Improper Gaussian signaling (IGS) has been recently shown to provide performance improvements in underlay cognitive radio systems as opposed to the conventional proper Gaussian signaling (PGS) scheme. For the first time, this paper implements IGS scheme in overlay cognitive radio system, where the secondary transmitter broadcasts a mixture of two different signals. The first signal is selected from the PGS scheme to support the primary message transmission. On the other hand, the second signal is chosen to be from the IGS scheme in order to reduce the interference effect on the primary receiver. We then optimally design the overlay cognitive radio that employs IGS to maximize the secondary link achievable rate while satisfying the minimum rate requirement of the primary network. In particular, we derive closed form expressions for the circularity coefficient used in the IGS scheme and the power distribution parameters. Simulation results are provided to support our theoretical derivations.

Improper Gaussian signaling (IGS) scheme has been recently shown to provide performance improvements in interference limited networks as opposed to the conventional proper Gaussian signaling (PGS) scheme. In this paper, we implement the IGS scheme in overlay cognitive radio system, where the secondary transmitter broadcasts a mixture of two different signals. The first signal is selected from the PGS scheme to match the primary message transmission. On the other hand, the second signal is chosen to be from the IGS scheme in order to reduce the interference effect on the primary receiver. We then optimally design the overlay cognitive radio to maximize the secondary link achievable rate while satisfying the primary network quality of service requirements. In particular, we consider full and partial channel knowledge scenarios and derive the feasibility conditions of operating the overlay cognitive radio systems. Moreover, we derive the superiority conditions of the IGS schemes over the PGS schemes supported with closed form expressions for the corresponding power distribution and the circularity coefficient and parameters. Simulation results are provided to support our theoretical derivations.

Sharing the spectrum with in-band full-duplex (FD) primary users (PUs) is a challenging and interesting problem in the underlay cognitive radio systems. The self-interference introduced at the primary network may dramatically impede the secondary user (SU) opportunity to access the spectrum. To tackle this problem, we use the so-called improper Gaussian signaling. Particularly, we assume the downlink transmission of a SU that uses improper Gaussian signaling while the FD PU pair implements the regular proper Gaussian signaling. First, we derive a closed-form expression and an upper bound for the SU and PUs outage probabilities, respectively. Second, we optimize the SU signal parameters to minimize its outage probability while maintaining the required PUs quality-of-service based on the average channel state information (CSI). Moreover, we provide the conditions to reap merits from employing improper Gaussian signaling at the SU. Third, we design the SU signal parameters based on the perfect knowledge of its direct link instantaneous CSI and investigate all benefits that can be achieved at both the SU and PUs. Finally, we provide some numerical results that demonstrate the advantages of using improper Gaussian signaling to access the spectrum of the FD PUs.

In this paper, we propose a new approach to proving results regarding channel coding schemes based on construction-A lattices for the Additive White Gaussian Noise (AWGN) channel that yields new characterizations of the code construction parameters, i.e., the primes and dimensions of the codes, as functions of the block-length. The approach we take introduces an averaging argument that explicitly involves the considered parameters. This averaging argument is applied to a generalized Loeliger ensemble [1] to provide a more practical proof of the existence of AWGN-good lattices, and to characterize suitable parameters for the lattice Gaussian coding scheme proposed by Ling and Belfiore [3].

Improper Gaussian signaling has the ability over proper (conventional) Gaussian signaling to improve the achievable rate of systems that suffer from interference. In this paper, we study the impact of using improper Gaussian signaling on the performance limits of the underlay cognitive radio system by analyzing the achievable outage probability of both the primary user (PU) and secondary user (SU). We derive the exact outage probability expression of the SU and construct upper and lower bounds of the PU outage probability which results in formulating an approximate expression of the PU outage probability. This allows us to design the SU signal by adjusting its transmitted power and the circularity coefficient to minimize the SU outage probability while maintaining a certain PU quality-of-service. Finally, we evaluate the derived expressions for both the SU and the PU and the corresponding adaptive algorithms by numerical results.

