Rate Splitting in the Presence of Untrusted Users: Outage and Secrecy Outage Performances

Abstract

In this contribution, a thorough investigation of the performance of rate splitting is conducted in terms of outage and secrecy outage for the simultaneous service to a near user and far user, where the latter attempts to overhear the message of the former. The source transmits a linear combination of the users' common stream and private streams. Once the common stream is retrieved, two decoding strategies can be adopted by each user. In the first strategy, the nodes (near or far) treat the far user's private stream as noise to retrieve the private stream of the near user, then the far user decodes its own stream. In the second strategy, the nodes decode the far user's private stream by treating the one of the near user as noise, then the near user retrieves its private stream while the far user decodes the stream of the near user in its attempt to overhear it. Considering the four decoding combinations, we obtain exact closed-form expressions for the outage probability, and provide tight approximations for the secrecy outage probability. Comparative results are also provided. In particular, it is shown that to achieve better outage probability, with no concern about secrecy, once the decoding of the common stream is completed, each user should first retrieve the private stream with lower target data rate by treating the other private stream as noise. To improve the secrecy outage probability, once the common stream is decoded, the near user must first decode the far user's private stream, and the far user should first retrieve the private stream with lower target data rate.

Outage Analysis of Millimeter Wave RSMA Systems

“…Subsequently, the analytical expressions for the SOP are derived respectively through the Gaussian-Chebyshev quadrature method. Nakagami-m OP [18] Transmitter Rayleigh ESR [19] Rayleigh OP [21] Nakagami-m SCP [22] Transmitter Rayleigh SOP [23] Transmitter DADC SOP [24] Transmitter DADC SOP [25] Transmitter & destination DADC SOP [26] Transmitter DADC SOP [28] Rayleigh OP and SOP [29] Transmitter Rayleigh OP and SOP [30] Transmitter Rayleigh ESR & ASR [32] Transmitter DADC OP Our Work…”

“…where P L (r i ) = r 0 r −α i , r 0 = 10 − β L 10 , β L = 32.4 + 20log 10 (f c ), f c = 28 GHz [29], r i is the distance between the transmitter and the receiver, α is the path 1 Although U 1 is fixed and U 2 is randomly distributed in our work, the results can be easily extended to the downlink mmWave RSMA system with two random users. Similar to [11], [12], [18], [25], the RSMA system with two users is considered in this work. As such, the results in this paper can serve as a benchmark for the performance of such systems.…”

“…δ1 , K is the summation items that reflect accuracy versus complexity, u v is the vth zero of Leguerre polynomials and q v is Gaussian weight, which are given in Table (25.9) of [37]. Based on (28) and utilizing (25.4.45), Ξ 3 is obtained as…”

“…Their results verified that the proposed beamform design frameworks could enhance spectral efficiency. The secrecy performance of two-user downlink systems with untrusted users was investigated and the closedform expressions for the OP and secrecy OP were derived in [18] and in [19]. The authors investigated the performance of a multi-cell RSMA network and derived the analytical expressions for sum rate and spectral efficiency based on stochastic geometry theory in [20].…”

The DoF Region of Order-(K - 1) Messages for the K-user MIMO Broadcast Channel with Delayed CSIT

“…The authors in [27] proposed a fullduplex cooperative rate-splitting (FD-CRS) scheme in a downlink two-group multicast system, in which the cell-center-receivers (CCUs) decode the multicast stream and their own private stream successively, then cooperatively form a distributed beamformer to assist the cell-edgereceivers (CEUs) in the multicast stream transmission. In the presence of untrusted receivers, the performance of rate-splitting considering outage probability and secrecy outage probability was analyzed in [28]. In [29], a RSMA-assisted downlink transmission framework for cell-free massive MIMO was proposed to ameliorate the effect of pilot contamination in the downlink and achieve a performance gain over a conventional cell-free massive MIMO network.…”