This work investigates the effect of channel estimation error on the average secrecy outage capacity of dual selection in the presence of multiple eavesdroppers. The dual selection selects a transmit antenna of Alice and Bob (i.e., user terminal) which provide the best received signal to noise ratio (SNR) using channel state information from every user terminals. Using Gaussian approximation, this paper obtains the tight analytical expression of the dual selection for the average secrecy outage capacity over channel estimation error and multiple eavesdroppers. Using asymptotic analysis, this work quantifies the high SNR power offset and the high SNR slope for the average secrecy outage capacity at high SNR.

In this paper, we explore the physical layer security of an Internet of Things (IoT) network comprised of multiple relay-user pairs in the presence of multiple malicious eavesdroppers and channel estimation error (CEE). In order to guarantee secure transmission with channel estimation error, we propose a channel estimation error oriented joint relay-user pair and friendly jammer selection (CEE-JRUPaFJS) scheme to improve the physical layer security of IoT networks. For the purpose of comparison, the channel estimation error oriented traditional round-robin (CEE-TRR) scheme and the channel estimation error oriented traditional pure relay-user pair selection (CEE-TPRUPS) scheme are considered as benchmark schemes. The exact closed-form expressions of outage probability (OP) and intercept probability (IP) for the CEE-TRR and CEE-TPRUPS schemes as well as the CEE-JRUPaFJS scheme are derived over Rayleigh fading channels, which are employed to characterize network reliability and security, respectively. Moreover, the security-reliability tradeoff (SRT) is analyzed as a metric to evaluate the tradeoff performance of CEE-JRUPaFJS scheme. It is verified that the proposed CEE-JRUPaFJS scheme is superior to both the CEE-TRR and CEE-TPRUPS schemes in terms of SRT, which demonstrates our proposed CEE-JRUPaFJS scheme are capable of improving the security and reliability performance of IoT networks in the face of multiple eavesdroppers. Moreover, as the number of relay-user pairs increases, CEE-TPRUPS and CEE-JRUPaFJS schemes offer significant increases in SRT. Conversely, with an increasing number of eavesdroppers, the SRT of all these three schemes become worse.

This paper analyzes the performance of single-cell massive multiple-input multiple-output (MIMO) systems with non-orthogonal pilots. Specifically, closed-form expressions of the normalized channel estimation error and achievable uplink capacity are derived for both least squares (LS) and minimum mean square error (MMSE) estimation. Then a pilot reconstruction scheme based on orthogonal Procrustes principle (OPP) is provided to reduce the total normalized mean square error (NMSE) of channel estimations. With these reconstructed pilots, a two-step pilot assignment method is formulated by considering the correlation coefficient among pilots to reduce the maximum NMSE. Based on this assignment method, a step-by-step pilot power allocation scheme is further proposed to improve the average uplink signal-to-interference and noise ratio (SINR). At last, simulation results demonstrate the superiority of the proposed approaches.

In this paper, we analyze the impact of channel estimation errors in an amplify-and-forward (AF)-based two-way relaying network (TWRN) where adaptive modulation (AM) is employed in individual relaying path. In particular, the performance degradation caused by channel estimation error is investigated over Nakagami-m fading channels. We first derive an end-to-end signal-to-noise ratio (SNR), a cumulative distribution function, and a probability density function in the presence of channel estimation error for the AF-based TWRN with adaptive modulation (TWRN-AM). By utilizing the derived SNR statistics, we present accurate expressions of the average spectral efficiency and bit error rates with an outage-constraint in which transmission does not take place during outage events of bidirectional communications. Based on our derived analytical results, an optimal power allocation scheme for TWRN-AM is proposed to improve the average spectral efficiency by minimizing system outages.

In this paper, we investigate the capacity performance of an in-band full-duplex (IBFD) amplify-and-forward two-way relay system under the effect of residual loop-back-interference (LBI). In a two-way IBFD relay system, two IBFD nodes exchange data with each other via an IBFD relay. Both two-way relaying and IBFD one-way relaying could double the spectrum efficiency theoretically. However, due to imperfect channel estimation, the performance of two-way relaying is degraded by self-interference at the receiver. Moreover, the performance of the IBFD relaying is deteriorated by LBI between the transmit antenna and the receive antenna of the node. Different from the IBFD one-way relay scenario, the IBFD two-way relay system will suffer from an extra level of LBI at the destination receiver. We derive accurate approximations of the average end-to-end capacities for both the IBFD and half-duplex modes. We evaluate the impact of the LBI and channel estimation errors on system performance. Monte Carlo simulations verify the validity of analytical results. It can be shown that with certain signal-to-noise ratio values and effective interference cancellation techniques, the IBFD transmission is preferable in terms of capacity. The IBFD two-way relaying is an attractive technique for practical applications.

