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Secrecy Performance of an Artificial Noise Aided Dual-Hop SWIPT MIMO-NOMA Network in Presence of Practical Impairments

Büşra Demirkol, Oğuz Kucur, Güneş Karabulut Kurt

arXiv:2610.03032v1eess.SP

TL;DR

The paper addresses the insufficiently characterized combination of SWIPT-based AF relaying, relay-generated AN, diversity processing, and practical impairments in secure NOMA. It analyzes a system combining these features and finds diversity and suitable AN allocation improve secrecy, while practical impairments produce high-SNR outage floors.

  • Problem

    The joint secrecy analysis of SWIPT-based AF relaying, relay-generated AN, OSTBC, RAS, MRC, and practical impairments remains insufficiently characterized.

    Source: A. Motivation and Contributions · p. 2

  • Method

    The system combines OSTBC, user-side RAS, eavesdropper-side MRC, and an energy-harvesting AF relay that allocates harvested energy to forwarding and AN.

    Source: A. Motivation and Contributions · p. 2, §V · p. 11

  • Results

    Transmit and receive diversity and properly allocated AN improve secrecy, while practical impairments produce non-zero high-SNR SOP floors.

    Source: §IV · p. 8, §V · p. 11

  • Takeaways & Limitations

    Under practical impairments, residual interference and channel uncertainty limit achievable secrecy performance despite the benefits of diversity and appropriate AN allocation.

    Source: §V · p. 11

Abstract

from arXiv · show

This paper investigates the secrecy performance of a cooperative non-orthogonal multiple access (NOMA) network under practical impairments. In the considered system, the source employs orthogonal space-time block coding (OSTBC) transmission, legitimate users adopt receive antenna selection (RAS), and the eavesdropper utilizes maximal-ratio combining (MRC) scheme. Moreover, an energy-constrained amplify-and-forward relay harvests energy from the received signal and allocates the harvested energy to information forwarding and artificial noise (AN) generation. To capture the realistic performance of a more practical transmission scenario, channel estimation errors (CEE), feedback delay (FBD), imperfect successive interference cancellation (SIC), and imperfect AN cancellation are taken into account. For this system, closed-form expressions for the legitimate-user signal-to-interference+noise ratios (SINR) cumulative distribution function (CDF) and the eavesdropper SINR probability density function (PDF) are derived, and a tractable analytical secrecy outage probability (SOP) expressions are obtained. In addition, the high-SNR secrecy behavior is characterized under ideal channel state information (CSI) conditions and practical impairments, revealing the achievable secrecy diversity order and the secrecy outage floor, respectively. Moreover, secrecy throughput and energy efficiency are analyzed based on the obtained SOP results. The numerical findings are in close agreement with the analytical results and further illustrate how the secrecy behavior of the proposed system is affected by key design parameters and practical impairments. The obtained results indicate that transmit and receive diversity and proper AN power allocation significantly improve the secrecy performance, whereas practical impairments lead to non-zero SOP floors in the high signal-to-noise ratio region.

I. INTRODUCTION

Dense IoT networks need spectrum- and energy-efficient access, while secure cooperative NOMA research has not fully examined the joint use of SWIPT relaying, diversity techniques, and practical impairments. This work analyzes that combination and characterizes its secrecy performance.

I. INTRODUCTION

  • Dense IoT connectivity and limited spectrum make conventional orthogonal access less efficient as active-device counts grow, motivating NOMA's shared-resource access.NOMA supports simultaneous access and spectral efficiency through superimposed messages, while practical ipSIC can degrade received signal quality.Source: §I · p. 1

