Closed-form Expression For Pairwise Error Probability Research Articles

Design and Analysis of Probabilistic Shaping Scheme for Uplink Nonorthogonal Multiple Access Systems

Probabilistic shaping (PS) combined with bipolar amplitude shift keying modulation is a promising transmission scheme to increase spectral efficiency. Different from the existing design of the point to point communications, we propose a PS-based uplink nonorthogonal multiple access (NOMA) scheme for fading channels to support multiple connections simultaneously, where successive interference cancellation (SIC)-based maximum a posterior (MAP) detection is implemented at the receiver. To exploit the shaping gain for each user, we first theoretically analyze the ergodic channel capacity and the constellation constrained (CC) capacity with discrete-constellation inputs, respectively. And then, a multi-step optimization scheme for maximizing the ergodic CC capacity is proposed to obtain the optimal probability mass function (PMF) of these input signals. The order of optimization is inverse to the SIC decoding order so that for each specific user, the remaining multiuser interference is calculated based on the optimal PMF of the later decoded users. Furthermore, based on this non-equiprobable transmission scheme, the closed-form pairwise error probability expressions for each user are obtained for the first time. Finally, compared with the uniform scheme, the simulations show that the proposed PS NOMA strategies achieve more than 1 dB gain in terms of the error performance.

PEP Analysis of AF Relay NOMA Systems Employing Order Statistics of Cascaded Channels

The precise error performance analysis is challenging for non-orthogonal multiple access (NOMA) systems due to nonlinear successive interference cancellation (SIC) processing among NOMA users. In this paper, the pairwise error probability (PEP) performance of different users is investigated for relay NOMA simultaneous wireless information and power transfer (SWIPT) systems. By employing the order statistics theory, we obtain the ordered probability density function of the cascaded channel through Source-to-Relay-to-User links. Then we derive the analytical closed-form PEP expressions for NOMA users. To obtain the approximate closed-form PEP, we explore the finite series representation of the power of the modified Bessel function to replace the integrand terms. Monte Carlo simulation results show that the approximate analytical PEP of each user is basically in agreement with the simulated PEP. Furthermore, on the basis of the closed-form PEP, the influence of relevant system parameters on the error performance is examined via numerical simulations, which manifests that the choice of power allocation coefficients should be balanced between the users’ channel conditions and the demanded quality of service.

An investigation of S-DF cooperative communication protocol over keyhole fading channel

This paper investigates the keyhole or pinhole effect on the pairwise error probability (PEP) performance of the multiple-input multiple-output (MIMO) space–time block-code (STBC) based selective decode and forward (S-DF) protocol. The closed form PEP expressions are derived for several configurations in terms of number of hops, phases, and relays over Nakagami-m fading channel, with perfect and imperfect channel state information (CSI), and with and without the keyhole condition. Further, a framework is developed for deriving the diversity order (DO) for each configuration. It demonstrates that full DO for cooperation protocol can be achieved when there is a knowledge of perfect CSI. A convex optimization framework is formulated for obtaining the optimal source–relay power allocation factors which significantly improve the end-to-end reliability of the system under power constraint scenarios. Monte Carlo simulations are performed for both equal and optimal power allocation factors and results show the substantial improvement in PEP performance with an increase in the value of the shape parameter and relay to destination (RD) link channel variance. Results show an improved PEP performance by increasing the RD link channel variance in comparison to increasing the source to relay (SR) link channel variance. Also PEP performance degrades for keyhole Nakagami-m fading channel as compared to Nakagami-m fading channel. Simulation results are in close agreement with the analytical results at high signal to noise ratio (SNR) regimes.

Performance of Full-Duplex AF Relaying in the Presence of Residual Self-Interference

This paper investigates the error and diversity performances of full-duplex (FD) amplify-and-forward (AF) singlerelay systems under the effect of residual self-interference. The variance of this interference is assumed to be proportional to the λ-th power of the transmitted power (0 ≤ λ ≤ 1). The study considers the cooperative linear relaying protocol with direct source-destination link and the dual-hop scheme without direct link, both under uncoded and coded frameworks. At first, closed-form pairwise error probability expressions are derived for the uncoded systems, which are then used to obtain tight bounds to the bit error rate (BER) of the coded systems. To shed an insight on the diversity behavior, asymptotic expressions at high transmission powers are also presented. Different from previous works that treat the direct link as interference, this paper shows that FD linear relaying systems with a suitable precoder can attain the same diversity function as their half-duplex (HD) counterparts. However, further analysis shows that HD orthogonal AF using a superposition constellation is asymptotically optimal in terms of maximum coding gain. In addition, it is shown that the diversity of FD dual-hop systems is a decreasing function of λ and is equal to zero when λ = 1. Although HD relaying is asymptotically optimal under the considered protocols and interference model, illustrative results show that FD relaying is advantageous at practical BER levels when λ is sufficiently small.

Performance Analysis of Differential Space–Time Modulation

In this paper, we analyze the performance of the differential space-time modulation (DSTM) in Rayleigh fading channels. By using the moment-generating function (MGF)-based approach, we derive a number of closed-form expressions for the pairwise error probability (PEP) of the DSTM in various fading environments. For spatially independent channels, we derive a closed-form expression for the exact PEP of the DSTM for both slow- and fast-fading cases. In the case of fast-fading channels, we show that an irreducible error floor exists in the PEP and in the block error rate of the DSTM, and derive a closed-form expression for the PEP error floor in terms of the fading rate. For spatially correlated channels, we derive a new closed-form expression for the PEP at asymptotically high signal-to-noise ratios and show that an existing asymptotic PEP expression derived by the residue method can also be obtained by using the MGF-based approach. Finally, we use computer simulations to verify the theoretical results.