Report

A Compressed Sensing Based UWB Communication System 1 F I N A L P R ESEN TA TI O N ANAT KLEMPNER SPRING 2012 SUPERVISED BY: MALISA MARIJAN YONINA ELDAR Contents 2 Background UWB – Ultra Wideband Project Motivation Compressed Sensing Project overview Project Goals Project Tasks Channel Estimation Theoretical Analysis Implementation & Results Signal Detection Summary UWB 3 A technology for transmitting information in bands occupying over 500 MHz bandwidth. Used for short-range communication Very low Power Spectral Density UWB - Advantages 4 Useful for communication systems that require: High bandwidth Low power consumption Shared spectrum resources UWB - Applications 5 In communications: High speed, multi-user wireless networks. Wireless Personal Area Networks / Local Area Networks Indoor communication UWB - Applications 6 Radar Through-wall imaging and motion sensing radar Underground imaging Long distance , Low data rate applications Sensor networks High precision location systems Project Motivation 7 The problem: The UWB signal has very high bandwidth, and therefore the UWB receiver requires high-speed analog-to-digital converters. High sampling rates are required for accurate UWB channel estimation. Project Motivation 8 The proposed approach relies on the following UWB signal properties: The received UWB signal is rich in multipath diversity. The UWB signal received by transmitting an ultrashort pulse through a multipath UWB channel has a sparse representation. Compressed Sensing 9 The main idea: A signal is called M-sparse if it can be written as the sum of M known basis functions: M x i i 1 i Compressed Sensing 10 An M-sparse signal can be reconstructed using a few number of random projections of the signal into a random basis which is incoherent with the basis in which the signal is sparse, thus enabling reduced sampling rate. y x Where Φ is the random projection matrix (measurement matrix). Project Goals 11 We wish to build a simulation environment for an UWB communication system with compressed sensing based channel estimation. The system will be based on the IEEE 802.15.4a standard for UWB communication. The simulation environment will be used to compare different compressed sensing strategies. Simulation Environment 12 Block-Diagram of the system: Channel Estimation Signal Generator Multipath Channel To be implemented according to IEEE 802.15.4a standard Detection Correlator Based Detector/ Rake Receiver Project Tasks 13 Phase 1 - Simulate the system and perform the channel estimation. Performance parameter: MSE of the estimation error as a function of the number of measurements. Phase 2 - Simulate signal detection methods: the RAKE receiver . Performance parameter: BER vs. input SNR for different sampling rates and number of pilot symbols. Further Research Possibilities 14 Phase 3- Compare the MSE and BER performance for the different sampling schemes: the randomized Hadamard scheme, Xampling method, and the random filter. Phase 4 -Compare the MSE and BER performance for the different sampling schemes and the reconstruction algorithms (e.g. , OMP, eOMP, and CoSaMP). Currently: Phase I – Channel Estimation 15 Block-Diagram of the process: Signal Generator Multipath Channel To be implemented according to IEEE 802.15.4a standard Analog preprocessing Randomized Hadamard Scheme/ Random Filter A/D Conversion Reconstruction Algorithm Variants of the MP algorithm Channel Estimation - Theory 16 The signal: Each block of data contains pilot symbols, which are used to estimate the channel parameters, and can be described as: s t N p 1 p t iT f i0 where is the transmission pulse. (Shape defined in the standard). Channel Estimation - Theory 17 Multipath Channel: A fading channel can be described as: h t L 1 t l l l0 where is the number of multipaths, is the l-th propagation path, and is the delay of the l-th propagation path. The goal of channel estimation is to estimate channel parameters , −1 . =0 Channel Estimation - Theory 18 Channel output: The received pilot waveform: s r t s t h t w t where is the channel noise. The pilot waveform in each frame: x t p t h t L 1 p t l l0 l Channel Estimation - Theory 19 Signal Model: An arbitrary signal can be described as a vector of its samples. The received signal in our case, can be written as a vector in the form: x where the non-zero coefficients of represent the channel gains, and Ψ is a Toeplitz Matrix with the elements: k , j p k j T s Channel Estimation - Theory 20 Analog Pre-Processing: Our goal is to achieve random projections of the signal. There are several ways to achieve random projections, the first method that will bet tested is the Randomized Hadamard Scheme. Channel Estimation - Theory 21 Analog Pre-Processing – Randomized Hadamard Scheme: The sampling matrix: = is used to create the sampled signal: = + R is a sub-sampling matrix – contains only one (Randomly chosen) non-zero value in each row. H is the Hadamard matrix. S is a diagonal matrix with a random binary modulation sequence on its digonal. Channel Estimation - Theory 22 Reconstruction Problem: The problem of finding unknown channel parameters can be described as: m in 1 s .t . y This problem can be solved using variants of the Matching Pursuit (MP) Algorithm. We will first try to use the OMP Algorithm – Orthogonal Matching pursuit. Channel Estimation - Implementation 23 The channel estimation system was implemented in MATLAB according to the theoretical description. Channel Estimation - Implementation 24 Channel Model Implementation: The UWB channel was at first implemented according to the IEEE 802.15.4a standard, using the code for channel generation which is given in the standard. The generated channel did not have the desired sparsity property, despite results shown in previous papers. It was decided to implement a simple version of the UWB channel. Channel Estimation - Implementation 25 Channel Model Implementation: The suggested simplified model: Ray arrival rate is Poisson distributed. Channel energy is exponentially decaying. Example of generated channel Channel Estimation - Results 26 The criterion used to evaluate the results is the MSE between the estimated and the original channel. Results were achieved using a single pilot symbol. MSE Vs. SNR for Channel Estimation Channel Estimation - Results 27 An exaple for channel estimation with SNR=25[dB] Signal Detection - Theory 28 The signal at the input of the detector can be represented as: r t x t h t w t L 1 x t w t l l l0 () is the sum of noise and MUI, and it is assumed to be a white Gaussian process. Signal Detection - Theory 29 Rake receiver structure: Signal Detection - Theory 30 Rake receiver structure: Where v i t waveform. si t si t TBPM , and s i t is the signal Signal Detection - Theory 31 The decision statistics is calculated using: i 1 T dsym L 1 zi ˆ l l0 r t v i t iT dsym ˆl dt iT dsym The estimated bit: 0 bi 1 zi 0 else Summary 32 In this project I learned the basics of the theory of compressed sensing and its application to UWB communications. In the first stage, channel estimation was performed. The signal detection phase was not successfully implemented in this project. Thank You! 33 References 34 [1] J. L. Paredes, et al., "Ultra-wideband compressed sensing: Channel estimation," Selected Topics in Signal Processing, IEEE Journal of, vol. 1, pp. 383-395, 2007. [2] A. Barbieri, et al., "Compressed channel estimation and data detection algorithms for IR-UWB," 2011, pp. 360-364. [3] F. M. 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