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Orthogonal time frequency space modulation is a two dimensional (2D) delay-Doppler domain waveform. It uses inverse symplectic Fourier transform (ISFFT) to spread the signal in time-frequency domain. To extract diversity gain from 2D spreaded signal, advanced receivers are required. In this work, we investigate a low complexity linear minimum mean square error receiver which exploits sparsity and quasi-banded structure of matrices involved in the demodulation process which results in a log-linear order of complexity without any performance degradation of BER.

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Generalised frequency division multiplexing (GFDM) has gained significant importance as a contender for the fifth generation (5G) air interface. The peak-to-average power ratio (PAPR) of GFDM is high due to the use of a same pulse shaping filter per subcarrier and the addition of different subcarriers at the transmitter. Proposed is the use of discrete Fourier transform (DFT) spreading-based GFDM transmission to reduce the PAPR. It is found that DFT spreading helps to reduce the PAPR of GFDM significantly. It is also seen that the bit error rate performance, which is computed through simulation and using an analytical expression of the signal-to-interference-plus noise ratio, is not compromised by DFT spreading but rather is improved in the frequency selective fading channel.Introduction: Generalised frequency division multiplexing [1] has been shown to meet the requirements of next generation (fifth generation (5G)) mobile communication networks, such as relaxed time and frequency synchronisation, low out of band radiation, very short symbol duration and flexible bandwidth of operations [2] quite well. Therefore, it is one of the contenders for the 5G air interface.GFDM is a block-based multicarrier transmission technology with multiple time slots. Each subcarrier is pulse shaped with a non-rectangular pulse shape to increase frequency localisation of the pulses [1]. It is shown in [3] that using the same and non-rectangular pulse shape for each subcarrier in multicarrier transmissions increases the peak-to-average power ratio (PAPR with respect to orthogonal frequency division multiplexing (OFDM). Hence, it is expected that GFDM will have a higher PAPR than OFDM for an equal number of subcarriers. The PAPR of GFDM is investigated in [4] and compared with OFDM. However, the comparison is done for an unequal number of subcarriers. The aim of this Letter is PAPR reduction for GFDM. It is shown in [5] that the discrete Fourier transform (DFT) matrix is one of the optimum precoding matrices that helps reduce PAPR in OFDM. Therefore, we investigate the effect of DFT spreading to reduce PAPR in GFDM in this Letter. Two subcarrier mapping schemes for DFT spreading [6], (i) localised frequency division multiple access (LFDMA) and (ii) interleaved frequency division multiple access (IFDMA), are considered. The bit error rate (BER) performance of DFT spreading-based GFDM system using the minimum mean square error (MMSE) receiver in frequency selective fading channels (FSFCs) is also presented. The BER of DFT spread GFDM is also obtained from an analytical expression of the signal-to-interference-plus noise ratio (SINR) developed in this Letter.