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Secure Precise Wireless Transmission with Random-Subcarrier-Selection-based Directional Modulation Transmit Antenna Array

Feng Shu, Xiaomin Wu, Jinsong Hu, Riqing Chen, Jiangzhou Wang

arXiv:1704.07996v2cs.ITmath.IT

TL;DR

Directional modulation can leave eavesdroppers within the desired beam able to intercept messages because its beamforming depends on angle rather than distance. The paper proposes RSCS-OFDM-DM, combining OFDM subcarrier selection, phase alignment, and artificial-noise projection. The scheme concentrates received confidential-message power near the desired position, while the paper also derives SINR and secrecy-rate expressions.

  • Problem

    Directional modulation's angle-only beamforming can allow an eavesdropper within the desired main beam to intercept messages, while prior RFDA-based designs require costly receiver structures as array size grows.

    Source: §I · pp. 1–2

  • Method

    RSCS-OFDM-DM replaces RFDA with OFDM-based random subcarrier selection and combines phase alignment/beamforming with artificial-noise projection.

    Source: §I · p. 2

  • Results

    The scheme forms a high SINR peak around the desired position with very little leakage into other wide regions, and increasing bandwidth and antenna count narrows the peak along distance and angle, respectively.

    Source: §I · p. 2, §IV · p. 8, §V · p. 9

  • Takeaways & Limitations

    The proposed OFDM-based structure reduces the desired receiver's RF-chain requirement to one and is presented as making secure precise communication feasible in medium- and large-scale systems.

    Source: §I · p. 2

Abstract

from arXiv · show

In this paper, a practical wireless transmission scheme is proposed to transmit confidential messages to the desired user securely and precisely by the joint use of multiple techniques including artificial noise (AN) projection, phase alignment (PA)/beamforming, and random subcarrier selection (RSCS) based on OFDM, and directional modulation (DM), namely RSCS-OFDM-DM. This RSCS-OFDM-DM scheme provides an extremely low-complexity structures for the transmitter and desired receiver and makes the secure and precise wireless transmission realizable in practice. For illegal eavesdroppers, the receive power of confidential messages is so weak that their receivers cannot intercept these confidential messages successfully once it is corrupted by AN. In such a scheme, the design of phase alignment/beamforming vector and AN projection matrix depend intimately on the desired direction angle and distance. It is particularly noted that the use of RSCS leads to a significant outcome that the receive power of confidential messages mainly concentrates on the small neighboring region around the desired receiver and only small fraction of its power leaks out to the remaining large broad regions. This concept is called secure precise transmission. The probability density function of real-time receive signal-to-interference-and-noise ratio (SINR) is derived. Also, the average SINR and its tight upper bound are attained. The approximate closed-form expression for average secrecy rate is derived by analyzing the first-null positions of SINR and clarifying the wiretap region.

I. INTRODUCTION

Directional modulation can leave eavesdroppers within the desired main beam able to intercept confidential messages because its beamforming depends on angle, not distance. The paper proposes RSCS-OFDM-DM to address this vulnerability and the circuit cost of prior frequency-diverse designs, combining phase alignment, artificial-noise projection, and RSCS.

I. INTRODUCTION

  • Angle-only directional modulation can expose confidential messages to eavesdroppers moving within the desired main beam.Its beamforming depends on direction angle and is independent of distance.Source: §I · p. 1
  • Replacing RFDA with RSCS-OFDM-DM enables FFT/IFFT-based reception with one RF chain instead of N_T RF chains.The proposed structure targets the receiver complexity and circuit cost of medium- and large-scale systems.Source: §I · p. 2
  • The transmitter combines frequency-domain phase alignment with RSCS to synthesize signals constructively at the desired receiver and destructively at eavesdroppers, with AN further degrading eavesdropper performance.The beamforming and AN projection designs depend on the desired direction and distance.Source: §I · p. 2
  • The paper derives the receive-SINR probability density function and average SINR when AN and channel noise have approximately equal receive power.It also derives an approximate closed-form average secrecy-rate expression from the first-null position and wiretap region, reported to be valid for medium- and large-scale arrays and close to the exact expression at low and medium SNR.Source: §I · p. 2
  • Simulation and analysis show a high SINR peak near the desired position, with very little confidential-message power leaking into the much larger remaining regions.The paper attributes low SINR at eavesdropper positions to AN projection, RSCS, and transmitter phase alignment.Source: §I · p. 2

II. SYSTEM MODEL

The system uses an OFDM-based RSCS array with directional modulation, phase alignment, and artificial-noise projection. Randomly assigned orthogonal subcarriers support coherent combination at the desired receiver while reducing the received signal sum at eavesdropper positions as the array grows.

