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We study the secret key rate (SKR) of a multiple-input multiple-output (MIMO) continuous variable quantum key distribution (CVQKD) system operating at terahertz (THz) frequencies, accounting for the effects of channel estimation. We propose a practical channel estimation scheme for the THz MIMO CVQKD system which is necessary to realize transmit-receive beamforming between Alice and Bob. We characterize the input-output relation between Alice and Bob during the key generation phase, by incorporating the effects of additional noise terms arising due to the channel estimation error and detector noise. Furthermore, we analyze the SKR of the system and study the effect of channel estimation error and overhead. Our simulation results reveal that the SKR may degrade significantly as compared to the SKR upper bound that assumes perfect channel state information, particularly at large transmission distances., Comment: Submitted to IEEE Transactions on Communications

A timing-based molecular communication (MC) system with a zero drift-force for the transmission of molecules via an aqueous channel is considered in this paper. The first arrival times of the molecules with a degradation period are modeled by truncated Levy distributions and for the cases of these propagation timings to be independent, uniformly, and exponentially correlated, the distance between the transmitter and the receiver and the diffusion coefficient of the aqueous medium are estimated using the maximum likelihood estimation technique. The Cramer-Rao Lower Bounds on the estimates of the system parameters are derived to obtain their normalized mean square errors, which show a predominant inverse dependency on the diffusion coefficient towards the estimation of the distance between the transmitter and the receiver. It is also observed that the estimation of the lower values of the diffusion coefficient is almost independent of the distance parameter. Further, the correlation of the propagation delays has a significant impact on the estimation of the system parameters for higher values of the diffusion coefficient.

A receive diversity power line communication (PLC) system subject to correlated multipath channel fading and corrupted by additive Nakagami- $m$ background noise is considered. The optimal receiver employing a 4-ary imbalanced-phase-amplitude modulation (I-PAM) scheme for data transmission is obtained, using which closed form expressions for the symbol error probability (SEP) in the union bound sense and the SEP in the asymptotic sense at high signal-to-noise ratio (SNR) are derived. The diversity order of the system is found to be independent of the shape parameter of the additive noise. Furthermore, the optimal 4-ary I-PAM constellation minimizing the SEP at lower SNR values is computed numerically. The optimal 4-ary I-PAM constellation is found to be elliptical in shape as opposed to the traditional circular QPSK constellation generally employed in wireless communication systems. The effects of the correlation among the multipath channel gains and the shape parameter of the noise on the optimality of the considered constellation are also presented via numerical studies.

The letter proposes a receive diversity PLC system subject to uncorrelated Rayleigh multipath channels and corrupted by Nakagami- $m$ background noise employing $M$ -ary phase-shift keying modulation for data transmission. The estimates of the channel gains are obtained prior to data transmission by the minimum mean square estimation technique utilizing pilot symbol transmission. A suboptimal receiver structure employing the maximum likelihood decision rule is proposed for the PLC system which is further used to obtain the closed form and the asymptotic expressions for the symbol error probability of the system via a characteristic function approach. The improvement of the system performance with the increase in the channel diversity, the effects of the pilot-to-signal strength ratio, and the noise shape parameter $m$ of the background noise on the system performance are studied via numerical results providing various insights into the design of the PLC system with various system parameters.

A single-input single-output visible light communication (VLC) system corrupted by additive white Gaussian noise is considered in this letter. Closed-form expressions for the symbol error probability (SEP) for the system with perfect knowledge of the channel, and with least square estimate of the channel at the receiver, are derived. The dependence of the SEP on the ratio of the vertical and horizontal distances between the transmitter and the receiver, the semi-angle of the LED transmitter, and on the powers of the transmitted data and pilot symbols provide various insights to the design of the VLC system for reliable communication.

This letter considers a single-input single-output powerline communication (PLC) system employing quadrature phase-shift keying (QPSK) modulation scheme under Rayleigh fading and Nakagami- $m$ noise environment. The series form expression of the symbol error probability (SEP) for the system is derived by considering the QPSK constellation as a combination of two orthogonal binary phase-shift keying constellations. Moreover, the optimal QPSK constellation minimizing the SEP under the constraint of given average transmission power is obtained. It is observed that the optimal solution of the QPSK constellation is elliptical in shape as compared to the traditional circular QPSK constellation. Further studies on the shape of the optimal elliptical QPSK constellation with varying shape parameter of the additive noise are carried out by numerical studies.

