In this paper, we investigate bit error rate (BER) performances of weighted-type fractional Fourier transform (WFRFT) precoded orthogonal frequency-division multiplexing (OFDM) and generalized frequency-division multiplexing (GFDM) waveforms with an integer time offset (TO) over additive white Gaussian noise and fading channels. First of all, theoretical BER expressions of hybrid carrier systems with TO are derived according to the linear combination characteristic of WFRFT. In addition, the fusion mechanism is also employed to calculate noise enhancement factor (NEF) of WFRFT precoded GFDM waveforms, and then analytical BER expressions are derived, including the cases with TO. Basically, analytical BER expressions of WFRFT precoded OFDM and GFDM waveforms are under the same framework, and BER of the latter could be simplified to the former when GFDM systems are reduced to OFDM systems. Through WFRFT precoding, the BER performance of GFDM waveforms could be improved by about 2 dB over fading channels with timing errors. Furthermore, using derived NEF of WFRFT precoded GFDM waveforms, theoretical BER expressions could be easily extended to space-time coded systems. Finally, when interblock interference and intercarrier interference are generated due to insufficient cyclic prefix and timing errors, BER performances of WFRFT precoded OFDM and GFDM waveforms also surpass their two special cases, i.e., nonprecoded and discrete Fourier transform precoded ones.

BER Analysis of WFRFT Precoded OFDM and GFDM Waveforms With an Integer Time Offset

In this paper, a multiuser space-time line code (MU-STLC) scheme is newly designed that concurrently delivers multiple STLC signals to multiple users, and a preprocessing matrix for the MU-STLC is derived based on the minimum mean square error criterion. The novel MU-STLC method retains the conventional STLC receiver structure so that each user linearly combines the received signals without using the full channel state information to decode the STLC signals. With more transmit antennas than the number of users having two receive antennas, a transmit antenna selection (TAS) scheme is investigated in combination with the proposed MU-STLC method, and the detection signal-to-interference-plus-noise ratio (SINR) is derived depending on a specific TAS pattern. The performance improvement obtained from the TAS is significant, yet finding the optimal TAS pattern is a combinatorial problem that requires prohibitively high computational complexity. To resolve this issue, a greedy TAS algorithm is also proposed that iteratively selects the transmit antenna maximizing the detection SINR in each greedy step. The numerical results verify the efficacy of the proposed MU-STLC system with the SINR-based greedy TAS algorithm in terms of the bit error rate performance and computational complexity. For example, comparing with a scheme that selects four antennas from eight antennas randomly to support four users, the proposed TAS scheme can reduce the required signal-to-noise ratio for achieving 10<sup>−3</sup> bit-error-rate by approximately <inline-formula> <tex-math notation="LaTeX">$6\;{\mathrm{ dB}}$ </tex-math></inline-formula> when quadrature phase-shift keying is employed. Furthermore, the proposed method can achieve comparable performance to the optimal antenna selection scheme with the reduced computational complexity by <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(M^{5})$ </tex-math></inline-formula> from <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(M^{U+3})$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$U$ </tex-math></inline-formula> are the numbers of transmit antennas and selected antennas (or users), respectively.

Multiuser Space-Time Line Code With Transmit Antenna Selection

In this article, we investigate the recently developed space time line code (STLC) scheme, which utilizes the channel state information (CSI) for encoding at the transmiter to achieve full spatial diversity gain. The theoretical analysis of the bit error rate (BER) performance for STLC is first evaluated. Moreover, aiming at alleviating the cost of radio frequency (RF) chains, antenna selection at both the transmitter and receiver sides is developed by minimizing the derived instantaneous BER. Furthermore, in the context of a flat Rayleigh fading channel, we derive an upper bound for quantifying the BER performance of STLC with both transmit and receive antenna selection. Finally, simulation results validate the accuracy of the above theoretical analysis results and show the performance improvement of the developed antenna selection schemes.

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Performance Analysis and Antenna Selection for Space Time Line Code

Recently, the idea of space-time line code (STLC) was developed in [1] as an efficient way to increase the diversity of multiple-input multiple-output (MIMO) communications, with a special code structure that exploits the channel state information (CSI) at the transmitter. In this paper, in order to evaluate the performance of STLC in practical transmission environment, we analyse the bit-error rate (BER) performance of STLC in the context of correlated Rayleigh and Rician fading MIMO channels. Finally, simulation results validate the accuracy of the above theoretical analysis.

Performance Analysis of Space-Time Line Code in Correlated Fading Channels

For multiple-input multiple-output systems with four receive antennas, conventional space–time line codes (STLCs) have supported code rates of 3/4, 4/7, and 1/2. To provide a wider range of transmission rates, we herein propose a rate-1 STLC for four-receive-antenna systems. We present an encoding method to achieve full rate and devise a simple decoding scheme that does not require full channel state information at the receiver. Assuming a large number of transmit antennas, we analyze the bit error rate performance and demonstrate that the proposed STLC can achieve full spatial diversity.

