SEFDM Signals Research Articles

Application of complex-valued convolutional neural networks for equalization and detection of SEFDM systems

Background. The disadvantage of spectrally efficient signals with frequency multiplexing is the occurrence of intersymbol interference, which is further aggravated when these signals propagate in frequency selective channels.
 Aim. The possibility and effectiveness of using neural network approaches for channel equalization and signal detection in communication systems using SEFDM signals has been assessed.
 Methods. A receiver structure for SEFDM systems based on a deep complex-valued convolutional neural network is proposed, which allows recovering bits from the temporal representation of the signal without using the fractional Fourier transform and inverting the cross-correlation matrix between frequency subcarriers. A two-stage network training scheme has been developed. Based on simulation modeling, a comparative analysis of the noise immunity of SEFDM systems was carried out both in a channel with white Gaussian noise and in a channel with Rayleigh fading, using classical and neural network receivers.
 Results. It is shown that there is no loss of noise immunity in channels with additive white Gaussian noise and an increase in noise immunity of the system up to 2 dB in the channel specified by the extended automotive model (3GPP-EVA).
 Conclusion. The effectiveness of using deep neural complex-valued convolutional networks as receivers for spectrally efficient communication systems, as well as their advantage over classical ones, is shown.
 Keywords – SEFDM; deep complex-valued convolutional neural network; turbocoding.

PEAK-TO-AVERAGE POWER RATIO OF SPECTRALLY EFFICIENT FDM SIGNALS

The change of the number of subcarriers in SEFDM signal from 5 to 1024 leads to the growth of the PAPR (peak-to-average power ratio) from 4.5 to 9 dB. PAPR of SEFDM signals stays about constant (instability is no more than 5%) while normalized subcarriers frequency spacing increase from 1/2 to 1. It indicates no additional energy loss during the transition from OFDM signals to SEFDM signals, caused by an increase in the PAPR. It is proposed to use a part of the resulting gain in the frequency band to reduce PAPR. The method, based on modification of Tone Insertion method, was developed. Developed method consists in adding additional subcarriers with randomly generated manipulation symbols to the SEFDM signal. SEFDM symbol with minimal PAPR is chosen to be send. According to this method the PAPR can be reduced in average of 1.4 dB. The degree of reduction of the PAPR depends on the size of the channel alphabet of additional subcarriers (changing of the average win is 0.6 dB for BPSK to 1.4 dB for QAM-64) and the number of combinations of symbols of additional subcarriers (1.6 dB for 1000 combinations for QAM-64). According to estimation of the FPGA resources for implementation of PAPR reduction algorithm it is required relatively small resource costs compared to the formation of SEFDM signal without reduction.

DFT Spread Spectrally Efficient Frequency Division Multiplexing for IM-DD Transmission in C-Band

In this article, we propose and experimentally demonstrate a new discrete Fourier transform spread (DFT-S) spectrally efficient frequency division multiplexing (DFT-S SEFDM) system. DFT-S technique is adopted to reduce the peak-to-average-power-ratio (PAPR) of SEFDM signal in optical intensity modulation and direct detection (IM-DD) system for the first time. The existing detection algorithms for SEFDM signal, such as logarithmic-maximum-a-posterior (log-MAP) Viterbi and cascaded binary-phase-shift-keying iterative detection (CBID), are successfully modified to our DFT-S SEFDM system. Experimental results show that DFT-S SEFDM outperforms conventional SEFDM owing to its lower PAPR. In our test, to verify the benefits of our scheme, a net data rate of beyond 100 Gb/s can be achieved after 2-km standard single mode fiber (SSMF) transmission, and DFT-S SEFDM also can outperform DFT-S DMT owing to its tolerance to bandwidth limitation. We further verify the advantage of DFT-S SEFDM in IM-DD C-band system, and show its resistance to the impact of dispersion-induced power fading.

Improving the effectiveness of the multi-frequency signals application under conditions of amplitude limitation

In this paper, simulation modelling of information transmission using spectrally efficient multi-frequency (SEFDM) signals with an amplifier and a limiter on transmission has been held. SEFDM signals have a high peak-to-average power ratio (PAPR). Therefore, we need to limit the value of PAPR to increase the efficiency of the amplifier stages of transceiver devices. An effective value for PAPR limiting has been found. For signal-to-noise ratio 7 dB, level of bit error rate reaches minimum value when the PAPR limit value is within 4.5-5.5 dB. Besides that, a comparison of the effectiveness of detection algorithms with and without feedback has been made. The results showed that detection algorithm with feedback increases the effectiveness of the multi-frequency signals application under conditions of amplitude limitation.

Trellis channel joint equalization and demodulation of SEFDM signals

An algorithm of channel joint equalization and demodulation of multicarrier signals with nonorthogonal frequency spacing (spectrally efficient frequency division multiplexing, SEFDM) is proposed. It is based on DFT (Discrete Fourier Transform) and BCJR (Bahl, Cocke, Jelinek and Raviv) algorithm adapted to work with frequency samples of received signal. The performance of proposed receiver is comparable with performance of classic OFDM-signal receivers.

Waveform Design of Zero Head DFT Spread Spectral Efficient Frequency Division Multiplexing

Zero head discrete Fourier transform (DFT) spread spectral efficient frequency division multiplexing (ZH-DFT-s-SEFDM) as a non-orthogonal multicarrier transmission scheme is proposed for the bandwidth compressing. A zero head DFT spread approach consists in this waveform design for reducing the peak-average-power-ratio (PAPR) and suppressing the out-of-band emissions introduced by the inter symbol interference and the inter carrier interference. Simultaneously, the corresponding receiver design is given, and a low complexity zero-forcing (ZF) detection algorithm is attached to the ZH-DFT-s-SEFDM receiver design. As the loss of orthogonality, the conventional SEFDM detector is overly complex, and however, the ZF detector as a linear detector performs well in the ZH-DFT-s-SEFDM system by adjusting the length of zero head. Simulation results show that the ZH-DFT-s-SEFDM signal achieves lower out-of-band emissions and a better PAPR performance than the conventional SEFDM signal at the same bandwidth compressing ratio. The binary error ratio (BER) performance of a ZH-DFT-s-SEFDM receiver with a ZF detector is also investigated. It performs better as the longer zero head inserted, and can achieve the better BER performance than conventional SEFDM and OFDM at the low signal-to-noise-ratio (SNR) for a particular number of zero head, and the BER performance of ZH-DFT-s-SEFDM remained the same as OFDM and traditional SEFDM at the high SNR.