Sanjeewa P. Herath

Energy Detection of Unknown Signals in Fading and Diversity Reception

A comprehensive performance analysis of the energy detector over fading channels with single antenna reception or with antenna diversity reception is developed. For the no-diversity case and for the maximal ratio combining (MRC) diversity case, with either Nakagami-m or Rician fading, expressions for the probability of detection are derived by using the moment generating function (MGF) method and probability density function (PDF) method. The former, which avoids some difficulties of the latter, uses a contour integral representation of the Marcum-Q function. For the equal gain combining (EGC) diversity case, with Nakagami-m fading, expressions for the probability of detection are derived for the cases L =2,3,4 and L >; 4, where L is the number of diversity branches. For the selection combining (SC) diversity, with Nakagami-m fading, expressions for the probability of detection are derived for the cases L =2 and L >; 2. A discussion on the comparison between MGF and PDF methods is presented. We also derive several series truncation error bounds that allow series termination with a finite number of terms for a given figure of accuracy. These results help quantify and understand the achievable improvement in the energy detectors performance with diversity reception. Numerical and simulation results are also provided.

Analysis of Equal Gain Combining in Energy Detection for Cognitive Radio over Nakagami Channels

This paper addresses the problem of energy detection of unknown deterministic signal of a primary user in a cognitive radio environment. As an extension to the previous works, we focus on equal gain combining technique when the wireless channel is modeled as Nakagami-m. We derive series form exact expressions for probability of detection and false alarm when the number of diversity branches are 1, 2, 3 and L ges 4. Finally, performance variation is shown against the number of diversity branches and the time bandwidth product in decision statistic with the aid of numerical results.

On optimal input distribution and capacity limit of Bernoulli-Gaussian impulsive noise channels

In this paper, we rigorously analyze the optimal input distribution and capacity of an additive Bernoulli-Gaussian (BG) impulsive noise (IN) channel in high and low input power regimes. First, we obtain an input distribution for which the channel output is Gaussian distributed. This distribution, if valid, shall result in the capacity of the channel. At an asymptotically high input power level, we then show that the derived input is always valid and in fact, it resembles a Gaussian distribution. As such, the Gaussian channel input is considered approximately optimal. Using the monotonicity property of the characteristic function (CF), we then develop a necessary condition for the existence of the derived optimal input for a finite level of input power. The condition indicates that a sufficiently high input power is usually required. Then focusing on the low power region, we first derive an upper bound on the channel capacity assuming full knowledge of noise state. A closed-form expression of the mutual information (MI) achieved by Gaussian inputs, which is considered as a lower bound on the channel capacity, is then developed. By comparing these two bounds, it is shown that a Gaussian input asymptotically results in the capacity. Interestingly, it is also demonstrated that such a capacity is the same as the capacity of an erasure channel in low power regimes.

Rotated Multi-D Constellations in Rayleigh Fading: Mutual Information Improvement and Pragmatic Approach for Near-Capacity Performance in High-Rate Regions

This paper studies the mutual information improvement attained by rotated multidimensional (multi-D) constellations via a unitary precoder G in Rayleigh fading. At first, based on the symmetric cut-off rate of the N-D signal space, we develop a design criterion with regard to the precoder G. It is then demonstrated that the use of rotated constellations in only a reasonably low dimensional signal space can significantly increase the mutual information in high-rate regimes. Based on parameterizations of unitary matrices, we then construct good unitary precoder G in 4-D signal space using a simple optimization problem, which involves only four real variables and it is applicable to any modulation scheme. To further illustrate the potential of multi-D constellation and to show the practical use of mutual information improvement, we propose a simple yet powerful bit-interleaved coded modulation (BICM) scheme in which a (multi-D) mapping technique employed in a multi-D rotated constellation is concatenated with a short-memory high-rate convolutional code. By using extrinsic information transfer (EXIT) charts, it is shown that the proposed technique provides an exceptionally good error performance. In particular, both EXIT chart analysis and simulation results indicate that a turbo pinch-off and a bit error rate around 10-6 happen at a signal-to-noise ratio that is well below the coded modulation and BICM capacities using traditional signal sets. For example, with code rates ranging from 2/3 to 7/8, the proposed system can operate 0.82 dB-2.93 dB lower than the BICM capacity with QPSK and Gray labeling. The mutual information gain offered by rotated constellations can be therefore utilized to design simple yet near Shannon limit systems in the high-rate regions.

Sum-rate performance and impact of self-interference cancellation on full-duplex wireless systems

We consider full-duplex (FD) bidirectional communication between a pair of nodes and investigate the impact of residual self-interference on sum-rate performance. We first analyze a situation where channel state information is available only at receiver (CSIR). For this case, we derive an exact expression and a lower bound to the sum-rate performance of FD and hence characterize the effect of residual self-interference. The study shows that, FD sum-rate performance is limited by the effective signal-to-residual self-interference power ratio (effective SIR). In particular, for a fixed effective SIR, FD achieves almost twice the sum-rate of half-duplex (HD) in low signal-to-noise ratio (SNR) regimes whilst FD performance is surpassed by HD in high SNR regions. A closed-form approximation to this crossover SNR is derived. We then investigate the sum-rate of FD assuming channel state information is available to both transmitter and receiver (CSIT). Comparison of FD sum-rates of CSIR and CSIT shows that, in low SNR regions, a significant benefit can be achieved with CSIT while the gain is small in high SNR levels.