A. Motivation and Contributions

  • The paper addresses the insufficiently characterized joint use of SWIPT-based AF relaying, relay-generated AN, OSTBC, RAS, MRC, and practical impairments in secrecy-oriented NOMA.The considered impairments include CEE, FBD, and ipSIC.Source: A. Motivation and Contributions · p. 2, §I · p. 2
  • The proposed system uses source OSTBC, user-side RAS, and EVE-side MRC, while an energy-constrained AF relay splits harvested energy between forwarding and AN generation.The relay-generated AN is intended to degrade the EVE link.Source: A. Motivation and Contributions · pp. 2–3
  • The analysis derives SINR models incorporating CEE, FBD, ipSIC, and imperfect AN cancellation, then obtains tractable SOP expressions for Nakagami-m fading.The SOP analysis accounts for OSTBC source-to-relay, RAS relay-to-user, and MRC relay-to-EVE links.Source: A. Motivation and Contributions · p. 3
  • Under ideal CSI, the high-SNR analysis identifies secrecy diversity order; with practical impairments, it finds a nonzero secrecy outage floor.The paper also characterizes secrecy throughput and SEE and verifies its analytical results numerically.Source: A. Motivation and Contributions · p. 3

II. SYSTEM MODEL

The system uses OSTBC at the source and a power-splitting AF relay to serve NOMA users and an eavesdropper. It models channel errors and delay, imperfect SIC, and residual AN at legitimate users.

II. SYSTEM MODEL

  • The source superimposes NOMA messages in an OSTBC block; users apply RAS and the eavesdropper applies MRC over the relay-assisted links.The model assumes direct source-to-terminal links are unavailable and communication proceeds through a single-antenna AF relay.Source: §II · p. 3
  • The channel model includes estimation error and feedback delay, with a correlation coefficient determined by Doppler frequency and delay; residual interference models imperfect SIC.The channel-error components are assumed independent and uncorrelated with available channel estimates.Source: §II · p. 4
  • The relay splits received power between information detection and energy harvesting, then allocates harvested power between AF forwarding and AN generation.The power-splitting fraction β goes to harvesting, while λ of harvested power is assigned to AN.Source: §II · p. 4
  • Legitimate-user signals include desired information, NOMA interference, residual AN, amplified relay noise, CEE/FBD impairments, and receiver noise.Users know the relay's AN sequence but are assumed to suppress it imperfectly, leaving a residual AN term.Source: §II · p. 4
  • The eavesdropper uses MRC without knowledge of the relay's AN sequence, and when decoding a user it retains interference from later-decoded NOMA messages.Messages decoded earlier in the adopted order are assumed perfectly canceled at the eavesdropper.Source: §II · p. 5

III. PERFORMANCE ANALYSIS

The performance analysis derives SOP from the instantaneous SINRs, then examines high-SNR secrecy behavior for ideal CSI and practical impairments. It also characterizes secrecy throughput and SEE.

III. PERFORMANCE ANALYSIS

  • The analysis first formulates an analytical SOP expression using the instantaneous SINRs of the legitimate user and eavesdropper.The secrecy capacity is the positive difference between main- and wiretap-channel capacities.Source: §III · p. 5
  • High-SNR analysis yields SOP and secrecy diversity order under ideal CSI, and a secrecy outage floor under practical impairments.The ideal and practical cases are treated separately.Source: §III · p. 5
  • The paper presents secrecy throughput and SEE based on the derived SOP expressions.These metrics follow the SOP and high-SNR analyses.Source: §III · p. 5

A. SOP Analysis

The SOP analysis expresses outage through the legitimate-user SINR CDF and eavesdropper SINR PDF. A Gaussian–Chebyshev quadrature approximation makes the resulting integral tractable.

A. SOP Analysis

  • Secrecy outage occurs when secrecy capacity falls below its target rate, expressed using the positive difference between legitimate-user and eavesdropper channel capacities.The SOP is recast in terms of the legitimate-user SINR CDF and eavesdropper SINR PDF.Source: A. SOP Analysis · p. 5
  • The SOP derivation uses a closed-form legitimate-user SINR CDF and eavesdropper SINR PDF to evaluate the outage probability.The legitimate-user CDF is obtained from the distributions of the source-relay and relay-user channel terms.Source: A. SOP Analysis · p. 5
  • Gaussian–Chebyshev quadrature provides a tractable approximation because the integral-form SOP is not straightforward to solve in exact closed form.Increasing the quadrature-point count improves numerical accuracy at the cost of higher computational complexity.Source: A. SOP Analysis · p. 6

B. High-SNR Secrecy Performance Analysis

The high-SNR analysis makes the dominant secrecy behavior easier to interpret than the involved analytical SOP forms. It examines secrecy diversity under ideal CSI and the outage floor under practical impairments.