Sharing the spectrum with in-band full-duplex (FD) primary users (PU) is a challenging and interesting problem in the underlay cognitive radio (CR) systems. The self-interference introduced at the primary network may dramatically impede the secondary user (SU) opportunity to access the spectrum. In this work, we attempt to tackle this problem through the use of the so- called improper Gaussian signaling. Such a signaling technique has demonstrated its superiority in improving the overall performance in interference limited networks. Particularly, we assume a system with a SU pair working in half- duplex mode that uses improper Gaussian signaling while the FD PU pair implements the regular proper Gaussian signaling techniques. First, we derive a closed form expression for the SU outage probability and an upper bound for the PU outage probability. Then, we optimize the SU signal parameters to minimize its outage probability while maintaining the required PU quality-of- service based on the average channel state information. Finally, we provide some numerical results that validate the tightness of the PU outage probability bound and demonstrate the advantage of employing the improper Gaussian signaling to the SU in order to access the spectrum of the FD PU.

Improper Gaussian signaling has proved its ability to improve the achievable rate of the systems that suffer from interference compared with proper Gaussian signaling. In this paper, we first study impact of improper Gaussian signaling on the performance of the cognitive radio system by analyzing the outage probability of both the primary user (PU) and the secondary user (SU). We derive exact expression of the SU outage probability and upper and lower bounds for the PU outage probability. Then, we design the SU signal by adjusting its transmitted power and the circularity coefficient to minimize the SU outage probability while maintaining a certain PU quality-of-service. Finally, we evaluate the proposed bounds and adaptive algorithms by numerical results.

Sharing the licensed spectrum of full-duplex (FD) primary users (PU) brings strict limitations on the underlay cognitive radio operation. Particularly, the self interference may overwhelm the PU receiver and limit the opportunity of secondary users (SU) to access the spectrum. Improper Gaussian signaling (IGS) has demonstrated its superiority in improving the performance of interference channel systems. Throughout this paper, we assume a FD PU pair that uses proper Gaussian signaling (PGS), and a half-duplex SU pair that uses IGS. The objective is to maximize the SU instantaneous achievable rate while meeting the PU quality-of-service. To this end, we propose a simplified algorithm that optimizes the SU signal parameters, i.e, the transmit power and the circularity coefficient, which is a measure of the degree of impropriety of the SU signal, to achieve the design objective. Numerical results show the merits of adopting IGS compared with PGS for the SU especially with the existence of week PU direct channels and/or strong SU interference channels.

Due to their ability to provide high data rates, multiple-input multiple-output (MIMO) systems have become increasingly popular. Decoding of these systems with acceptable error performance is computationally very demanding. In this paper, we employ the Sequential Decoder using the Fano Algorithm for large MIMO systems. A parameter called the bias is varied to attain different performance-complexity trade-offs. Low values of the bias result in excellent performance but at the expense of high complexity and vice versa for higher bias values. Numerical results are done that show moderate bias values result in a decent performance-complexity trade-off. We also attempt to bound the error by bounding the bias, using the minimum distance of a lattice. The variations in complexity with SNR have an interesting trend that shows room for considerable improvement. Our work is compared against linear decoders (LDs) aided with Element-based Lattice Reduction (ELR) and Complex Lenstra-Lenstra-Lovasz (CLLL) reduction.

In this paper, the performance limits and the computational complexity of the lattice sequential decoder are analyzed for the unconstrained additive white Gaussian noise channel. The performance analysis available in the literature for such a channel has been studied only under the use of the minimum Euclidean distance decoder that is commonly referred to as the lattice decoder. Lattice decoders based on solutions to the NP-hard closest vector problem are very complex to implement, and the search for low complexity receivers for the detection of lattice codes is considered a challenging problem. However, the low computational complexity advantage that sequential decoding promises, makes it an alternative solution to the lattice decoder. In this work, we characterize the performance and complexity tradeoff via the error exponent and the decoding complexity, respectively, of such a decoder as a function of the decoding parameter - the bias term. For the above channel, we derive the cut-off volume-to-noise ratio that is required to achieve a good error performance with low decoding complexity.

