Fractionally Spaced Equalization and Frequency Diversity Methods for Block Transmission with Cyclic Prefix

Fractionally Spaced Equalization and Frequency Diversity Methods for Block Transmission with Cyclic Prefix Yuki Yoshida, Kazunori Hayashi, Hideaki Sakai Department of System Science, Graduate School of Informatics, Kyoto University

Outline Background & Motivation The System Configuration of the Proposed Fractionally Spaced Equalizer (FSE) Derivation of the Equalizer Weights Frequency Diversity Method using the FSE Simulation Results Summary

Background & Motivation Block Transmission with Cyclic Prefix (CP) OFDM (Orthogonal Frequency Division Multiplexing) DTV, DAB, Wireless LAN DMT (Discrete Multitone) ADSL SC-CP (Single Carrier block transmission with CP) FDE (Frequency Domain Equalization) Simple Implementation using FFT Robustness to Frequency Selective Fading Channels Existing FDEers work at symbol rate (SSE : Symbol Spaced Equalizer )

Background & Motivation (cont d) Fractionally Spaced Equalizer (FSE) based on oversampling the received signal ex) 4 times oversampling T/4 - FSE How can we adopt the FSE to FDE systems? Zero- Forcing (ZF) based T/2-FSE has been proposed by Vaidyanathan and Vrcelj, 2002 Extension of Vaidyanathan s method to general oversampling factor cases (T/K-FSE) Derivation of ZF and minimum mean-square-error (MMSE) weights of the T/K-FSE A simple frequency diversity method using the T/K-FSE

Fractionally Spaced Equalization SSE Transmitted Signal Equalizer Output Channel Noise SSE FSE (Oversampling Factor K) FSE (Uniformly Sampled Version of Continuous quantity ) Expander Decimator (If m is multiple of K) (else)

SC-CP Scheme System Configuration of SC-CP Scheme (Single Carrier with CP) Remove CP S/P P/S Add CP Tx filter Fading & Additive Noise Rx filter S/P DFT FDE IDFT P/S Frequency Domain Equalization Block Diagram of SC-CP Scheme Noise Block n-th Input Signal Block Received Signal Block n-th Equalizer Output Block Channel Matrix DFT Equalizer Weights IDFT (Circulant) Matrix Matrix Matrix

SC-CP Scheme CP Length: Channel Order System Configuration of SC-CP Scheme (Single Carrier with CP) Remove CP S/P P/S Add CP Tx filter Fading & Additive Noise Rx filter S/P :Channel Impulse Response, DFT FDE IDFT P/S Frequency Domain Symbol Equalization Spacing Block Diagram of SC-CP Scheme M M Circulant Matrix Noise Block n-th Input Signal Block Received Signal Block n-th Equalizer Output Block Channel Matrix DFT Equalizer Weights IDFT (Circulant) Matrix Matrix Matrix

SC-CP Scheme System Configuration of SC-CP Scheme (Single Carrier with CP) Remove CP S/P M M TxDFT Matrix filter Fading & Additive Noise Add CP P/S Rx filter S/P DFT FDE IDFT P/S Frequency Domain Equalization Block Diagram of SC-CP Scheme Noise Block Unitary n-th Input Signal Block Received Signal Block n-th Equalizer Output Block Channel Matrix DFT Equalizer Weights IDFT (Circulant) Matrix Matrix Matrix

SC-CP Scheme System Configuration of SC-CP Scheme (Single Carrier with CP) S/P P/S Add CP Tx filter Fading & Additive Noise Diagonalized by DFT Rx filter DFT S/P Remove CP DFT FDE IDFT P/S Frequency Domain Diagonal IDFT Equalization Block Diagram of SC-CP Scheme Noise Block n-th Input Signal Block Received Signal Block Efficiently Equalized n-th Equalizer Output Block Channel Matrix DFT Equalizer Weights IDFT (Circulant) Matrix Matrix Matrix

OFDM Scheme System Configuration of OFDM Scheme (Orthogonal Frequency Division Multiplexing) Remove CP S/P IDFT P/S Add CP Tx filter Fading & Additive Noise Rx filter S/P DFT FDE P/S Frequency Domain Equalization Block Diagram of OFDM Scheme Noise Block n-th Input Signal Block Received Signal Block n-th Equalizer Output Block IDFT Matrix Channel Matrix (Circulant) DFT Equalizer Weights Matrix Matrix

Fractionally Spaced Equalization SSE Transmitted Signal Equalizer Output Channel Noise FSE (Oversampling Factor K) SSE FSE Expander Decimator (If m is multiple of K) (else)