In this paper, we consider a two-hop communication system with an amplify-and-forward (AF) relay under channel estimation errors. According to the channel quality of the link between the base station (BS) and the relay, we investigate two typical relay scenarios. We study the capacity performance for both In-Band Full-Duplex (IBFD) and Half-Duplex (HD) transmission modes. Moreover, we consider two operation modes of the user equipment (UE) for each scenario. Closed-form expressions of ergodic capacities with channel estimation errors are obtained for scenario-1. And we derive accurate approximations of ergodic capacities for scenario-2. Numerical experiments are conducted to verify the analytical results and show that our theoretical derivations are perfectly matched with the simulations. We show that with practical signal-to-noise ratio values and effective interference cancellation techniques, IBFD transmission is preferable in terms of capacity.

This paper studies a novel iterative detection algorithm for data detection in orthogonal frequency division multiplexing systems in the presence of phase noise (PHN) and channel estimation errors. By simplifying the maximum a posteriori algorithm based on the theory of variational inference, an optimization problem over variational free energy is formulated. After that, the estimation of data, PHN and channel state information is obtained jointly and iteratively. The simulations indicate the validity of this algorithm and show a better performance compared with the traditional schemes.

In this letter, efficient closed-form formulas for the exact and asymptotic average bit error probability (ABEP) of space shift keying (SSK) systems are derived over Rayleigh fading channels with imperfect channel state information (CSI). Specifically, for a generic 2×NR multiple-input multiple-output (MIMO) system with the maximum likelihood (ML) detection, the impact of imperfect CSI is taken into consideration in terms of two types of channel estimation errors with the fixed variance and the variance as a function of the number of pilot symbols and signal-to-noise ratio (SNR). Then, the explicit evaluations of the bit error floor (BEF) and asymptotic SNR loss are carried out based on the derived asymptotic ABEP formula, which accounts for the impact of imperfect CSI on the SSK system. The numerical results are presented to validate the exactness of our theoretical analysis.

In this paper, we study the impact of imperfect channel information on an amplify-and-forward (AF)-based two-way relaying network (TWRN) with adaptive modulation which consists of two end-terminals and multiple relays. Specifically, we consider a single-relay selection scheme of the TWRN in the presence of outdated channel state information (CSI) and channel estimation errors. First, we choose the best relay based on outdated CSI, and perform adaptive modulation on both relaying paths with channel estimation errors. Then, we discuss the impact of the outdated CSI on the statistics of the signal-to-noise ratio (SNR) per hop. In addition, we formulate the end-to-end SNRs with channel estimation errors and offer statistic analyses in the presence of both the outdated CSI and channel estimation errors. Finally, we provide the performance analyses of the proposed TWRN with adaptive modulation in terms of average spectral efficiency, average bit error rate, and outage probability. Numerical examples are given to verify our obtained analytical results for various system conditions.

In this paper, we consider a two-way multi-relay scenario and analyze the bit error rate (BER) and outage performance of an amplify-and-forward (AF) relaying protocol. We first investigate the bit error probability by considering channel estimation error. With the derivation of effective signal-to-noise ratio (SNR) at the transceiver and its probability density function (PDF), we can obtain a closed form formulation of the total average error probability of two-way multi-relay system. Furthermore, we also derive exact expressions of the outage probability for two-way relay through the aid of a modified Bessel function. Finally, numerical experiments are performed to verify the analytical results and show that our theoretical derivations are exactly matched with simulations.

The Multiple-Input Multiple-Output (MIMO) Zero-Forcing (ZF) receiver requires accurate Channel State Information (CSI), which is impacted by channel estimation error, to perform properly. Moreover, interference occurs due to the change of channel coefficients between the channel estimation events in fading channels. Thus, in practice, both channel estimation error and interference greatly influence Bit Error Rate (BER) performance. In this letter, we derive an Signal-to-Interference-and-Noise Ratio (SINR) expression considering both channel estimation error and interference and develop approximate closed-form BER expressions of M-PSK and M-QAM for the MIMO ZF receiver in Nakagami-m fading channels. We then analyze the effects of channel estimation error, interference, and the numbers of transmit and receive antennas.

In this paper, we analyze the impact of channel estimation errors for both decode-and-forward (DF) and amplify-and-forward (AF) cooperative communication systems over Nakagami-m fading channels. Firstly, we derive the exact one-integral and the approximate expressions of the symbol error rate (SER) for DF and AF relay systems with different modulations. We also present expressions showing the limitations of SER under channel estimation errors. Secondly, in order to quantify the impact of channel estimation errors, the average signal-to-noise-ratio (SNR) gap ratio is investigated for the two types of cooperative communication systems. Numerical results confirm that our theoretical analysis for SER is very efficient and accurate. Comparison of the average SNR gap ratio shows that DF model is less susceptible to channel estimation errors than AF model.

