Abstract In this paper, we investigate the secrecy performance of multiple‐input–multiple‐output wiretap channels with outdated channel state information (CSI) at the transmitter. The joint effect of multiple jamming signals and noise at the eavesdropper is studied assuming that the transmitter adopts a transmit antenna selection technique, while both the legitimate receiver and the eavesdropper use a maximal‐ratio combining scheme to achieve spatial diversity in reception. Exact closed‐form expressions for the nonzero secrecy rate probability and the secrecy outage probability for an arbitrary number of power distributed jamming signals are derived, by assuming both perfect and imperfect CSI. The general secrecy outage probability expressions are simplified for 2 special cases, ie, different and equal power distributed interferers. Furthermore, we conduct an asymptotic secrecy outage analysis at high signal‐to‐noise ratio, which reveals that the expected diversity gain cannot be realized for imperfect CSI and full diversity order can only be achieved under the perfect CSI condition. In addition, our results reveal that the number of antennas at the eavesdropper as well as the number of jamming signals do not affect the system diversity order. Simulation results are performed to illustrate the effects of imperfect feedback and other key system parameters on the secrecy performance. Finally, our analytical results are validated through Monte Carlo simulations.
Abstract In this paper, we investigate the secrecy performance of multiple‐input–multiple‐output wiretap channels with outdated channel state information (CSI) at the transmitter. The joint effect of multiple jamming signals and noise at the eavesdropper is studied assuming that the transmitter adopts a transmit antenna selection technique, while both the legitimate receiver and the eavesdropper use a maximal‐ratio combining scheme to achieve spatial diversity in reception. Exact closed‐form expressions for the nonzero secrecy rate probability and the secrecy outage probability for an arbitrary number of power distributed jamming signals are derived, by assuming both perfect and imperfect CSI. The general secrecy outage probability expressions are simplified for 2 special cases, ie, different and equal power distributed interferers. Furthermore, we conduct an asymptotic secrecy outage analysis at high signal‐to‐noise ratio, which reveals that the expected diversity gain cannot be realized for imperfect CSI and full diversity order can only be achieved under the perfect CSI condition. In addition, our results reveal that the number of antennas at the eavesdropper as well as the number of jamming signals do not affect the system diversity order. Simulation results are performed to illustrate the effects of imperfect feedback and other key system parameters on the secrecy performance. Finally, our analytical results are validated through Monte Carlo simulations.
In this paper, the joint effect of multiple jamming signals and noise at the eavesdropper in wiretap channels is studied in terms of the secrecy outage probability, where all nodes are deployed with multiple antennas. Specifically, the transmitter employs a transmit antenna selection (TAS) technique; the legitimate receiver uses either a selection combining (SC) or a maximal-ratio combining (MRC) scheme; and the eavesdropper adopts the MRC technique. Exact closed-form expressions for the secrecy outage probability are derived for both SC and MRC schemes at the legitimate receiver, which are applicable for arbitrary number of power distributed jamming signals. An asymptotic secrecy outage analysis is conducted, which shows that the diversity gains for all combining schemes equal to the product of the number of antennas at the transmitter and the legitimate receiver. Representative numerical examples are presented to illustrate the effects of the key system parameters on the secrecy outage performance. Finally, the proposed analysis is validated through Monte Carlo simulation results.
In this paper, assuming an interference-limited eavesdropper scenario, the secrecy outage performance ofmultiple-input multiple-output wiretap channels with transmit antenna selection is investigated. Considering that the transmitter (Tx) and the receiver (Rx) are equipped with NA and NB antennas, respectively, while the passive eavesdropper is set with NE antennas, closed-form expressions for the secrecy outage probability and non-zerosecrecy rate are derived. In our analysis, both maximal-ratio combining (MRC) and selection combining (SC) are employed at the Rx, while the eavesdropper uses a MRC scheme. The derived outage expressions hold for arbitrary power distributed jamming signals and some of their special cases (i.e., distinct power distributed and equal power distributed jamming signals) are presented. An asymptotic analysis is carried out to show the impact of the number of jamming signals and number of antennas on the secrecy outage performance. Interestingly, our results show thatthe diversity order equals to min(M,NANB), with M denoting the number of jamming signals. This allows us to conclude that the number of jamming signals at the eavesdropper limits the secrecy performance via diversity such that a high number of antennas does not imply necessarily in a performance improvement, unless for a large number of jamming signals.
