On the error probability of quasi‐orthogonal space–time block codes

In this paper, we derive the exact pairwise error probabilities (PEPs) of various quasi‐orthogonal space–time block codes (QO‐STBCs) using the moment generating function. By classifying the exact PEPs of QO‐STBCs into three types, we derive the closed‐form expression for each type of PEP. Based on these closed‐form expressions, we obtain the union bounds on the symbol error probability and bit error probability for QPSK modulation. Through simulation, it is shown that these union bounds are quite tight. Copyright © 2008 John Wiley & Sons, Ltd.     

Outage performance of orthogonal space–time block code transmission in opportunistic decode‐and‐forward cooperative networks

Outage performance is analyzed for opportunistic decode‐and‐forward cooperative networks employing orthogonal space–time block codes. The closed‐form expressions of diversity order and the end‐to‐end outage probability at high signal‐to‐noise ratio regime are derived for arbitrary relay number (K) and antenna configuration (N antennas at the source and each relay, N_D antennas at the destination) under independent but not necessarily identical Rayleigh fading channels. The analysis is carried out in terms of the availability of the direct link between the source and the destination. It is demonstrated that the diversity order is min{N, N_D} ⋅ KN if the direct link is blocked, and if the direct link is available, the diversity order becomes min{N, N_D} ⋅ KN + NN_D. Simulation and numerical results verify the analysis well. Copyright © 2011 John Wiley & Sons, Ltd.     

Cognitive amplify‐and‐forward relay networks with beamforming under primary user power constraint over Nakagami‐m fading channels

In this paper, we analyze the performance of cognitive amplify‐and‐forward (AF) relay networks with beamforming under the peak interference power constraint of the primary user (PU). We focus on the scenario that beamforming is applied at the multi‐antenna secondary transmitter and receiver. Also, the secondary relay network operates in channel state information‐assisted AF mode, and the signals undergo independent Nakagami‐m fading. In particular, closed‐form expressions for the outage probability and symbol error rate (SER) of the considered network over Nakagami‐m fading are presented. More importantly, asymptotic closed‐form expressions for the outage probability and SER are derived. These tractable closed‐form expressions for the network performance readily enable us to evaluate and examine the impact of network parameters on the system performance. Specifically, the impact of the number of antennas, the fading severity parameters, the channel mean powers, and the peak interference power is addressed. The asymptotic analysis manifests that the peak interference power constraint imposed on the secondary relay network has no effect on the diversity gain. However, the coding gain is affected by the fading parameters of the links from the primary receiver to the secondary relay network. Copyright © 2012 John Wiley & Sons, Ltd.     

Joint sensing and transmission for cognitive amplify‐and‐forward two‐way relay networks

In this paper, we propose a cognitive transmission scheme for Amplify‐and‐Forward (AF) two‐way relay networks (TWRNs) and investigate its joint sensing and transmission performance. Specifically, we derive the overall false alarm probability, the overall detection probability, the outage probability of the cognitive TWRN over Rayleigh fading channels. Furthermore, based on these probabilities, the spectrum hole utilization efficiency of the cognitive TWRN is defined and evaluated. It is shown that smaller individual or overall false alarm probability can result in less outage probability and thus larger spectrum hole utilization efficiency for cognitive TWRN, and however produce more interference to the primary users. Interestingly, it is found that given data rate, more transmission power for the cognitive TWRN does not necessarily obtain higher spectrum hole utilization efficiency. Moreover, our results show that a maximum spectrum hole utilization efficiency can be achieved through an optimal allocation of the time slots between the spectrum sensing and data transmission phases. Finally, simulation results are provided to corroborate our proposed studies. Copyright © 2016 John Wiley & Sons, Ltd.     

MMSE‐based transceiver design for distributed MIMO amplify‐and‐forward cooperative networks in correlated channels

In this paper, the source‐precoder, multiple‐relay amplifying matrices, and destination‐equalizer joint optimization is investigated in distributed MIMO amplify‐and‐forward multiple‐relay networks with direct source–destination transmission in correlated fading channels. With the use of taking both the direct link and spatial correlation between antenna elements into account, the cooperative transceiver joint design is developed based on the minimum mean‐squared error criterion under individual power constraints at the source and multiple‐relay nodes. Simulation results demonstrate that the cooperative transceiver joint design architecture for an amplify‐and‐forward MIMO multiple‐relay system outperforms substantially the noncooperative transceiver design techniques on the BER performance under the spatial‐correlation channels.Copyright © 2012 John Wiley & Sons, Ltd.     

