fading channel comprised of Ni impinging plane [], the lowpass fading process is given by Ni s(t) = E0 Cn exp[j(2πfm tcosαn + φn )] (2.8) n=1 where E0 is a scaling constant, Cn , αn and φn are the random path gain, angle of incoming wave, and initial phase associated with the nth impinging plane respectively. fm is the maximum radian Doppler frequency occurring when αn =0. Assuming that Cn is real valued, (2.8) can be written as s(t) = sc (t) + jss (t) (2.9) where Ni sc (t) = E0 ss (t) = E0 2.2.2 n=1 Ni n=1 Cn cos[j(2πfm tcosαn + φn )] (2.10) Cn sin[j(2πfm tcosαn + φn )] Clarke’s Model The central limit theorem justifies that sc (t) and ss (t) can be approximated as Gaussian random processes for large Ni . Assuming that αn andφn are mutually independent and uniformly distributed over [−π, pi) for all n, and adopting 2.2 Rayleigh Fading Generator 18 Clarke’s two-dimensional (2-D) isotropic scattering model, some desired secondorder statistics for fading simulators are manifested in the autocorrelation and cross-correlation functions [7] Rsc sc (τ ) = E [sc (t)sc (t + τ )] = J0 (2πfm τ ) Rss ss (τ ) = J0 (2πfm τ ) Rsc ss (τ ) = 0 (2.11) Rss sc (τ ) = 0 Rss (τ ) = E [s(t)s∗ (t + τ )] = 2J0 (2πfm τ ) R|s|2 |s|2 (τ ) = 4 + 4J02 (2πfm τ ), where E[·] denotes expectation, J0 (·) is the zero-order Bessel function of the first kind, and without loss of generality, we have set Ni n=0 E[Cn2 ] = 1 and E0 = 1. The first-order PDFs of the fading envelope, |s(t)|, and the phase, Θs (t) = arctan[sc (t), ss (t)], are given by 2 f|s| (x) = x exp − x2 fΘs (θs ) = 1 , θs 2π ,x ≥ 0 (2.12) ∈ [− π, π) Clearly, the fading envelope |s(t)| is Rayleigh distributed, and the phase Θs (t) is uniformly distributed according to (2.12). The clarke’s model simulator is shown in Fig. 2.4. 2.2.3 Jakes’ Model Generator Based on mathematical reference model (2.8), by selecting 2.2 Rayleigh Fading Generator g *N 1 2 g *N / 2 g N 1 19 S EZ ( f ) 2 gN / 2 IFFT  fm  fm fm ([...]... Outline 8 this thesis is presented First we describe the fading propagation environment and the key considerations for a CDMA system Followed by the development of the system and channel model used throughout the rest of the thesis Chapter 3 gives the principles of the wireless CDMA transmitter and receiver Furthermore, the RAKE receiver and the multiuser PIC are also discussed in this chapter In the last... and it is used for the rest of the thesis 1.3 Thesis Outline The thesis is organized as follow: The introductory chapter has briefly addressed the problem definition for the thesis and the need for efficient solutions to channel estimation problem The motivations and contributions of research have also been described In the next chapter, the background knowledge for the subject material of 1.3 Thesis... exploit these replicas, RAKE receiver is still the receiver structure of choice for the first round of low-complexity receiver for broadband transmission However, the performance of RAKE is very much dependent on the quality of its channel estimates To attain more accurate channel estimation in the presence of MAI and multipath, many joint multiuser detection and parameter estimation techniques [10,... the structure of the transmitted signal in a CDMA system, the effects of the channel and the structure of the received signal at the receiver are developed 2.3 DS- CDMA System and Channel Model 21 The system under consideration is an uplink asynchronous K-user DS- CDMA system operating in a fading environment The transmitted symbols are simply either +1 or -1 (Binary Phase Shift Keying modulation) with. .. parallel interference (interference from undesired users and paths) cancellation After the process of PIC, signals are fed back to the DEML channel estimator module for fine estimation of channels for next symbol interval The major difference between the ordinary DEML scheme and the devised scheme is the input to the channel estimator However, the later uses direct received signal as input in the decision-directed... detection of the transmitted symbols of each user at the receiver is the low cross-correlation between the spreading sequences of various users and the peak auto-correlation property of each sequence In wireless systems, two radio links are involved: the uplink from the mobile to the base station, and the downlink from the base station to the mobile In this thesis, we study the channel parameter estimation. .. and their user capacity is fairly restrictive Therefore, in this thesis one of the algorithms which has been featured prominently in the literature [12], because of the various advantages in terms of performance and computational reduction, called decoupled maximum likelihood (DEML) is examined and used This algorithm finds the maximum likelihood (ML) estimates of timing offsets of all possible users... W K ,1 user K path 2 T W K ,2 path M W K ,M T Figure 1.2: Asynchronous nature of uplink transmission together with multipaths 1.1 Problem Description 5 Accurate estimate of the user’s timing offset is necessary for accurate correlation In addition to the delays of the different propagation paths of the different users, the detection schemes also require estimates for the complex coefficients of each... energy falls to a pre-specified level below the maximum However, with a large number of paths, root-mean-square (rms) delay 2.1 Propagation Channel 13 spread is more representative of the effect of delay spread on the performance of radio receivers, and can be used as one qualitative measure of the severity of multipath propagation The rms delay spread of a profile, στ , is described as [4] (τ − τ¯)2... m=1 (2.19) 2.3 DS- CDMA System and Channel Model 22 where n(t) denotes the additive noise, assumed to be zero-mean complex white Gaussian The channel gains and delays are assumed to be constant during estimation process The DEML channel estimation provides the estimates of the individual delays and channel gains for all users and their respective paths And this will be described later in the following .. .IMPROVED CHANNEL ESTIMATION SCHEMES FOR DS-CDMA RAKE RECEIVER WITH THE USE OF MULTIUSER INTERFERENCE CANCELLER TIE LOK TIING (B Eng (Hons.), National University of Singapore) A THESIS... is used for the rest of the thesis 1.3 Thesis Outline The thesis is organized as follow: The introductory chapter has briefly addressed the problem definition for the thesis and the need for. .. throughout the rest of the thesis Chapter gives the principles of the wireless CDMA transmitter and receiver Furthermore, the RAKE receiver and the multiuser PIC are also discussed in this chapter In the