Configuration of the SC-CP Scheme with Proposed T/K-FSE Transmitter: S/P P/S Add CP Tx filter Frequency Selective Fading & Additive Noise Remove CP Receiver: Rx filter K times Oversampling S/P KM-point DFT KM-point IDFT One-tap FDE using KM-point DFT S/P Decimator

Signal Modeling Input Signal Noise Received Signal Equalizer Output Expander Channel (Circulant) DFT Equalizer Weights (Diagonal) IDFT Decimator Received Signal Equalizer Output

Signal Modeling Input Signal Noise Received Signal Equalizer Output Expander Channel DFT KM M (Circulant) Expander Matrix Equalizer Weights (Diagonal) IDFT Decimator Received Signal Equalizer Output denotes the M x KM Decimator Matrix

Signal Modeling Input Signal Noise Received Signal Equalizer Output Expander Channel DFT (Circulant) KM KM Channel Matrix (Circulant) Equalizer Weights (Diagonal) IDFT Decimator Received Signal Equalizer Output : Channel Response including Tx and Rx filter :Symbol Period :Channel Order

Signal Modeling Input Signal Noise Received Signal Equalizer Output Expander Channel (Circulant) DFT Equalizer Weights (Diagonal) IDFT Decimator Received Signal Equalizer Output

Simplification of T/K-FSE Equalizer Output Same as the (m, n) element of M-point DFT matrix : M x M Identity Matrix

Simplification of T/K-FSE (cont d) Equalizer Output: is M M diagonal submatrix of (k=1, 2,, K)

Simplification of T/K-FSE (cont d) Received Signal Equalizer Output DFT IDFT Decimator Equalizer Weights Block Diagram of the proposed T/K-FSE M-point IDFT KM-point DFT

Input and Output relation is M M submatrix of (k=1, 2,, K)

ZF Weights of Proposed T/K-FSE ZF Condition s.t. SSE (K=1) Channel nulls result in Noise enhancement Uniquely determined T/K-FSE (K>1) Certain Degree of Freedom in the choice of Equalizer Weights

ZF Weights of Proposed T/K-FSE (cont d) Minimization of the noise power at the equalizer output Noise component at the equalizer output Minimization Problem min s.t.

ZF Weights of Proposed T/K-FSE (cont d) Minimization Problem min s.t. ZF Weights of Proposed T/K-FSE:

MMSE Weights of Proposed T/K-FSE Cost function ( Mean-Square-Error ): MMSE Weights of Proposed T/K-FSE:

Optimum Linear MMSE T/K-FSE Expander Channel Equalizer (M X KM) Optimum Linear MMSE T/K-FSE: Optimum Linear MMSE Equalizer can t be realized by the one-tap FDE because of the colored noise

Simulation Settings Mod/Demod. Scheme QPSK / Coherent Detection Block Size M = 256 Length of CP 32 Channel Model Tx & Rx Filter Channel Estimation Channel Noise -path rayleigh fading channels with an exponentially decaying power profile square-root raised-cosine filter (roll-off factor = 0.5) Ideal AWGN Oversampling Rate K = 1, 2, 4 (i.e. SSE, T/2-FSE, T/4-FSE) # of Iteration,000

BER Performance of Proposed T/K-FSE SC-CP Scheme OFDM Scheme

Performance of T/K-FSE Passband width and Performance Improvement via FSE Not exploited in SSE case Exploiting Band No energy on this band We can t expect any performance Improvement in K >2

Frequency Diversity Method using Proposed T/K-FSE CP Insertion S/P P/S Tx filter Transmit Signal Spectrum Original Spectrum Band Width: P times Symbol Rate (P-1) Copies CP Removal M Rx filter K times Oversampling S/P KM-point DFT M Equalization and diversity combining are achieved simultaneously M-point IDFT S/P

BER Performance of the SC-CP via Proposed FDE/DC BER 1-1 -2-3 ZF MMSE K=P=1 Mod./ Demod. QPSK Block Size M = 256 CP Length N=32 Channel: -path rayleigh fading channels Order of Channel L=30-4 K=P=4 K=P=2-5 0 5 15 20 25 [db] Energy per Bit over Noise Power Density Tx/Rx Filter: square-root raised-cosine filter ( α=0.5) Channel Estimation: Ideal

