Pre-Coding in a Faster-Than-Nyquist Transmission System
US-2016308697-A1 · Oct 20, 2016 · US
US10003390B2 · US · B2
| Field | Value |
|---|---|
| Publication number | US-10003390-B2 |
| Application number | US-201615341227-A |
| Country | US |
| Kind code | B2 |
| Filing date | Nov 2, 2016 |
| Priority date | Apr 21, 2016 |
| Publication date | Jun 19, 2018 |
| Grant date | Jun 19, 2018 |
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Systems and methods of precoded faster than Nyquist (FTN) signalling are provided. In the transmitter, Tomlinson-Harashima Preceding (THP) is applied to produce precoded symbols. The THP is based on inter-symbol interference (ISI) due to using faster than Nyquist (FTN) signalling. An inverse modulo operation is not performed in the receiver. Instead, in the receiver, FTN processing is performed based on a matched filter output by determining log a-posteriori probability ratio LAPPR values computed for an n th bit b n of a k th received symbol and pre-computed a-priori probabilities of an extended constellation for a given pulse shape h(t) and FTN acceleration factor combination.
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The invention claimed is: 1. A method comprising: in a receiver, receiving a signal containing a plurality of received symbols, each received symbol comprising a symbol of an extended constellation multiplied by a faster than Nyquist (FTN) pulse shape characterized by roll-off factor β and time acceleration factor τ after transmission over a channel; in the receiver, performing matched filtering of the received signal based on the FTN pulse shape to produce a matched filter output; in the receiver, for a kth received symbol v of the plurality of received symbols, without performing a modulo M operation, performing FTN processing based on the matched filter output by determining log a-posteriori probability ratio (LAPPR) values computed for each bit of the kth received symbol based on x′[k] and pre-computed a-priori probabilities of the extended constellation for a given pulse shape h(t) and τ combination, where x′[k] is the matched filter output for the kth received symbol v[k]; in the receiver, performing forward error correction (FEC) decoding based on the LAPPR values. 2. The method of claim 1 further comprising: in the receiver, whitening filtering the matched filter output x′[k] to produce a whitening filtered output v′[k]; wherein performing FTN processing based on x′[k] comprises performing FTN processing based on the whitening filter output v′[k]. 3. The method of claim 2 wherein the whitening filtering has a frequency response that is an inverse of a maximum phase representation of a spectral factorization of h(t)*h(−t), where h(t) is the faster than Nyquist pulse shape. 4. The method of claim 1 wherein determining LAPPR values comprises employing LAPPR ( k ) ( b n ) = log P ( b n = 1 | v ′ [ k ] ) P ( b n = 0 | v ′ [ k ] ) = log Σ c i ∈ C 1 P ( v ′ [ k ] | v [ k ] = c i ) . P ( v [ k ] = c i )
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Correlative coding using Tomlinson precoding, Harashima precoding, Trellis precoding or GPRS · CPC title
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