Outage performance of cognitive radio networks with multiple decode‐and‐forward relays

This paper considers the cognitive radio network with one primary user (PU), one secondary user (SU), and multiple decode‐and‐forward relays. We propose a relaying scheme to ensure the priority of primary transmission, where the relays are used to forward PU's message and sometimes also SU's message. First, SU is allowed to use the spectrum to transmit only when its transmission would not affect the decoding status of PU's message at all relays. Second, once the secondary transmission happens, the relays that successively decode SU's message are allowed to retransmit this message when it would not affect the decoding status of PU's message at primary receiver. The interference from PU to SU and the interference from SU to PU are both considered. By analyzing the decoding status of primary message and secondary message at different relays, we formulate the outage probabilities of both primary transmission and secondary transmission. When all channels follow Rayleigh distributions, we derive the analytical expressions for the general case of any number of relays, which are validated by means of Monte Carlo simulations. Copyright © 2016 John Wiley & Sons, Ltd.     

Evolution from symbol‐level space–time coded MIMO to chip‐level space–time coded MIMO: a review

Space–time coded multiple‐input multiple‐output (MIMO) technology is an important technique that improves the performance of wireless communication systems significantly without consuming bandwidth resource. This paper first discusses the characteristics and limitations of traditional symbol‐level space–time coding schemes, which work largely on the basis of an assumption that signals are sent to a block‐fading channel. Therefore, the symbol‐level space–time coding schemes rely on symbol‐level signal processing. Taking advantage of orthogonal complementary codes, we propose a novel MIMO scheme, in this paper, based on chip‐level space–time coding that is different from the traditional symbol‐level space–time coding. With the help of space–time–frequency complementary coding and multicarrier modem, the proposed scheme is able to achieve multipath interference‐free and multiuser interference‐free communications with simple a correlator detector. The proposed chip‐level space–time coded MIMO works well even in a fast fading channel in addition to its flexibility to achieve diversity and multiplexing gains simultaneously in varying channel environments. Copyright © 2012 John Wiley & Sons, Ltd.     

Decode‐and‐forward with partial relay selection

Exact expressions for outage probability and symbol error rate are presented for a decode‐and‐forward cooperative network with partial relay selection. An independent but not identically distributed Nakagami‐m fading environment is considered. Numerical and simulated results show the validity of the analytical results. Copyright © 2010 John Wiley & Sons, Ltd.     

Nearly optimal linear transceiver design for amplify‐and‐forward MIMO multiple‐relay systems under MMSE criterion

In this paper, we consider amplify‐and‐forward multiple‐input multiple‐output multiple‐relay systems, where all the nodes have multiple antennas. For enhancing link reliability, we address the problem of designing optimal linear transceiver to minimize the mean squared error (MSE) of symbol estimations subject to the total relay transmit power constraint. This problem is highly complex and has not been solved in the literature. We first simplify this optimization problem to one that takes a singular value vector and a unitary matrix as optimization variables. Then based on the analyses for the simplified problem, we develop an iterative algorithm consisting of one boundary optimization and one unitary matrix constrained optimization. We show analytically that the proposed iterative algorithm always converges, and the MSE is monotonically decreasing from one iteration to the next. Finally, numerical results demonstrate the nearly optimal performance of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Iterative receiver for amplify‐and‐forward relay networks with unknown noise correlation

For amplify‐and‐forward relay networks, we propose an iterative scheme to estimate channel and detect information symbols for the multi‐antenna destination in spatially correlated noise. The equivalent channel coefficients and noise covariance are estimated by expectation–maximization algorithm. In addition, we discuss the initialization of iteration and analyze the modified Cramér–Rao bound to show the performance of the proposed iterative estimation. Moreover, on the basis of the structure of the proposed iterative estimator, a joint channel estimation and detection receiver is also provided. Finally, simulation results show that the proposed channel estimator and receiver can achieve the optimal performances in amplify‐and‐forward relay networks with unknown noise correlation. Copyright © 2012 John Wiley & Sons, Ltd.     

Joint precoding and power allocation for multiuser transmission in MIMO relay networks

This paper proposes a joint precoding and power allocation strategy to maximize the sum rate of multiuser multiple‐input multiple‐output (MIMO) relay networks. A two‐hop relay link working on amplify‐and‐forward (AF) mode is considered. Precoding and power allocation are designed jointly at the base station (BS). It is assumed that there are no direct links between the BS and users. Under individual power constraints at the BS and relay station, precoders designed based on zero forcing, minimum mean‐square error and maximum ratio transmission are derived, respectively. Optimal power allocation strategies for these precoders are given separately. To demonstrate the performance of the proposed strategies, we simulate the uncoded bit error rate performance of the underlined system. We also show the difference of the sum rate of the system with the optimal power allocation strategies and with average power transmission. The simulation results show the advantages of the proposed joint precoding and power allocation strategies as expected. Copyright © 2011 John Wiley & Sons, Ltd.     