In this paper, the outage probability and diversity order of opportunistic decode-and-forward (DF) cooperation are analyzed under Rayleigh fading channels, where the impacts of channel estimation error, relay selection feedback delay and the availability of the direct link between the source and the destination are considered comprehensively. The closed-form expressions of outage probability in the high signal-to-noise ratio (SNR) region are derived as well as the diversity order. The theoretical results demonstrate that the achievable diversity order is zero when channel estimation error exists, and this conclusion holds no matter whether the direct link is available, even if the relay selection feedback is delay-free. For the perfect channel estimation scenario, the achievable diversity order is related to the potential relay number K, the channel delay correlation coefficient ρd and the availability of the direct link. If relay selection feedback is not delayed, i.e., ρd = 1, the diversity order is K when the direct link is blocked, and it becomes K+1 when the direct link is available. For delayed relay selection feedback, i.e., ρd < 1, the diversity order achievable is only related to the availability of the direct link. In this case, if the direct link does not exist, the diversity order is 1, otherwise the diversity order of 2 can be obtained. Simulation results verify the analytical results of outage probability and diversity order.

An improved soft-input soft-output (SISO) minimum mean-squared error (MMSE) detection method is proposed for joint coding and precoding OFDM systems under imperfect channel estimation. Compared with the traditional mismatched detection which uses the channel estimate as its exact value, the signal model of the proposed detector is more accurate and the influence of channel estimation error (CEE) can be effectively mitigated. Simulations indicate that the proposed scheme can improve the bit error rate (BER) performance with fewer pilot symbols.

Space-time block codes (STBCs) from coordinate interleaved orthogonal designs (CIODs) have attracted a great deal of attention due to their full-diversity and linear maximum likelihood (ML) decodability. In this letter, we propose a simple detection technique, particularly for full-rate STBCs from CIODs to overcome the performance degradation caused by time-selective fading channels. Furthermore, we evaluate the effects of time-selective fading channels and imperfect channel estimation on STBCs from CIODs by using a newly-introduced index, the results of which demonstrate that full-rate STBCs from CIODs are more robust against time-selective fading channels than conventional full-rate STBCs.

Traditionally, it has been considered that the received signal to noise power ratio should be uniformly preserved to maximize system capacity for uncoded system with reliable feedback channel. However, once channel coding is employed as a building block, another power control scheme presents better performance. In this paper, we consider several power reallocation schemes for an effective use of limited power in a turbo coded system in lognormal shadowing channel. We show that the proposed power reallocation can reduce the decoding error probability by almost two orders of magnitude and provide a power gain of 0.87 dB at a target bit error rate of 10-4 over the equal power allocation among all code symbols. We also propose applying different power levels and cut-off thresholds on systematic and parity bits, and investigate the effect of channel estimation error.

We investigate the MIMO broadcast channels with imperfect channel knowledge due to estimation error and much more users than transmit antennas to exploit multiuser diversity. The channel estimation error causes the interference among users, resulting in the sum-rate loss. A tight upper bound of this sum-rate loss based on zeroforcing beamforming is derived theoretically. This bound only depends on the channel estimation quality and transmit antenna number, but not on the user number. Based on this upper bound, we show this system maintains full multiuser diversity, and always benefits from the increasing transmit power.

The minimum mean square error (MMSE) multiple antenna transmission scheme for a code division multiple access (CDMA) system was recently developed by Choi and Perreau [1]. In this paper, we first show that the zero-forcing (ZF) transmit beamformer for multiple antenna CDMA system has the same form as the MMSE beamformer given by Choi and Perreau. We then develop an analytical method to obtain a closed-form expression of the bit error rate (BER) of the ZF transmit beamformer when there are channel estimation errors. The analytical and simulation results show good agreement, and confirm the importance of accurate channel state information (CSI) at the transmitter when using the ZF transmit beamformer.

Spatial multiplexing (SM) offers a linear increase in transmission rate without bandwidth expansion or power increase. In SM systems, the LMMSE receiver establishes a good tradeoff between the complexity and performance. The performance of the LMMSE receiver would be degraded by MIMO channel estimation errors. This letter focus on obtaining the asymptotic convergence of output interference power and SIR performance for the LMMSE receiver with channel uncertainty. Exactly matched simulation results verify the validity of analysis in the large-system assumption. Furthermore, we find that the analytical results are also valid in the sense of average results for limited-scale system in spite of the asymptotic assumption used in derivation.

We propose reallocating the power resource among the code symbols in such a way to minimize the post decoding error probability of turbo code. We consider several power reallocation policies and investigate their performance in slowly-varying Rayleigh flat fading channel. We show that the proposed scheme can reduce the post decoding error probability by two orders of magnitude and provide a power gain of 0.86 dB at BER=10-6 over the traditional equal power allocation among all code symbols. We also propose applying different power levels and cut-off thresholds on systematic and parity check bits depending on the channel gain, and investigate the effect of channel gain estimation error.