II. SYSTEM MODEL

  • The proposed system has an N_T-element linear transmit array, a desired receiver, and single-antenna eavesdroppers at other positions.It combines OFDM, random-subcarrier selection, and directional modulation.Source: §II · p. 2
  • The same symbol is radiated from different antennas on randomly selected, mutually orthogonal OFDM subcarriers.The paper assumes NΔf ≪ f_c and defines total bandwidth as B = NΔf.Source: §II · p. 2
  • Block-level RSCS holds one selection pattern across several OFDM symbols, whereas symbol-level RSCS changes it every symbol.Symbol-level selection offers more security but raises receiver complexity and uncertainty in active-subcarrier testing; block size trades security against performance and detection probability.Source: §II · p. 3
  • The phase-alignment condition makes all N_T antenna signals with random orthogonal frequency shifts combine coherently at the desired receiver.The phase-alignment/beamforming vector is designed using the desired receiver's position.Source: §II · p. 5
  • Because random subcarrier selection makes the received phases independently identically distributed, the eavesdropper's summed signal tends to zero as N_T reaches medium or large scale.This asymptotic behavior applies to the received signal sum at an undesired position.Source: §II · p. 5

TRANSMISSION METHOD

RSCS, multiple transmit antennas, and phase alignment concentrate confidential-message power near the intended position, with weak leakage beyond that neighborhood. Adding artificial noise further improves transmission security.

TRANSMISSION METHOD

  • RSCS, multiple transmit antennas, and phase alignment direct confidential messages toward the desired direction and distance while limiting leakage beyond a small neighborhood.The scheme’s security is further improved by combining it with artificial noise.Source: TRANSMISSION METHOD · p. 5
  • Artificial-noise projection places noise in the eavesdropper steering space or desired steering-vector null space, with small or no leakage into the desired steering space.The confidential-message precoder instead directs most signal power into the desired steering space, with slight or no leakage into its null space.Source: TRANSMISSION METHOD · p. 6
  • The confidential-message precoder directs most signal power into the desired steering space, with slight or no leakage into its null space.This complements the artificial-noise projection, which targets eavesdropper space while limiting noise leakage into the desired space.Source: TRANSMISSION METHOD · p. 6

A. General beamforming and AN projection scheme

The general scheme combines random subcarrier selection, phase-aligned confidential signaling, and projected artificial noise. At the receiver, active subchannels are identified and summed, and the resulting signal components are used to define average SINR.

A. General beamforming and AN projection scheme

  • The transmit codeword uses a phase-alignment vector for coherent combining and a projected random AN vector, with β1 and β2 as power-allocation factors.The factors are stated to ensure total transmit power equals PS.Source: A. General beamforming and AN… · p. 6
  • The AN projection matrix is chosen to put as much noise as possible in the desired steering vectors’ null space while minimizing noise in the useful signal space.The passage notes that null-space projection and leakage are among the possible optimization rules.Source: A. General beamforming and AN… · p. 6
  • Average receive SINR is defined using the useful confidential signal, artificial noise, and channel noise.The three components are described as zero-mean random variables.Source: A. General beamforming and AN… · p. 6
  • The receiver can identify the active subcarrier indices by energy detection and sum the corresponding active subchannels.The passage assumes a receiver capable of this identification.Source: A. General beamforming and AN… · pp. 6–7

B. Analysis of receive SINR performance in the case of phase alignment and null-space projection

With ideal desired-position information, the paper uses a phase-alignment beamformer and projects artificial noise onto the desired steering vector’s null space. It also states a practical optimization criterion that constrains eavesdropper SINR.

B. Analysis of receive SINR performance in the case of phase alignment and null-space projection

  • When the ideal desired direction and distance are available, a simple beamforming form is used to obtain maximum coherent combining at the desired receiver.The beamforming vector is defined using the desired-position steering vector.Source: B. Analysis of receive SINR… · p. 7
  • The artificial-noise projection matrix projects AN onto the null space of the desired steering vector.At the desired position, this projection is perpendicular to the desired steering vector.Source: B. Analysis of receive SINR… · p. 7
  • The constant-envelope phase-alignment beamformer is used to derive the average SINR.The passage states that all beamformer elements have the same magnitude.Source: B. Analysis of receive SINR… · p. 7
  • In a practical system, desired-position SINR is maximized subject to eavesdropper-position SINR staying below a predefined value such as 0 dB.Source: B. Analysis of receive SINR… · p. 7

C. Analysis of average secrecy rate

The average secrecy rate is expressed as the desired-user rate minus the maximum eavesdropper rate within the wiretap region. The paper gives an approximation using phase-alignment precoding and null-space AN projection, and notes that power allocation can reduce eavesdropper SINR.