There has been tremendous work done on designing space-time codes for the quasi-static multiple-input multiple-output (MIMO) channel. All the coding design to date focuses on either high- performance, high rates, low complexity encoding and decoding, or targeting a combination of these criteria. In this paper, we analyze in detail the performance of diagonal lattice space-time codes under lattice decoding. We present both upper and lower bounds on the average error probability. We derive a new closed form expression of the lower bound using the so-called sphere-packing bound. This bound presents the ultimate performance limit a diagonal lattice space-time code can achieve at any signal-to-noise ratio (SNR). The upper bound is simply derived using the union- bound and demonstrates how the average error probability can be minimized by maximizing the minimum product distance of the code.

In this paper, the performance limits and the computational complexity of the lattice sequential decoder are analyzed for the unconstrained additive white Gaussian noise channel. The performance analysis available in the literature for such a channel has been studied only under the use of the minimum Euclidean distance decoder that is commonly referred to as the lattice decoder. Lattice decoders based on solutions to the NP-hard closest vector problem are very complex to implement, and the search for low complexity receivers for the detection of lattice codes is considered a challenging problem. However, the low computational complexity advantage that sequential decoding promises, makes it an alternative solution to the lattice decoder. In this work, we characterize the performance and complexity tradeoff via the error exponent and the decoding complexity, respectively, of such a decoder as a function of the decoding parameter - the bias term. For the above channel, we derive the cut-off volume-to-noise ratio that is required to achieve a good error performance with low decoding complexity.

There has been tremendous work done on designing space-time codes for the quasi-static multiple-input multiple output (MIMO) channel. All the coding design up-to-date focuses on either high-performance, high rates, low complexity encoding and decoding, or targeting a combination of these criteria . In this paper, we analyze in details the performance limits of diagonal lattice space-time codes under lattice decoding. We present both lower and upper bounds on the average decoding error probability. We first derive a new closed-form expression for the lower bound using the so-called sphere lower bound. This bound presents the ultimate performance limit a diagonal lattice space-time code can achieve at any signal-to-noise ratio (SNR). The upper bound is then derived using the union-bound which demonstrates how the average error probability can be minimized by maximizing the minimum product distance of the code. Combining both the lower and the upper bounds on the average error probability yields a simple upper bound on the the minimum product distance that any (complex) lattice code can achieve. At high-SNR regime, we discuss the outage performance of such codes and provide the achievable diversity-multiplexing tradeoff under lattice decoding.

The optimal diversity-multiplexing-delay tradeoff for the multi- input multi-output (MIMO) automatic repeat request (ARQ) channel can be achieved using an incremental redundancy lattice space- time codes. The optimal tradeoff has been shown in to be achieved using a list lattice decoder for joint detection and decoding. However, such decoder suffers from high computational complexity for low-to-moderate signal-to-noise ratios, especially for large signal's dimension. In this paper, we would like to construct a more efficient decoder that is capable of achieving the optimal tradeoff with much lower complexity. We show, analytically and via simulation, that using a modified lattice sequential decoder for joint error detection and correction in the MIMO ARQ channel, the optimal tradeoff can be achieved with significant reduction in decoder complexity at a very small degradation in performance.

In this paper, the performance limit of lattice sequential decoder for coded $M\times N$ MIMO channel is analysed. We determine the rates achievable by lattice coding and sequential decoding applied to such channel. The diversity-multiplexing trade- off under lattice sequential decoding is derived as a function of its parameter---the bias term. Such parameter is critical for controlling the amount of computations required at the decoding stage. Achieving low decoding complexity requires increasing the value of the bias term. However, this is done at the expense of losing the optimal trade- off of the channel. We show how such decoder can bridge the gap between lattice decoder and low complexity decoders [e.g., minimum mean-square error successive interference cancellation (MMSE-SIC)]. We argue that, MMSE-SIC may achieve close to the maximum diversity gain of the channel $MN$ at very low multiplexing gain.

In this paper, the performance limits and computational complexity of lattice sequential decoder for coded MIMO channel are analyzed. It is shown that using nested lattice codes, the optimal diversity-multiplexing tradeoff of the channel can be achieved in the presence of such very low complexity decoder. We show that the computational complexity distribution, at high signal-to-noise ratio, is dominated by the outage probability.