Abstract
In this paper, we investigate a robust joint precoder-decoder design scheme for a multiple-input multiple-output physical layer network coding (PNC)-based two-way relay system. An orthogonal training sequence is used to estimate the channels. The estimate is imperfect, and a robust design is proposed to find precoders at the source nodes and decoder at the relay node to facilitate PNC operations during multiple-access stage. Both channel estimation error and antenna correlations are used to formulate the optimization problem to minimize the weighted mean square error (WMSE) under a total power constraint. The problem becomes non-convex, and we propose an algorithm to solve it optimally. During the broadcast stage, an algorithm is proposed to find a precoder at the relay node and decoders at source nodes. The system performance is evaluated with estimation error and antenna correlation parameters. The effect of weighting parameters, relay location, and number of antennas at nodes are also considered in the numerical analysis. Numerical results confirm that our joint precoder-decoder algorithms provide the optimal solution to the minimization of WMSE with the total available power.
Highlights
Cooperative relay communication is introduced to improve the throughput, extend the coverage area, and reduce the energy consumption at the transmitter in wireless communication systems
Subject to Tr(FrFHr ) ≤ PT /2 (34). We can transform this problem into quadratically constrained quadratic programming (QCQP), which is given by the following: The proposed algorithm converges with a small number of iterations, and initial point does not have any effect on the final solution
In the low signal-to-noise ratio (SNR) region, the first design scheme gives a small variation in average BER (ABER) performance, whereas when SNR increases, the joint design has a significant performance improvement
Summary
Cooperative relay communication is introduced to improve the throughput, extend the coverage area, and reduce the energy consumption at the transmitter in wireless communication systems. The authors in [15-18] have used MIMO two-way relaying schemes and discussed the detection mechanisms and performances of such systems Most of these need complex processing at the relay to estimate the XOR of two received signal vectors. Their work is limited to a single antenna with expressions for bit error rate (BER) of BPSK scheme Another imperfect CSI model is discussed in [29-31] for a scenario where the channel parameters are estimated at the receiver and fed to the information to the transmitter and relay node. This can cause feedback delays, and the main concern is the difference between the actual CSI and the outdated CSI. A similar notation with mean vector and covariance matrix is valid when the variable is a vector
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