BER BER Performance of the OFDM via Proposed FDE/DC 1-1 -2-3 -4 K=P=4-5 0 5 15 20 25 [db] ZF & MMSE K=P=1 K=P=2 Energy per Bit over Noise Power Density Mod./ Demod. QPSK Block Size M = 256 CP Length N=32 Channel: -path rayleigh fading channels Order of Channel L=30 Tx/Rx Filter: square-root raised-cosine filter ( α=0.5) Channel Estimation: Ideal

Applications of FDE/DC Robust Communication with Poor Receivers ex) Sensor Network, Traffic lights Network, Inter Vehicle Communication, etc One Alternative Rate Reduction Technique for Adaptive Modulation Systems ex) Wi-Fi Im Im Original Block Expanded Version 1 0 2 0 3 0 4 0 Re Re 1 2 3 4 5 6 7 8 FDE/DC QPSK BPSK

Rate Reduction Technique via FDE/DC OFDM IDFT Reduce the Rate Add Expander Channel DFT Equalizer Weights Change the Weights Add Decimator Expander IDFT Channel DFT Equalizer Weights Decimator

BER BER Performance of the SC-CP via FDE/DC for a given transmission rate 1-1 -2-3 K=P=2 M=256 QPSK ZF K=P=1 M=512 BPSK ZF Mod./ Demod. BPSK, QPSK, 16QAM Block Size M =128, 256, 512 (FFT size = 512) CP Length N=32 Channel: -path rayleigh fading channels -4 Order of Channel L=30 K=P=4 M=128 16QAM ZF -5 Tx/Rx Filter: square-root raisedcosine filter ( α=0.5) 0 5 15 20 25 [db] Channel Estimation: Ideal

Pre- and Post- Equalization Expander Channel DFT FDE IDFT Decimator Post-FDE/DC (Frequency Domain Equalizer and Diversity Combiner) Expander DFT FDE IDFT Channel Decimator Pre-FDE/DC

Pre- and Post- Equalization Expander Channel DFT FDE IDFT Decimator Post-FDE/DC (Frequency Domain Equalizer and Diversity Combiner) Expander DFT FDE IDFT Channel Decimator Pre-FDE/DC

Configuration of the SC-CP Scheme with Proposed Pre-FDE/DC Transmitter: CP Insertion Transmitted Signal S/P DFT IDFT P/S Rx filter Band Width: P times Symbol Rate Receiver: Rx filter Sampling at Symbol Rate S/P CP Removal P/S Output

Weights of Proposed Pre-FDE/DC ZF based: MMSE based:

BER Performance of the SC-CP via Proposed Pre-FDE/DC BER 1-1 -2-3 ZF MMSE K=P=1 Mod./ Demod. QPSK Block Size M = 256 CP Length N=32 Channel: -path rayleigh fading channels Order of Channel L=30-4 K=P=4 K=P=2-5 0 5 15 20 25 [db] Tx/Rx Filter: square-root raised-cosine filter ( α=0.5) Channel Estimation: Ideal AWGN

BER Performance of the OFDM via Proposed Pre-FDE/DC BER 1-1 -2-3 ZF MMSE K=P=1 Mod./ Demod. QPSK Block Size M = 256 CP Length N=32 Channel: -path rayleigh fading channels Order of Channel L=30-4 K=P=2 K=P=4-5 0 5 15 20 25 [db] Tx/Rx Filter: square-root raised-cosine filter ( α=0.5) Channel Estimation: Ideal AWGN

Summary T/K-FSE methods for block transmission with cyclic prefix are proposed ZF and MMSE weights of the proposed T/K-FSE are derived Based on the idea of T/K-FSE, two simple frequency diversity method is also proposed Computer simulations reveal the performance improvements by proposed methods

PAPR of the SC-CP via Proposed Pre-FDE/DC CCDF=complementary cumulative distribution function CCDF 1-1 -2-3 K=P= SC-CP (M=256) ZF MMSE OFDM (M=256) Mod./ Demod. QPSK Block Size M = 256 CP Length N=32 Order of Channel L=30 Tx/Rx Filter: square-root raised-cosine filter ( α=0.5) -4 0 2 4 6 8 12 14 16 PAPR [db]

PAPR of the OFDM via Proposed Pre-FDE/DC CCDF=complementary cumulative distribution function 1-1 OFDM (M = 256) K=P=2 ZF MMSE Mod./ Demod. QPSK Block Size M = 256 CP Length N=32 CCDF -2-3 Order of Channel L=30 Tx/Rx Filter: square-root raised-cosine filter ( α=0.5) -4 0 2 4 6 8 12 14 16 PAPR [db]