B. High-SNR Secrecy Performance Analysis

1) Asymptotic SOP under Ideal CSI Conditions:

With CEE and FBD removed but ipSIC and imperfect AN cancellation retained, the ideal-CSI analysis characterizes high-SNR SOP through its dominant scaling. The resulting secrecy diversity order is the minimum of the two stated diversity terms.

1) Asymptotic SOP under Ideal CSI Conditions:

  • The ideal-CSI case sets the CEE- and FBD-related parameters to zero while retaining ipSIC and imperfect AN cancellation.Source: 1) Asymptotic SOP under Ideal CSI… · p. 6
  • The asymptotic legitimate-user CDF is obtained from small-argument channel-gain behavior, with its dominant form depending on the relative values of M and Dl.The analysis uses the equivalent source-to-relay channel and the RAS channel gain with NOMA user ordering.Source: 1) Asymptotic SOP under Ideal CSI… · p. 7
  • As transmit SNR grows, the eavesdropper link affects only the SNR-independent coefficient of the asymptotic SOP.This follows under the stated assumption that the eavesdropper’s average SNR remains fixed.Source: 1) Asymptotic SOP under Ideal CSI… · p. 7
  • Gd,l = min {m1Ns, l m2Nl} gives the ideal-CSI secrecy diversity order.It is the minimum of the two diversity terms M and Dl.Source: 1) Asymptotic SOP under Ideal CSI… · p. 7

2) Secrecy Outage Floor under Practical Impairments:

With practical impairments, residual interference remains as noise becomes negligible at high SNR. The legitimate-user SINR then becomes SNR-independent, yielding a nonzero secrecy outage floor and zero diversity order.

2) Secrecy Outage Floor under Practical Impairments:

  • The limiting legitimate-user SINR is independent of transmit SNR because CEE- and FBD-related interference remains as noise becomes negligible.The limiting expression follows by dividing the SINR numerator and denominator by transmit SNR.Source: 2) Secrecy Outage Floor under… · p. 7
  • The SOP converges to a nonzero constant at high SNR under practical impairments, implying a secrecy outage floor and zero diversity order.Source: 2) Secrecy Outage Floor under… · p. 7

C. Secrecy Throughput Analysis

The section defines user secrecy throughput using the target secrecy rate and SOP, then gives an expression for overall throughput across the L-user system.

C. Secrecy Throughput Analysis

D. SEE Analysis

SEE measures secrecy throughput per unit of total system power, while numerical results show that AN allocation and diversity jointly shape secrecy outcomes. Across the tested configurations, increasing AN initially improves performance, but excessive allocation weakens information forwarding; practical impairments also produce high-SNR SOP floors.

D. SEE Analysis

  • SEE is achievable secrecy throughput divided by total consumed power, so increased transmit power can raise throughput in some regimes while its power cost limits SEE.Total consumed power comprises source transmit power and circuit power.Source: D. SEE Analysis · p. 8