An $N$ -branch receive diversity power line communication (PLC) system subject to Rayleigh fading and corrupted by additive Nakagami- $m$ background noise is considered. A suboptimal maximal-ratio-combining (MRC), an optimal diversity combining, and a Gauss-optimal receiver are proposed for the PLC system. A closed form expression for the exact symbol error probability (SEP) and a union bound SEP expression are obtained for the proposed MRC and Gauss-optimal receivers, respectively, using a characteristic function (c.f.) approach for the system employing $M$ -ary phase-shift keying (MPSK) at the transmitter, conditioned to $mN$ being an integer. The asymptotic expression for the SEP obtained for the MRC receiver at high signal-to-noise (SNR) demonstrates that the diversity order of the system is independent of the shape parameter $m$ of the additive noise which is identical to the diversity order of the optimal and the Gauss-optimal receivers. Further, numerical studies justify the advantages of employing receive diversity to achieve superior SEP performance. The effect of increasing the diversity branches on the PLC system performance with varying $m$ and the power efficiency of the PLC system are also presented.

In this paper, we consider a hybrid smart grid communication network consisting of power line communication (PLC) at the transmitter side and the device-to-device (D2D) cellular communication on the receiver side which provides last mile connectivity. The PLC channel is assumed to experience Rayleigh fading and is corrupted by impulsive noise, and the D2D communication being a short range communication system, is assumed to experience Nakagami- $m$ fading with additive Gaussian noise. We propose a maximal-ratio combining (MRC) receiver for the considered hybrid smart grid communication system employing binary phase shift keying (BPSK) modulation at the transmitter and derive a closed-form symbol error probability (SEP) expression for the proposed receiver. The interference between the D2D links is assumed to be negligible for the tractability of the error probability analysis. Numerical results demonstrate the optimality of operating the D2D links at lower signal-to-noise ratio (SNR) values to overcome the effect of the impulsive PLC channel by utilizing diversity branches.

A noncoherent diversity detection power line communication (PLC) system employing multi-level amplitude-shift keying (ASK) modulation in the presence of Middleton Class-A impulsive noise is considered. Hermite numerical integration technique is used iteratively to obtain the statistics of the decision variable of an asymptotically optimal detector, which is utilized to derive series expressions for the symbol error probability (SEP). Numerical optimization of the ASK levels is done to achieve the minimum SEP, which results in the optimal solution being close to the equally spaced ASK constellation. The asymptotic optimality of the proposed detector is validated by the SEP variation with the impulsive index of the noise.

In a communication system employing coherent reception, pilot symbols are used for estimating the channel state information (CSI) at the receiver. The amount of training, which is quantified by the fractional pilot duration for a fixed-length pilot-plus-data frame, should be kept as low as possible for saving bandwidth and increasing data rate. However, reducing training leads to degraded error performance due to poor CSI estimate although it increases data rate, while increasing training improves error performance but reduces data rate. Expressing the tradeoff between symbol error probability (SEP) and data rate by the normalized error-free data rate, we present an analytical framework for its maximization with respect to pilot symbol duration fraction in a pilot-aided single-input multiple-output wireless communication system with reception over independent and identically distributed flat Rayleigh fading diversity branches, employing $M$ -ary phase-shift keying, and using maximal-ratio combining. Closed-form expressions for the approximate optimal pilot symbol duration fraction are derived for the high signal-to-noise ratio (SNR) case. Numerical results are presented to highlight the system behavior with changes in parameters like SNR, pilot symbol quality, and number of receive diversity branches. It is found that the optimization maximizes normalized error-free data rate with close to minimum SEP.

A noncoherent quadratic diversity reception system for multilevel amplitude-shift keying (ASK) signals in Rayleigh fading with different cases of the channel covariance matrix is considered. These include the important case of distributed antennas, which exhibit uncorrelated fading with distinct mean-squared channel gains (uncorrelated nonidentical fading) and weighted energy detectors, and the cases of exponentially correlated and uniformly correlated channels with equal mean-squared channel gains. For these cases, closed-form expressions for the symbol error probability (SEP) of the system are derived using the decision statistics obtained from the maximum likelihood receiver. The problem of determining the optimal amplitude levels that minimize the SEP under a total signal energy constraint is formulated and solved analytically for the high signal-to-noise ratio (SNR) configuration and numerically for the general configuration. For the high SNR configuration, it is shown that the optimal ASK levels should follow an approximately geometric progression. It is also observed that an equally spaced ASK constellation is not optimal in terms of achieving the minimum SEP. Numerical results are presented to highlight performance trends for channel gain imbalance and correlation.