In this paper, we propose a novel user cooperation scheme based on weighted fractional Fourier transform (WFRFT), to enhance the physical (PHY) layer security of wireless transmissions against eavesdropping. Specifically, instead of dissipating additional transmission power for friendly jamming, by leveraging the features of WFRFT, the information bearing signal of cooperators can create an identical artificial noise effect at the eavesdropper while causing no performance degradation on the legitimate receiver. Furthermore, to form the cooperation set in an autonomous and distributed manner, we model WFRFT-based PHY-layer security cooperation problem as a coalitional game with non-transferable utility. A distributed merge-and-split algorithm is devised to facilitate the autonomous coalition formation to maximize the security capacity while accounting for the cooperation cost in terms of power consumption. We analyze the stability of the proposed algorithm and also investigate how the network topology efficiently adapts to the mobility of intermediate nodes. Simulation results demonstrate that the WFRFT-based user cooperation scheme leads to a significant performance advantage, in terms of secrecy ergodic capacity, compared with the conventional security-oriented user cooperation schemes, such as relay-jamming and cluster-beamforming.

On Physical Layer Security: Weighted Fractional Fourier Transform Based User Cooperation

Internet of Things (IoT) is regarded as the fundamental platform for many emerging services, such as smart city, smart home, and intelligent transportation systems. With ever-increasing penetration of IoT, it becomes of great importance to ensure the IoT security, as the security threats are extended from the cyber world to the physical world. In this article, we investigate physical-layer authentication to help verify the identity of IoT entities for preventing unauthorized access to information or service. Specifically, we propose a Gaussian-tag-embedded physical-layer authentication (GTEA) scheme by using a weighted fractional Fourier transform (WFRFT). Through the superimposition of a low-power Gaussian WFRFT tag onto the message signal, the legitimate receiver can verify the authenticity of the received signal at the physical layer, without being detected by adversaries. Moreover, security analysis shows that with the deliberately designed Gaussian tag, the GTEA scheme is robust against spoofing and replaying attacks. In addition, tradeoff analysis and simulation results are provided to demonstrate the capability of the GTEA scheme in achieving reliability of the message delivery, stealth of the embedded tag signal, and balancing the tradeoff among the robustness of user authentication. Moreover, a prototype is further developed using FPGA and experiments are conducted to demonstrate the effectiveness and performance improvement of the proposed GTEA scheme.

Physical-Layer Authentication for Internet of Things via WFRFT-Based Gaussian Tag Embedding

The artificial noise (AN) aided multi-beam directional modulation (DM) technology is capable of wireless physical layer secure (PLS) transmissions for multiple desired receivers in free space. The application of AN, however, makes it less power-efficient for such a DM system. To address this problem, the weighted fractional Fourier transform (WFRFT) technology is employed in this paper to achieve power-efficient multi-beam DM transmissions. Specifically, a power-efficient multi-beam WFRFT-DM scheme with cooperative receivers and a power-efficient multi-beam WFRFT-DM scheme with independent receivers are proposed based on frequency diverse array (FDA), respectively. The bit error rate (BER), secrecy rate, and robustness of the proposed multi-beam WFRFT-DM schemes are analyzed. Simulations demonstrate that 1) the proposed multi-beam WFRFT-DM schemes are more power-efficient than the conventional multi-beam AN-DM scheme; 2) the transmission security can also be guaranteed even if the eavesdroppers are located close to or the same as the desired receivers; and 3) the proposed multi-beam WFRFT-DM schemes are capable of independent transmissions for different desired receivers with different modulations.