Physical‐layer network coding with limited feedback using orthogonal space–time block codes

This paper introduces limited feedback technique into physical‐layer network coding (PLNC) scheme, which is the most spectrally efficient protocol in two‐way relay channels, consisted of one relay and two end nodes (sources). Decode‐and‐forward (DF) and partial‐decode‐and‐forward (PDF) strategies are considered for PLNC, and all nodes are assumed to have two antennas to allow transmission by Alamouti's orthogonal space–time block code to provide diversity. In DF, by limited feedback, one of the sources is informed about instantaneous channel state information (CSI) to increase the bit error rate (BER) performance at relay. The closed‐form upper and lower bounds on the bit error probability are derived for binary phase‐shift keying (BPSK) and quadrature PSK (QPSK) modulations and approved via computer simulations. In PDF strategy, each source has to know CSI between relay and the other source for decoding, which causes extra protocol complexity. Moreover, for the system in which all nodes have two antennas, classical PDF strategy does not satisfy orthogonality at the end nodes. Therefore, in this paper, a modified‐PDF (MPDF) strategy with limited feedback is proposed. In MPDF, for decoding at the end nodes, differential phase information between channel fading coefficients having maximum amplitudes is fed back to the sources by relay. This approach enables single‐symbol decoding, besides full diversity, and sources do not need to know CSI between relay and the other source. It is shown via computer simulations that MPDF strategy provides significantly better BER performance than the classical PDF for BPSK and QPSK modulations.Copyright © 2012 John Wiley & Sons, Ltd.     

Performance analysis and power allocation for decode‐and‐forward cooperative communications over Rician fading channel

This paper derives the asymptotic symbol error rate (SER) and outage probability of decode‐and‐forward (DF) cooperative communications over Rician fading channels. How to optimally allocate the total power is also addressed when the performance metric in terms of SER or outage probability is taken into consideration. Analysis reveals the insights that Rician factor has a great impact on the system performance as compared with the channel variance, and the relay–destination channel quality is of importance. In addition, the source–relay channel condition is irrelevant to the optimal power allocation design. Simulation and numerical evaluation substantiate the tightness of the asymptotic expressions in the high‐SNR regions and demonstrate the accuracy of our theoretical analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

Differential space–time network coding in MIMO two‐way relay channel network

This paper focuses on noncoherent detection scheme for multiple‐input multiple‐output two‐way relay channel network with two two‐antennas source nodes and one single‐antenna relay node. An orthogonal differential space–time network coding (ODSTNC) scheme based on relay detection and forward protocol is proposed. The proposed scheme combines space–time coding with network coding, and the differential modulation and detection are used in both multiple access stage and broadcast stage. The multiple‐symbol differential detection is employed at the relay. The maximum likelihood decision and its low‐complexity sphere decoding decision are given. The upper and lower bounds on the average symbol error probability for this system under differential binary phase shift keying (DBPSK) are derived, and a diversity order of 2 is confirmed to be achieved. The simulation results show that the ODSTNC scheme has good performance, and it is available for the applications of far distance signal transmission between two terminals where channel state information is unknown. Copyright © 2014 John Wiley & Sons, Ltd.     

Exact SEP and performance bounds for orthogonal space‐time block codes in cooperative multiantenna AF relaying networks

In this paper, we derive a moment generating function (MGF) for dual‐hop (DH) amplify‐and‐forward (AF) relaying networks, in which all nodes have an arbitrary number of antennas, with orthogonal space‐time block code (OSTBC) transmissions over Rayleigh fading channels. We present an exact error rate expression based on the derived MGF and another analytical approach to derive achievable performance bounds as closed‐forms of symbol error rate, outage probability, and normalized channel capacity. Furthermore, we derive the asymptotic behavior of symbol error rate and outage probability. From this asymptotic behavior, it is shown that the diversity order and its dependence on antenna configurations can be explicitly determined. Simulation results are also presented to verify their accuracy by comparing with numerical results and to provide an insight to the relationship between relaying networks' antenna configuration and diversity order. It is confirmed that the transmit antenna gain of the source node and the receive antenna gain of the relay node can be obtained only when the relay is close to the destination, and then, the transmit antenna gain of the relay node and the receive antenna gain of the destination node can be obtained only when the relay is close to the source.     