C. Analysis of average secrecy rate

  • The secrecy-rate definition subtracts the maximum eavesdropper rate in the wiretap region from the desired-user rate.The wiretap region is bounded using first-null offsets around the desired receiver; its complement is the desired region.Source: C. Analysis of average secrecy rate · p. 7
  • Adjusting the power-allocation factors β1 and β2 can make eavesdropper SINR low enough to prevent correct detection of the message.Source: C. Analysis of average secrecy rate · pp. 7–8
  • Theorem 1 approximates average secrecy rate using the phase-alignment confidential-message precoder and AN null-space projection.Its two terms represent the desired-user rate and an upper bound on eavesdropper rate.Source: C. Analysis of average secrecy rate · p. 8

IV. SIMULATION RESULTS AND ANALYSIS

The simulations show that bandwidth and antenna count localize the useful SINR peak along distance and angle, respectively. Power allocation trades desired-user performance against eavesdropper suppression, while the derived secrecy-rate expression approximates simulated results.

IV. SIMULATION RESULTS AND ANALYSIS

  • Larger bandwidth narrows the useful SINR peak along distance but does not change its width along angle.The simulations compare bandwidths of 5, 20, and 100 MHz.Source: §IV · p. 8
  • Increasing the transmit-antenna count narrows the SINR peak along angle; large bandwidth and antenna arrays narrow it along both dimensions.The peak approaches a line perpendicular to the angle-distance plane at the desired position.Source: §IV · p. 8
  • More AN power degrades eavesdropper-region SINR, while more confidential-signal power improves desired-user SINR but lowers security.The power allocation should balance energy efficiency, security, and performance.Source: §IV · p. 8
  • The theoretical average secrecy-rate curve approaches the simulated curve as transmit-antenna count increases and closely matches it at low and medium SNR.The comparison covers 8, 32, and 128 transmit antennas.Source: §IV · p. 8
  • At low SNR, AN has a weaker influence because channel noise is large; at higher SNR, the secrecy-rate curve is concave in β1 and has an optimal power allocation.As SNR increases, the optimal β1 decreases, allowing more power for AN.Source: §IV · pp. 8–9

V. CONCLUSION

The conclusion presents RSCS-OFDM-DM as a low-complexity approach to secure precise transmission. It reports localized confidential power, low eavesdropper SINR, and an approximate secrecy-rate expression validated by simulation.

V. CONCLUSION

  • RSCS-OFDM-DM combines random subcarrier selection, phase alignment or beamforming, and null-space projection of AN.The scheme is proposed for secure precise transmission of confidential messages.Source: §V · p. 9
  • The scheme produces a high SINR peak near the desired position and low SINR across other regions, where AN-corrupted messages are not reliably intercepted.Confidential power mainly gathers near the desired position, with only a small fraction leaking to eavesdropper regions.Source: §V · p. 9
  • Increasing bandwidth and antenna count narrows the main peak along distance and angle, respectively.The conclusion links both increases to narrowing along both dimensions.Source: §V · p. 9
  • The derived approximate average secrecy-rate expression is supported by simulations, and the scheme is described as easier to implement than conventional RFDA.The conclusion also gives a tight upper bound for SINR in the wiretap region.Source: §V · p. 9

APPENDIX A APPROXIMATE DERIVATION OF MEAN OF SINR(θ, R) FOR

The appendix approximates sums of random variables as complex Gaussian, then uses distributional transformations to derive an SINR density and its mean.

APPENDIX A APPROXIMATE DERIVATION OF MEAN OF SINR(θ, R) FOR

  • The three SINR-related random variables are sums of NT terms and are approximated as complex Gaussian using the central limit theorem.Their means are stated to be zero.Source: Appendix A · p. 9
  • The derivation introduces transformed variables with chi-squared distributions having two degrees of freedom.The appendix then approximates a weighted sum of two such variables as a chi-squared distribution with four degrees of freedom.Source: Appendix A · p. 9
  • A transformed SINR variable is assigned a PDF using the F-distribution, supporting the subsequent SINR-density derivation.The appendix states that the derivation completes the proof of the SINR PDF and its mean.Source: Appendix A · p. 10
  • The appendix obtains average SINR by integrating the derived SINR density.The displayed formula is presented as the expectation of SINR.Source: Appendix A · p. 10

APPENDIX B TIGHT UPPER BOUND OF SINR(θE, RE)

The appendix bounds eavesdropper-region SINR by locating first nulls and bounding the sidelobe parameter. It defines the wiretap region outside the desired-position main peak.

APPENDIX B TIGHT UPPER BOUND OF SINR(θE, RE)

  • The wiretap region is defined as all locations outside the SINR main peak around the desired position, where λ is below one.At the desired position, λ equals one.Source: Appendix B · p. 10
  • The first nulls along angle and distance mark positions where λ equals zero and SINR reaches its lowest value.The appendix determines null points for both dimensions to clarify the wiretap region.Source: Appendix B · p. 10
  • The maximum sidelobe value occurs between the first and second nulls, with λ reaching λmax at the sidelobe peak.The appendix considers maxima along both phase and distance dimensions.Source: Appendix B · pp. 10–11
  • The eavesdropper-region SINR is bounded above by the larger of its values at the two first-sidelobe maxima.The appendix identifies this as a tight upper bound.Source: Appendix B · pp. 10–11
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