WFRFT-Aided Power-Efficient Multi-Beam Directional Modulation Schemes Based on Frequency Diverse Array

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

From the points of spectral efficiency, low latency and massive connectivity, novel modulation and multiple access schemes have been proposed in fifth generation (5G) wireless networks. However, the combinations of multiplexing and multiple access techniques have not been widely investigated in most literatures. Therefore, we joint generalized frequency division multiplexing (GFDM) waveforms and power-domain non-orthogonal multiple access (NOMA) systems together in order to further extend the framework of multi-carrier NOMA, and also achieve performance evaluations for NOMA networks with one base station and two users. Basically, theoretical BER expressions of downlink and uplink GFDM assisted NOMA schemes are mathematically derived and then verified by simulation results. In addition, combined performance advantages, including higher achievable sum rate, lower peak-to-average power ratio (PAPR) and out of band power (OOBP) radiation, can be obtained in GFDM assisted NOMA networks.

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On the Performance of GFDM Assisted NOMA Schemes

Carrier frequency offset (CFO) due to Doppler shift or misaligned frequency between the transmitter and the receiver has a serious impact on both orthogonal frequency division multiplexing (OFDM) and single carrier (SC) communication systems. Inter-carrier interference coefficients of OFDM system produced by CFO have been proposed and applied in analysing exact bit error rate (BER) upon diverse channel models. In this Letter, interference of hybrid carrier communication system based on weighted-type fractional Fourier transform impaired by CFO is investigated, which is a weighted form of multi-carrier and SC schemes, and then exact BER expression of BPSK modulation HC system is derived and verified by simulations.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/el.2015.1027

BER analysis of hybrid carrier system based on WFRFT with carrier frequency offset

Generalised frequency division multiplexing (GFDM) as a non-orthogonal waveform candidate is posed to reduce the high out of band radiation of orthogonal frequency division multiplexing system via pulse shaping. In this study, an analytical model of introduced interference from neighbouring subcarriers caused by pulse shaping is firstly proposed. Signal-to-interference-plus-noise ratio (SINR) is calculated according to related GFDM models with different weighted-type fractional Fourier transform (WFRFT) precoding orders. Approximated bit error rate (BER) expressions are derived for the low complexity GFDM system over additive white Gaussian noise and fading channels based on the analysis of SINR. Particularly, the BER superiority of WFRFT precoding is highlighted over the fading channels. Furthermore, peak-to-average power ratio and out of band power suppression performances are simulated at different WFRFT orders to illustrate the advantages of WFRFT precoding.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-com.2016.0772

Bit error rate analysis of generalised frequency division multiplexing with weighted-type fractional Fourier transform precoding

The invention discloses a signal emission and reception method of a GFDM system based on weight fraction Fourier transform, relating to the signal emission and reception technology of the GFDM system based on the weight fraction Fourier transform. The invention can obtain better bit error rate and reduces the peak-to-average power ratio. The invention can flexibly regulate the subcarrier and the WFRFT order in the unit carrier wave block according to the channel state information and user demands, and the order in each subcarrier can maintain different in order to achieve to the need of the system performance. Besides, the invention performs precoding through WFRFT and reasonably chooses the appropriate transformation order according to the channel condition, which enables the encoded system to obtain a better bit error rate performance and have lower peak-to-average power ratio.

Signal emission and reception method of GFDM system based on weight fraction Fourier transform

In this letter, we investigate theoretical BER performances of generalized frequency division multiplexing (GFDM) systems with receivers based on Gabor window. Considering relationships between zero forcing and minimum mean square error (MMSE) receivers, theoretical BER expressions of GFDM systems with an MMSE receiver are derived over AWGN and fading channels through calculating noise enhancement factor at the receiver. To demonstrate the generality of proposed methods, analytical BER expressions of DFT and weighted-type fractional Fourier transform precoded GFDM systems are also given and verified by simulation results.

Zhenduo Wang

Papers

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

BER analysis of hybrid carrier system based on WFRFT with carrier frequency offset

Bit error rate analysis of generalised frequency division multiplexing with weighted-type fractional Fourier transform precoding

Signal emission and reception method of GFDM system based on weight fraction Fourier transform

BER Analysis for GFDM Systems With Gabor MMSE Receiver