Time Localization and Capacity of Faster-Than-Nyquist Signaling

In this paper, we consider communication over the bandwidth limited analog white Gaussian noise channel using non-orthogonal pulses. In particular, we consider non-orthogonal transmission by signaling samples at a rate higher than the Nyquist rate. Using the faster-than-Nyquist (FTN) framework, Mazo showed that one may transmit symbols carried by sinc pulses at a higher rate than that dictated by Nyquist without loosing bit error rate. However, as we will show in this paper, such pulses are not necessarily well localized in time. In fact, assuming that signals in the FTN framework are well localized in time, one can construct a signaling scheme that violates the Shannon capacity bound. We also show directly that FTN signals are in general not well localized in time. Therefore, the results of Mazo do not imply that one can transmit more data per time unit without degrading performance in terms of error probability. We also consider FTN signaling in the case of pulses that are different from the sinc pulses. We show that one can use a precoding scheme of low complexity to remove the inter-symbol interference. This leads to the possibility of increasing the number of transmitted samples per time unit and compensate for spectral inefficiency due to signaling at the Nyquist rate of the non sinc pulses. We demonstrate the power of the precoding scheme by simulations

Serial and parallel concatenations based on faster than Nyquist signaling

We investigate the performance of concatenated coding schemes based on Faster Than Nyquist(FTN) signaling over the AWGN channel. We test both serial and parallel concatenations. In serial concatenation the FTN signaling is considered as the inner encoder and the outer code is a rate b/c convolutional code. In parallel schemes we use two parallel Gaussian channels and transmit FTN pulse trains in both; here a precoding device turns out to be crucial. The convergence behaviour is analysed using EXIT charts. The overall spectral density of the schemes varies but is roughly 1–2 bit/s/Hz. The results, in terms of needed Eb/N0 for reliable communication versus spectral density, are very good

Faster-than-Nyquist Signaling for MIMO Communications

Faster-than-Nyquist (FTN) signaling is a non-orthogonal transmission technique, which has the potential to provide significant spectral efficiency improvement. This paper studies the capacity of FTN signaling for both frequency-flat and for frequency-selective multiple-input multiple-output (MIMO) channels. We show that precoding in time and waterfilling in space is capacity achieving for frequency-flat MIMO FTN. For frequency-selective fading, joint waterfilling in time, space and frequency is required.Comment: Have been submitted to IEEE transactions on wireless communication

On the study of faster-than-Nyquist multicarrier signaling based on frame theory

Multicarrier transmissions are classically based on undercomplete or exact Weyl-Heisenberg Riesz (biorthogonal or orthogonal) bases implemented thanks to oversampled filter-banks. This can be seen as a transmission below the Nyquist rate. However, when overcomplete Weyl-Heisenberg frames are used, we obtain a “faster-than-Nyquist” (FTN) system and it is theoretically impossible to recover exactly transmitted symbols using a linear receiver. Various studies have shown the interest of this high density signaling scheme as well as practical implementations based on trellis and/or iterative decoding. Nevertheless, there is still a lack of theoretical justifications with regard to pulse design in the FTN case. In this paper, we consider a linear transceiver operating over an additive white Gaussian noise channel. Using the frame theory and simulation results, we show that the mean squared error (MSE) is minimized when tight frames are used

An investigation into a DSP implementation of partial response signaling for 4800 bits per second full-duplex data communications over M.1020 telephone lines

Includes bibliographical references.This thesis investigates high-speed digital transmission over a conditioned, voice-grade telephone circuit (M.1020), using a technique known as partial response signaling, or PRS. In particular, the case where 4800 bps, full-duplex transmission is required in a CCI'PT V. 22 type format is investigated. The main v.22 criterion to be adhered to, is that frequency-division multiplexing (FDM) is to be used as the means of separating thetransmit and receive channels. The carrier frequencies should be 1200 Hz and 2400 Hz respectively. The investigation concerns the modulation and demodulation sections only