On the performance of two‐way relay channels using space–time codes

In this paper, we explore the advantages of network coding and space–time coding in improving the performance of two‐way‐relayed communications where two terminals absent of direct links exchange information through a single relay in between. Network coding allows embracing the interference from other terminals thereby turning it into a capacity boost. The application of space–time codes yields higher capacity by exploiting the spatial diversity. The joint performance of both techniques is studied in this paper. Specifically, we consider the class of decode‐and‐forward (DF) relaying strategy, evaluated in terms of symbol error rate using BPSK and QPSK modulations by both theoretical analysis and simulation. Based on our results, DF outperforms the amplify‐and‐decode and partial‐decode‐and‐forward protocols. Copyright © 2011 John Wiley & Sons, Ltd.     

Interlevel‐correlated orthogonal space–time block codes based on the expanded signal constellation

Orthogonal space–time block codes provide full diversity with a very simple decoding scheme. However, they do not provide much coding gain. For a given space–time block code, we combine several component codes in conjunction with set partitioning of the expanded signal constellation according to the coding gain distance (CGD) criterion. By providing proper interlevel coding between adjacent blocks, we can design an orthogonal space–time block code with high rate, large coding gain, and low decoding complexity. The error performance of an example code is compared with some codes in computer simulation. These codes are compared based on the situation of the same transmission rate, space diversity order, and state complexity of decoding trellis. Copyright © 2010 John Wiley & Sons, Ltd.     

Secrecy sum rate optimization in MISO nonorthogonal multiple access systems with orthogonal space‐time block coding

In this paper, we investigate the secrecy sum rate optimization problem for a multiple‐input single‐output (MISO) nonorthogonal multiple access (NOMA) system with orthogonal space‐time block codes (OSTBC). This system consists of a transmitter, two users, and a potential eavesdropper. The transmitter sends information by orthogonal space‐time block codes. The transmitter's precoder and the power allocation scheme are designed to maximize achievable secrecy sum rate subject to the power constraint at the transmitter and the minimum transmission rate requirement of the weak user. We consider two cases of the eavesdropper's channel condition to obtain positive secrecy sum rate. The first case is the eavesdropper's equivalent channel is the weakest, and the other is the eavesdropper's equivalent channel between the strong user and weak user. For the former case, we employ the constrained concave convex procedure (CCCP)‐based iterative algorithm with one‐dimensional search. While for the latter, we adopt the method of alternating optimization (AO) between precoder and power allocation. We solve a semidefinite programming to optimize the precoder and drive a closed‐form expression of power allocation. The simulation results obtained by our method demonstrate the superiority of our proposed scheme.     

Peroformance analysis of decode-and-forward MIMO relay channels with OSTBCs

Performance analysis is presented for multiple-input multiple-output(MIMO) relay channels employing transmit antenna diversity with orthogonal space-time block codes(OSTBCs),where the source and the destination are equipped with Ns and Nd antennas,and communicate with each other with the help of a multiple-antenna relay operating in decode-and-forward(DF) mode.Over independent,not necessarily identical Rayleigh fading channels,exact closed-form symbol error rate(SER) expressions are derived for various digi...     

Outage performance of cognitive AF relay networks with direct link and heterogeneous non‐identical constraints

Although there have been many interesting works on outage performance analysis of cognitive AF relay networks, we have not found works taking into consideration all the following issues: multiple primary users (PUs), the existence of the direct link from secondary user (SU) source to SU destination, non‐identical, independent Rayleigh‐fading channels, non‐identical interference power limits of PUs, and non‐identical noise powers in signals. Additionally, in outage performance analysis for such networks, the correlation issue, which results from the channel gain of interference links from the SU nodes to the PU, requires elaborate treatments. Hence, analyzing outage performance of non‐identical‐parameter networks (where all channels are fully non‐identical Rayleigh‐fading channels, the PUs have different interference power limits, and received signals have different noise powers) from the beginning is highly complicated. To overcome this problem, we conduct the analysis in two steps. In the first step, expressions of both exact and asymptotic outage probability of identical‐parameter cognitive AF relay networks (where all channels are fully non‐identical Rayleigh‐fading channels but all other parameters are identical) are obtained. Then in the second step, we propose a method for transforming a network with all non‐identical parameters into a new identical‐parameter network, meanwhile guaranteeing that outage performance of the two networks before and after the transformation are the same. Hence, OP of the original non‐identical‐parameter network can be obtained indirectly by using the analysis results obtained in the first step. Our analysis results are validated through numerical simulations. The effects of the number of PUs and the diversity level of channel parameters (which means the range of the channel parameter values) are also inspected by simulations. The results show that taking these factors into consideration is of key importance in obtaining a more accurate estimation of outage performance of such networks. Copyright © 2014 John Wiley & Sons, Ltd.