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MWC-System Expander Implementation using Filter Banks MidTerm Presentation

MWC-System Expander Implementation using Filter Banks MidTerm Presentation. Raz Lifshitz 052856721 Assaf Bismut 300316684 Supervisors: Deborah Cohen Professor Yonina Eldar. System Structure – Part I. MWC - Analog Component. MWC - Analog Component.

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MWC-System Expander Implementation using Filter Banks MidTerm Presentation

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  1. MWC-SystemExpander Implementation using Filter BanksMidTerm Presentation RazLifshitz 052856721 AssafBismut 300316684 Supervisors: Deborah Cohen Professor YoninaEldar

  2. System Structure – Part I • MWC - Analog Component

  3. MWC - Analog Component • Input: The sparse signal (original signal) • Output: M digital channels

  4. System Structure – Part II MWC - DSP

  5. DSP • The DSP is digital component • Input: M digital channels • Output: The final recovered signal

  6. Project Target Preventing burden on hardware Trading channels for sampling rate The main issue: In order to reconstruct the original signal, M equations are necessary, where every equation is represented by a physical channel. M must fulfill: M>2N, where N is the number of bands of the original signal. Thus, the burden on hardware becomes significant. The solution:For reducing hardware overload, we will combine some channels (Q channels) into one channel. The trade off will be in the sampling rate in the end of the MWC (multiplied by Q). For separating back the channels, we will use the Expander.

  7. Goals • Main Goal: • Implement the expander unit using filter banks • Sub goals: • Learn the principles of the Sub Nyquist theory and MWC system • Understand the theory of polyphase, including using FFT in the output of the polyphase instead of adder. • Implement the changes in the Expander • Compare the performance between the old implementation and the new implementation

  8. Expander – General Description Yi[n] M channels Expander Yi,Q[n] Q*M channels For example, Q=3, in the Frequency domain: Yi,1[n] Expander Yi[n] Yi,2[n] Yi,3[n]

  9. Expander Implementation Old implementation New implementation

  10. Polyphase - Theory • Given FIR Filter order N: • The filter can be written by:

  11. Or: The result is M decimated filters

  12. How the FFT will serve the purpose of the Expander??

  13. How the FFT will serve the purpose of the Expander?? The main idea is to implement q Band Pass filters, while every one is: And H0 is the main LPF.

  14. H0 can be written as a sum of its polyphase parts: Set it to the Hk (z) phrase (the wanted filter):

  15. DFT of (P0,P1….Pq-1 )

  16. The final implementation of the Expander is:

  17. Advantages of the new implementation

  18. MATLAB – Code Flowchart Start.m Set the basic parameters mwcSimolator.m GenerateAnalogSignal.m Each time the simulator is being use it: Generate a random signal according to the basic parameters it receive from start.m Sample the generated signal – in a subnyquist rate Expend each channel into Q channels Calculate and recover the support of the sampled signal. Recover Support also return success. MWC_SubNyquistSample.m MWC_DigitalProccess.m Calculate_Support.m RecoverSupport.m

  19. MWC_DigitalProccess.m • … • X[0] • … • X[q] • X[1] • X[q+1] • … • … Original implementation • … • … • … • … For each channel M • … • … • … • … For each factor q • X[2q-1] • X[q-1] • … • … Multiple the signal from channel M, with a current exponent Move it through LPF (Not decimated) Decimate the output from the LPF Locate the signal in the current line of the output Matrix New implementation Reshape example For each channel M Reshape The signal and the filter Filter each line of the signal matrix with the suitable Link of the filter matrix (separately) Move the filtered signal through an FFT/IFFT Meaning execute FFT\IFFT for each column Locate the calculated Matrix (q lines) in the output Matrix (q*M lines)

  20. Current status Input mwcSimulator.m MWC_DigitalProccess.m • Original Implementation • New Implementation • Comparison  Output - mwcSimolator.m Debugging Output - Debugging Output - Debugging

  21. Simulation example General Basic Parameters' The result of the simulation refSupport is the support of the original signal Support is the support of the sampled signal. A success is when refSupport is contained in Support

  22. Performance metrics Software Simulation • Execution time • Hardware burden Hardware Simulation • Over sampling rate • Synchronization with mixing sequences

  23. Gantt chart until final presentation:

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