Bound Of Pairwise Error Probability Research Articles

An Efficient SCMA Codebook Design Based on 1-D Searching Algorithm

This letter proposes an efficient sparse code multiple access (SCMA) codebook design, in which 1-D searching algorithm is introduced to minimize the upper bound of pair-wise error probability (PEP). Firstly, an SCMA signal model is given according to superposition modulation. Our analysis shows that under the proposed amplitude and phase rotation settings, each user has the same mutual information lower bound. In addition, the superimposed constellation points on each sub-channel belong to the same set, which depends on only one amplitude variable. Therefore, 1-D searching on this variable is introduced and the performance metric is upper bound of PEP. It is demonstrated that the calculated upper bound can well predict the receiver performance with maximum likelihood detection. In addition, the performance of the proposed codebook is verified with message passing algorithm at the receiver. The simulation results show that the PEP and bit error rate of the proposed codebook is better than that of the existing codebooks.

A Worst-Case Robust Combination Method of Beam-Forming and Orthogonal Space–Time Block Coding

In this paper, a new robust multi-input multi-output system is proposed in a perturbed wireless channel which is to model imperfect channel information at the source side when beam-forming and orthogonal space–time block coding is utilized. The channel perturbation is bounded by a predefined variation based on worst-case robust design. Beam-forming is used to improve the performance of the system expressed by the upper bound of pairwise error probability of symbols. In this paper firstly, the maximum value of pairwise error probability is obtained in a closed form when channel perturbation is kept below a threshold. Then the beam-forming matrix is designed to minimize the pairwise error probability subject to a predefined maximum transmitting power. This approach provides near optimal results due to using the upper bound of pairwise error probability. It shows good performance based on the symbol error rate criterion compared with other existing methods of the multiple input multiple output system.

Distributed Concatenated Recursive Alamouti-Circulant STBC for Two-Way Multi-Relay Networks

A general distributed multi-antenna two-way relaying network with multiple relays is considered in this paper. We first obtain a tight lower bound of pairwise error probability (PEP) of a maximum likelihood detector for the general distributed linear dispersion code for a half-duplex amplify-and-forward two-way relaying network (TWRN) consisting of two sources with each having single antenna and $N$ relays with each having two antennas. Furthermore, by jointly considering signal precoding at the sources and signal processing at the relays, a general distributed concatenated recursive Alamouti-circulant space-time block code is proposed for the considered TWRNs. Our design ensures that the equivalent channel matrices at both source nodes are the so-called the recursive Alamouti-circulant matrices, with each block being a product of the two Alamouti channel matrices. Based on a lower–upper bound strategy and an induction method, asymptotic PEP formula is attained to show that given the optimal angle rotation matrix and the precoding matrix, the code can meet the lower bound of the diversity gain, as well as the maximum coding gain. In addition, the proposed rate one code turns to be effectively decodable.

A Maximum Likelihood Combining Algorithm for Spatial Multiplexing MIMO Amplify-and-Forward Relaying Systems

Using a spatial multiplexing transmission scheme can improve the data rate in multiple-input–multiple-output (MIMO) relaying systems, while making signal detection more difficult at receivers. Aiming at lowering the computational complexity of the receiver, this paper proposes a maximum likelihood combining (MLC) algorithm for spatial multiplexing MIMO amplify-and-forward (AF) relaying systems in a Rayleigh flat-fading environment, which is implemented before maximum likelihood (ML) detection. The combining signal and equivalent channel are opportunely designed based on the ML rule in the MLC algorithm. We also formulate the diversity gain of the systems that employ the MLC algorithm mathematically, induced by the Chernoff bound of pairwise error probability (PEP). An upper bound on the symbol error probability (SEP) for the MLC algorithm with multiple modulations is also given, based on the derived bound of PEP. Moreover, the complexities of ML receivers adopting the MLC algorithm and the conventional vector combining (VC) algorithm are analyzed. Numerical simulations indicate that systems with the MLC algorithm achieve the same performance while consuming lower computational complexity compared to that with the VC algorithm.

Criterions of designing codebooks and a relay selection scheme for a relay network

SummaryFor a relay network system with amplify and forward protocol, in this paper, analysis of performance is conducted, and an upper bound of pairwise error probability is obtained. Moreover, a scheme of relay selection is analyzed under assumptions that (i) the relays amplify and forward received signals without any signal processing; (ii) the receiver only knows channel state information from the relays to the receiver; and (iii) the transmitter and the relays do not have any channel state information. Based on the upper bound, a criterion of designing codebook is proposed. Surprisingly, this bound shows that increasing the number of relays can hardly improve performance. Furthermore, the error probability is decreasing with a speed of P−1, no matter how large the relay number is, where P is the total energy. Also, for the relay selection, the optimal selecting way is to select only one relay with the largest channel gain, which is very different from existing schemes. These results are all confirmed by simulations. Copyright © 2015 John Wiley & Sons, Ltd.

Novel Distributed Quasi-Orthogonal Space-Time Block Codes for Two-Way Two-Antenna Relay Networks

A half-duplex amplify-and-forward two-way relay network consisting of two single-antenna sources and N relays with each having two antennas is considered in this paper. For such a system, a tight lower bound of pairwise error probability (PEP) of a maximum likelihood (ML) detector for any distributed linear dispersion code with a fixed average amplifier is derived, revealing that diversity gain function cannot decay faster than ln <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sup> SNR/SNR <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2N</sup> , where rm SNR is signal to noise ratio. Particularly for the network having two relays, a novel distributed quasi-orthogonal space-time block code (QO-STBC) is proposed with two significant advantages. One is that the equivalent channel matrices at both source nodes turn out to be the block-circulant matrices, with each block being a product of the two Alamouti channel matrices. The other is that the equivalent noises at the both source nodes are Gaussian and white. Therefore, like QO-STBC for a multi-antennas system, the proposed code for the relay system still maintains low-decoding complexity for the ML detector. Asymptotic PEP formula is attained to show that the proposed code enables the optimal diversity gain function, i.e., meeting the lower bound of diversity gain, and the optimal coding gain. In addition, a near optimal power allocation that maximizes the received SNR of the worse link is presented and examined through comprehensive computer simulations for various kinds of asymmetric relay channels.