IV. NUMERICAL RESULTS

  • For a target SOP of 10^-4, G3 gains 4.75, 5.52, and 5.13 dB over G2 for U1, U2, and U3, respectively; practical CSI produces high-SNR SOP floors.With m = 1 and Nl = 2, ideal-CSI diversity orders are 2 for all users with G2 and 2, 3, and 3 for U1, U2, and U3 with G3.Source: §IV · p. 8, Figure 2 · p. 8
  • At SOP = 10^-3, raising λ from 0 to 0.6 gains U2 5.10 dB for Nl = 1 and 6.68 dB for Nl = 2, with joint OSTBC, RAS, and AN giving the best secrecy performance.The benchmark (NS, Nl) = (1, 1) has the highest SOP; G2 and additional receive antennas each improve it.Source: §IV · p. 8
  • As NE grows, U2 SOP increases, but more legitimate receive antennas improve secrecy, and properly chosen λ makes the added EVE antenna less damaging.Excessive AN allocation reduces AF transmission power, so receive diversity and AN allocation must be considered jointly.Source: §IV · p. 9, Figure 5 · p. 9
  • Imperfect SIC degrades U2 and U3, with U3 more sensitive because it performs more SIC operations; increasing NS shifts SOP lower through transmit diversity.U1 does not perform SIC and is unaffected by ipSIC; degradation is especially evident at moderate and high SNR.Source: §IV · p. 9, Figure 6 · p. 10
  • SOP first falls and then rises with PS ratio β because low β limits harvested energy, whereas high β leaves less power for information processing.G3 has lower SOP than G2, and higher-order users attain their optimum secrecy performance at smaller β.Source: §IV · p. 10, Figure 8 · p. 10
  • Near the optimum λ, sum secrecy throughput and SEE improve with more source or legitimate-user antennas, while the effect of a third EVE antenna is limited.For both metrics, performance first rises and then falls with λ; the optimum λ values lie in a similar range.Source: §IV · p. 10, Figure 9 · p. 11, Figure 10 · p. 11

V. CONCLUSION

The paper analyzes an AN-aided cooperative SWIPT-NOMA system with OSTBC, RAS, and practical impairments. Its results show that diversity and suitable AN allocation improve secrecy, while practical impairments produce non-zero high-SNR SOP floors.

V. CONCLUSION

  • Transmit diversity from OSTBC and receive diversity from RAS improve secrecy, while more EVE antennas degrade it.Monte Carlo simulations closely agree with the analytical results; appropriate AN allocation improves secrecy by degrading the EVE link while retaining sufficient AF power.Source: §V · p. 11
  • Under practical impairments, SOP converges to non-zero high-SNR floors; under ideal CSI, it decreases as transmit SNR increases.Residual interference and channel uncertainty limit secrecy; ipSIC particularly degrades users performing SIC.Source: §V · p. 11
  • An appropriate AN power allocation can improve secrecy throughput and SEE and help alleviate performance loss from additional EVE antennas.The paper highlights jointly selecting the OSTBC structure, legitimate-user receive antennas, PS ratio, and AN power allocation while accounting for practical impairments and EVE combining.Source: §V · p. 11

APPENDIX A DERIVATION OF Fγl(x)

The appendices derive closed-form distributions for legitimate-user and eavesdropper SINRs, then use asymptotic CDF coefficients to form a tractable SOP representation.

APPENDIX A DERIVATION OF Fγl(x)

  • The legitimate-user SINR CDF is derived by combining the distributions of the source-to-relay gain and the ordered relay-to-user gain in the SINR expression.The source-to-relay gain is a sum of independent Gamma variables; the relay-to-user gain follows from antenna selection and NOMA user ordering.Source: Appendix A · pp. 11–12

APPENDIX B DERIVATION OF THE PDF OF γE,l

  • The eavesdropper SINR PDF is obtained by first deriving its CDF from the SINR expression and then differentiating that CDF.The eavesdropper channel gain is modeled as a sum of independent, identically distributed Gamma variables.Source: Appendix B · p. 12

APPENDIX C DERIVATION OF THE ASYMPTOTIC P ∞

This appendix provides coefficients for the asymptotic CDF across three cases and uses them to obtain a numerically tractable asymptotic SOP approximation.

APPENDIX C DERIVATION OF THE ASYMPTOTIC P ∞

  • The asymptotic CDF coefficients are specified separately for M < Dl, M > Dl, and M = Dl.The M = Dl case has a coefficient associated with a logarithmic term.Source: Appendix C · p. 13
  • The coefficients are used with Gaussian–Chebyshev quadrature to obtain a numerically tractable asymptotic SOP representation.The integration limit uses the fact that F∞γl(x) = 1 for x ≥ al/κ1.Source: Appendix C · p. 13
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