Full-Rate Space–Time Line Code for Four Receive Antennas

In this paper, we investigate a class of new multiple-input multiple-output (MIMO) transmission schemes, dubbed space time line code (STLC), in the context of different mobility situations. We extend its original structure into space and frequency domains and propose a novel frequency line code (SFLC) for combining with orthogonal frequency division multiplexing (OFDM) in order to achieve potential diversity gains in time-varying multipath fading channels. Specifically, at the transmitter, the STLC/SFLC-OFDM scheme exploits the channel state information (CSI) to linearly encode successive modulated symbols in the time/frequency domain to achieve full diversity gain. At the receiver, it can retrieve the transmit symbols without full CSI, thanks to its special structure. We analyse the impact of time-variant channels to STLC and SFLC to show the expected performance degradation in practical channel, especially in the case of different mobile speeds. Our analysis and simulations show that the BER performance degrades with increasing correlation coefficient, which makes STLC-OFDM more robust in channels with abundant multipath spread, and SFLC-OFDM more robust in channels with high mobility speed. Meanwhile, a guideline is provided for switching when the communication environment changes. Finally, we carry out the practical implementation of STLC-OFDM and SFLC-OFDM schemes and characterize their performance with both computer simulations and an experimental testbed.

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Space-Time/Frequency Line Coded OFDM: System Design and Practical Implementation

Prefix-based multicarrier transmission is in wide application in current wireless communications, at the expense of extra redundancy and reduced spectral efficiency. In this contribution, we propose a novel hybrid prefix (HP) structure, which can offer higher spectral efficiency for orthogonal frequency division multiplexing (OFDM) based future wireless communications, such as 5G and beyond systems. Compared with the conventional prefix aided OFDM scheme, the proposed HP-OFDM scheme is capable of reducing the average length of the prefix with the aid of a proposed low-complexity detector for efficient signal restoration. We also quantify the signal to interference plus noise and the achievable rate of the proposed HP-OFDM scheme through a theoretical analysis. Furthermore, the bit-error rate (BER) of the proposed HP-OFDM is also theoretically derived. Our scheme results demonstrate that HP-OFDM is capable of reducing the prefix overhead by 50% compared with prefix-aided OFDM, while achieving a BER comparable to that of prefix-aided OFDM.

Hybrid Prefix OFDM Transmission Toward Future Wireless Communications

The invention belongs to the technical field of wireless communication, specifically an optimum power allocation method for a hybrid prefix orthogonal frequency division multiplexing (HP-OFDM) technology. According to the method, channel information and signal information are acquired mainly through estimation; and through application of a theoretical bit error rate formula, derivation is carriedout to obtain the optimum power allocation. Compared with a traditional hybrid prefix orthogonal frequency division multiplexing technology, the method has the advantages that the power load of a transmitting end is not increased and the system bit error rate performance also can be improved.

Power allocation method for hybrid prefix orthogonal frequency division multiplexing

A field programmable gate array (FPGA) based universal modulating-demodulating module has been designed in order to fulfil the requirement of wireless data transmission radio with multimode and good anti-interference capability using in the maritime combat scene. This module is designed using the thought of software defined ratio and digital modulating-demodulating technology. It has realized the function of multimode and variable rate. Meanwhile, the direct sequence spread spectrum technique is utilized in this design to improve the anti-jamming ability and confidentiality. Software simulation is done for the module using differential quadrature reference phase shift keying (DQPSK) modulation mode with 64 bit direct sequence spread spectrum technique. The Signal Tap Logic Analyzer is used for online verification. The performance of the designed module is good, which could fulfil the communication requirements of shipborne data transmission radio working in the complex marine environment.

Design of universal modulating-demodulating module for shipborne data transmission radio

$N$ -continuous (NC) precoder is a class of efficient sidelobe suppression techniques by smoothing the consecutive multicarrier symbols at the cost of additional interference to the transmit signals. In this paper, we firstly investigate the $N$ -continuous precoder in recently developed Subcarrier-Index Modulation Orthogonal Frequency Division Multiplexing (SIM-OFDM) systems, when the channel is modeled by frequency-selective fading. On the one hand, the Signal to Interference Plus Noise Ratio (SINR) is derived through theoretical analysis. Furthermore, with the quantified SINR, the achievable rate is first acquired for evaluating the performance of NC precoded SIM-OFDM. We also show that the above-mentioned performance analysis matches well with the simulation results.

Xun Li

Papers

Space-Time/Frequency Line Coded OFDM: System Design and Practical Implementation

Hybrid Prefix OFDM Transmission Toward Future Wireless Communications

Power allocation method for hybrid prefix orthogonal frequency division multiplexing

Design of universal modulating-demodulating module for shipborne data transmission radio

Achievable Rate of $N$ -Continuous Precoded SIM-OFDM