Signal Processing for Digital Data Storage (11)

Transcription

1 Outline Signal Processing for Digital Data Storage (11) Assist.Prof. Piya Kovintavewat, Ph.D. Data Storage Technology Research Unit Nahon Pathom Rajabhat University Partial-Response Maximum-Lielihood (PRML) Equalization Target Design Viterbi Algorithm -Predictive Maximum-Lielihood (NPML) Motivation NPML Detector Simulation Results Dr. Piya Kovintavewat 1 Dr. Piya Kovintavewat PRML Equivalent Discrete-Time Channel Model a { ±1} Channels Receiver filter Equalizer Detector â A ˆ( D ) Target response PRML is a technique of using a partial response (PR) equalizer in conjunction with the Viterbi detector to detect the signal, which is done in two steps: Equalize to a PR target whose response is as close to a channel response as possible. Perform maximum-lielihood (ML) equalization on the resulting PR trellis. Advantage Low noise enhancement with low complexity. Received signal P ( A( + N( Generally, can be represented by an FIR filter with an infinite number of taps (resulting in long ISI). Drawbac Lead to a complex detector Solution Use an equalizer to suppress the ISI enhancement will remain small even when amplitude distortion is severe [Bergmans, 1996]. Dr. Piya Kovintavewat 3 Dr. Piya Kovintavewat 4

2 Full Response Equalization Partial Response (PR) Equalization Full response equalizer 1 F ( Partial response (PR) equalizer where H( is the target response. H ( F ( { A( C ( N ( } F ( ) Y ( + D N ( A ( + Advantage Simple detector (e.g., a multi-level slicer) Disadvantage Lead to noise enhancement if has a spectral null { A( C ( N ( } F ( ) Y ( + D H ( A ( H ( + N ( Wanted signal Key: A controlled amount of ISI will be suppressed by the detector. This is why we want the target response to match as close to the channel response as possible to reduce the effect of the noise. A proper match of the target response to the channel permits noise enhancement to remain small even with amplitude distortion is severe. Dr. Piya Kovintavewat 5 Dr. Piya Kovintavewat 6 PR Target GPR Target Generally accepted PR target: Longitudinal Perpendicular H ( (1 (1 + H ( (1 + n n where n is an integer By using a generalized partial response (GPR) target, the performance gain can be substantially improved, especially at high NDs. Design criteria: The higher the ND, the larger the n. Matching the time or frequency domain of a dibit or transition response. Minimizing the mean-squared error (MSE) between signals at the equalizer output and the desired signals. Minimizing the noise power at the equalizer output. Maximizing the effective SNR. It has been shown that the MMSE approach is more practical to be employed in the system. Dr. Piya Kovintavewat 7 Dr. Piya Kovintavewat 8

3 MMSE Target Design Frequency Response Comparison - Longitudinal a {±1} b t T s y â r w The target, H(, and its corresponding equalizer, F(, can be obtained simultaneously by minimizing E[ w ] E[{( s h )} ] based on a monic constraint (i.e., h 0 1) [Moon and Zeng, 1995] f ) ( a Dr. Piya Kovintavewat 9 Dr. Piya Kovintavewat 10 Frequency Response Comparison - Perpendicular Performance Comparison (Perp.) Parameter: 1 SNR 10 log 10 σ (db) σ j /T 0% Dr. Piya Kovintavewat 11 Dr. Piya Kovintavewat 1

4 Performance Comparison (Perp.) Parameter: 1 SNR 10 log 10 σ (db) Correlation (Perp.) Parameters: ND.5 σ j /T 0% SNR db ND.5 Dr. Piya Kovintavewat 13 Dr. Piya Kovintavewat 14 -Predictive Maximum-Lielihood (NPML) Motivation NPML Detector Simulation Results Motivation: NPML Recall: A( C D where H( is the target response Let n(t) ~ N (0, σ ) white noise The input to the Viterbi detector: N( PR equalizer F( H ( Y( Viterbi detector A ˆ( D ) { A( C ( N ( } F ( ) Y ( + D H ( A ( H ( + N ( C ( Wanted signal It is impractical to mae this term equal to one. Thus, when this term is not unity, it will mae the white noise to be the colored noise. Dr. Piya Kovintavewat 15 Dr. Piya Kovintavewat 16

5 Practically, noise seen at the input of the Viterbi detector is colored (i.e., the noise samples are correlated). To obtain a good performance, we need to whiten the colored noise so that it loos lie white noise, before sending it to the Viterbi detector. This noise prediction/whitening process can be directly embedded in the Viterbi detector, resulting in the NPML detector. NPML Detector Embed a noise prediction/whitening process into the branch metric computation of the Viterbi algorithm. Reliable operation of the prediction/whitening process is achieved by using decisions from the path memory of the Viterbi detector. It has been shown to outperform the PRML detector. Dr. Piya Kovintavewat 17 Dr. Piya Kovintavewat 18 The noise predictor: Traditionally, the predictor is a finite impulse response (FIR) filter, whose prediction error decreases monotonically with increasing number of filter taps. It is well nown that an infinite impulse response (IIR) filter can perform as good as the FIR filter, but with a smaller number of filter taps at the expense of stability concern. By carefully designing the IIR filter, it has been shown in longitudinal recording that the IIR predictor with at most two zeros and two poles yields the best possible performance [Coer et al, 1998] in the range of 0.5 < ND < 3.5. Complexity of NPML The NPML detector requires trellis expansion, i.e., Number of trellis states ( target memory + predictor taps ) states Reduced-complexity of the NPML detector has also been proposed in the literature [Altear 1997]. Dr. Piya Kovintavewat 19 Dr. Piya Kovintavewat 0

6 BER Performance ND ) BER Performance (@ ND.5) Dr. Piya Kovintavewat 1 Dr. Piya Kovintavewat