Multiple antennas at the transmitter enhance the diversity performance of multiple-input single-output (MISO) wiretap channels by selecting a single antenna that maximizes the instantaneous signal-to-noise ratio (SNR) at the intended receiver. However, the expected diversity performance may not be fully realized when channel state information (CSI) is outdated at the transmitter. Owing to this fact, in this letter we analyze the effects of outdated CSI on the secrecy outage performance of MISO wiretap channels with transmit antenna selection. More specifically, assuming Nakagami-m fading, a closed-form expression for the exact secrecy outage probability is derived, from which an asymptotic analysis is carried out. Our asymptotic results reveal that the expected diversity gain cannot be realized when CSI is outdated during the antenna selection process. The validity of our formulations is corroborated by Monte Carlo simulations.
In this paper, the secrecy outage performance of multiple-input single-output (MISO) wiretap channels with transmit antenna selection (TAS) at the transmitter (Tx) is investigated assuming that the eavesdropper is affected by multiple interferers M and noise. An exact closed-form expression for the secrecy outage probability is derived, and simplified for two special cases (i.e., distinct power distributed and equal power distributed jamming signals). Based on the attained results, an asymptotic secrecy analysis is carried out, which shows that the diversity order of the considered system equals to NA, with NA being the number of antennas at the Tx. Although previous works have shown that the diversity gain is impacted by both NA and M when an interference-limited eavesdropper scenario is considered, our results reveal that assuming multiple interferers and noise at the eavesdropper, the diversity gain equals to NA so that the number of jamming signals does not affect anymore the diversity gain. The proposed analysis is corroborated through Monte Carlo simulation results.
In this paper, assuming an interference-limited eavesdropper scenario, the secrecy outage performance of multiple-input multiple-output wiretap channels with transmit antenna selection is investigated.Considering that the transmitter (Tx) and the receiver (Rx) are equipped with NA and NB antennas, respectively, while the passive eavesdropper is set with NE antennas, closed-form expressions for the secrecy outage probability and non-zero secrecy rate are derived.In our analysis, a selection combining (SC) scheme is employed at the Rx, while the eavesdropper uses a maximal-ratio combining (MRC) one.The derived outage expressions hold for arbitrary power distributed jamming signals.An asymptotic analysis is carried out to show the impact of the number of jamming signals and number of antennas on the secrecy outage performance.Interestingly, our results show that the diversity order equals to min(M, NANB), with M denoting the number of jamming signals.
In this paper, we propose general-order transmit antenna selection to enhance the secrecy performance of multiple-input-multiple-output multieavesdropper channels with outdated channel state information (CSI) at the transmitter. To evaluate the effect of the outdated CSI on the secure transmission of the system, we investigate the secrecy performance for two practical scenarios, i.e., Scenarios I and II, where the eavesdropper's CSI is not available at the transmitter and is available at the transmitter, respectively. For Scenario I, we derive exact and asymptotic closed-form expressions for the secrecy outage probability in Nakagami-m fading channels. In addition, we also derive the probability of nonzero secrecy capacity and the ε-outage secrecy capacity, respectively. Simple asymptotic expressions for the secrecy outage probability reveal that the secrecy diversity order is reduced when the CSI is outdated at the transmitter, and it is independent of the number of antennas at each eavesdropper NE, the fading parameter of the eavesdropper's channel mE, and the number of eavesdroppers M. For Scenario II, we make a comprehensive analysis of the average secrecy capacity obtained by the system. Specifically, new closed-form expressions for the exact and asymptotic average secrecy capacity are derived, which are valid for general systems with an arbitrary number of antennas, number of eavesdroppers, and fading severity parameters. Resorting to these results, we also determine a high signal-to-noise ratio power offset to explicitly quantify the impact of the main channel and the eavesdropper's channel on the average secrecy capacity.