Minimum Intersymbol Interference Methods for Time Domain Equalizer

Minimum Intersymbol Interference Methods for Time Domain Equalizer Design M. Ding and B. L. Evans The University of Texas at Austin, TX 78712 -1084 USA {ming, bevans}@ece. utexas. edu R. K. Martin and C. R. Johnson, Jr. Cornell University Ithaca, NY 14853 USA {frodo, johnson}ece. cornell. edu December 2, 2003

Discrete Multitone Modulation § Wireline multicarrier modulation method § Symbol: real inverse FFT output samples § Cyclic prefix (CP) is last n samples of symbol copy CP s y m b o l v samples i CP s y m b o l i+1 N samples § Linear convolution w/ channel impulse resp. § Circular convolution if channel length < CP length + 1 § Frequency equalization accomplished in DFT domain December 2, 2003

Two-Step Equalization +1 § Time domain equalizer (TEQ) § Channel and TEQ modeled as finite impulse response filters § Cascade of channel and TEQ has response of at most +1 samples § Frequency domain equalizer § Single division per subchannel § Compensate for amplitude and phase distortions § Training sequence December 2, 2003 channel impulse response effective channel impulse response D: transmission delay n: cyclic prefix length N: symbol/FFT length

Minimum ISI TEQ Design [Arslan, Evans & Kiaei, 2001] § Minimize frequency weighted ISI energy w/r to TEQ taps w Hwin, Hwall : channel in/outside window qi : ith fast Fourier transform vector +1 channel impulse response effective channel impulse response D: transmission delay n: cyclic prefix length § Eigenvector corresponding to minimum generalized eigenvalue of (X, Y) § Cholesky decomposition of Y December 2, 2003

Minimum ISI TEQ Design [Arslan, Evans & Kiaei, 2001] § Advantages § Pushes ISI to unused and low SNR subchannels § Has real-time implementation in DSP software § Disadvantages § Inability to design TEQs longer than + 1 taps § Y not invertible in this case § X invertible only if all subchannel weights non-zero § High computational cost for delay optimization search § Both Hwin and Hwall depend on delay D § Cholesky decomposition needed for each delay D § Cholesky decomposition sensitive to fixed-point computation: TEQ limited to ~15 taps on 16 -bit DSP December 2, 2003

Extending Min-ISI TEQ Lengths § Define new objective function : weight for subchannel i, e. g. SNR in ith subchannel HTH : always positive definite and invertible § Suitable for arbitrary length TEQ design § Reduces delay optimization search complexity December 2, 2003

Quantize Frequency Weighting § Subchannel weight § Sx, i : transmit power in subchannel i § Sn, i : noise power in subchannel i § On-off quantization removes multiplication § Compare noise power with threshold § Put zeros in those subchannels with larger-thanthreshold noise power and ones in others § One choice of threshold is noise power that only can support 2 bits in subchannel given transmitted power: December 2, 2003

Iterative Min-ISI Method 1. 2. 3. 4. Obtain weighting values Precompute Decide step size , and precompute Compute non-zero initial guess w 0 and iteratively calculate wk, using deterministic gradient search a) Gradient: b) Update: c) Normalization: December 2, 2003

Simulation Results Simulation Parameters Cyclic prefix 32 samples FFT size (N) 512 samples Coding gain 5 d. B Margin 6 d. B Input power 23 d. Bm Noise power -140 d. Bm/Hz Crosstalk noise 24 HDSL POTS splitter 5 th order IIR December 2, 2003

Conclusion § Reformulated objective function § TEQs may have arbitrary length § Orders of magnitude reduction in delay search complexity § Iterative Min-ISI implementation § Uses iterative gradient search § Low complexity, avoids Cholesky decomposition § Achieves comparable bit rate performance. § Freely distributable discrete multitone equalizer Matlab toolbox 3. 1 from UT Austin http: //www. ece. utexas. edu/~bevans/projects/adsl/dmtteq/index. html December 2, 2003

BACKUP SLIDES December 2, 2003

Constrained Minimization of Iterative Min-ISI § Use the Lagrange multipliers Noted here X is Hermitian and Y is symmetric. § Iterative updates: § where December 2, 2003

Introduction § Multicarrier wireline broadband communications to home and small businesses via x. DSL § Wireline systems fix bit error rate and vary bit rate § Key to maximize bit rate is equalizer design § Design equalizer to max. bit rate subject to § Reducing intersymbol and intercarrier interference § Compensating channel frequency distortion Message bit stream Transmitter Channel December 2, 2003 Equalizer Received bit stream