Capacity limit of cognitive radio with dynamic frequency hopping under imperfect spectrum sensing

In this paper, we investigate the capacity limit of a single secondary user (SU) communication link in a cognitive radio system. An SU transmitter establishes the communication with its receiver by dynamically hopping in a frequency spectrum pool, and by sensing the spectrum to exploit the temporal communication opportunities. We characterize the performance of sensing by false-alarm and miss-detection probabilities. Firstly, focusing on a high channel input power region, we develop an upper bound on the SU capacity by assuming a Gaussian distributed output. A lower bound on the SU capacity is also derived using a Gaussian input. We then show that the lower bound closely approaches the upper bound at a high channel input power level. This means that the Gaussian input is nearly optimal in this case. Furthermore, we characterize the impact of primary user activities and sensing performance on the SU capacity by developing a closed-form tight approximation. Secondly, paying attention to a low channel input power region, we propose a genie-aided upper bound and a lower bound using the Gaussian input. By comparing these two bounds, a closed-form approximation to the capacity is developed and the near optimality of the Gaussian input is demonstrated. Finally, numerical results are provided to complement the theoretical discussion.

Vector Perturbation Precoding Under Quantized CSI

This paper focuses on the design of vector perturbation (VP) precoding for multiuser multiple-input-single-output (MU-MISO) downlink transmission under quantized channel side information (CSI). In particular, each receiver decomposes its downlink channel vector in forms of channel direction information (CDI) and channel magnitude information (CMI) for feedback to the transmitter. The CMI contribution is studied in two scenarios: i) perfect CMI available to the transmitter and ii) only CMI statistics known at the transmitter. Under these two scenarios, using the quantized CDI and quantization error statistics, we propose a unified approach to design the VP precoders that minimize the mean square error (MSE) between channel input and output. Closed-form expressions to the precoders are then derived. Bit-error-rate (BER) results indicate that the proposed VP precoder designs are less sensitive to quantization errors, and CMI availability offers significant performance improvements.

Optimal Signaling Scheme and Capacity Limit of PLC Under Bernoulli-Gaussian Impulsive Noise

This paper studies the optimal signaling scheme and capacity of the Bernoulli-Gaussian impulsive noise channel to shed new light on the impact of impulsive noise on spectral efficiency of power-line communications systems. First, by focusing on the practically typical case with impulse power that is much higher than signal power, we develop a tight approximation to the differential entropy of Bernoulli-Gaussian noise. Closed-form tight lower and upper bounds on the capacity are then derived. By comparing these bounds, it is demonstrated that the capacity decreases with an increasing impulse occurrence rate and the Gaussian signaling scheme is nearly optimal. We then focus on the case with an impulse power lower than signal power to develop tight lower and upper bounds. We subsequently show that the Gaussian signaling can approach the capacity in this region as well. In addition, channel erasure is shown to be very effective for the impulsive noise channel when impulse power is higher than signal power, but it introduces rate loss when impulse power is sufficiently lower than signal power. Illustrative simulation results confirm the analytical derivations and show their applications to estimate the maximum achievable rate of a power-line communication link with practical parameters.

Vector Perturbation Precoding for Multi-User CoMP Downlink Transmission

This paper focuses on the design of vector perturbation (VP) precoding for coordinated multi-point (CoMP) multi-user downlink transmission. Precoding is performed by individual base stations (BSs) in a distributed manner using only the downlink channel coefficients and user data local to a BS. A cascade precoder structure with an outer precoder managing the inter-cell interference (ICI) and an inner precoder performing mean-squared-error (MSE) minimization-based VP to mitigate the intra-cell interference is proposed. Three different outer precoding techniques are considered. In the first technique, the outer precoder is designed to fully eliminate the ICI by trading off the degrees of freedom (DoFs) available through multiple antennas. While the proposed technique outperforms existing conventional-VP based designs, a large portion of DoF is consumed by the ICI elimination. To overcome this issue, in the second technique, interference alignment-based outer precoding that minimizes the total leakage interference is proposed. To further improve the system performance, in the third approach, precoding by joint minimization of total leakage interference plus MSE is performed. Numerical results show that the proposed cascade precoding structure is an efficient way to use the DoF of CoMP multi-user downlink transmission.

Rotated multi-D constellations in Rayleigh fading: Mutual information improvement and a pragmatic approach for near-capacity performance in high-rate regions

This paper studies the mutual information improvement attained by rotated multidimensional (multi-D) constellations via a unitary precoder G ε CN×Nin Rayleigh fading. At first, based on the symmetric cut-off rate of the N-D signal space, we develop a design criterion with regard to the precoder G. It is then demonstrated that the use of rotated constellations in only a reasonably low dimensional signal space can significantly increase the mutual information in high-rate regimes. By considering the QPSK system, we then propose a class of good unitary rotation G in 4-D signal space using parameterization approach, which are shown to provide remarkable improvement. To further illustrate the potential of multi-D constellation and to show the practical use of mutual information improvement, we propose a simple yet powerful coded modulation scheme in which a (multi-D) mapping technique employed in a multi-D rotated constellation is concatenated with a short-memory high-rate convolutional code (CC). By using extrinsic information transfer (EXIT) charts, it is demonstrated that the proposed technique provides an exceptionally good error performance. For example, by using the derived 4×4 rotation, together with QPSK constellation, and a simple rate-3/4 outer convolutional code, it is shown that the proposed system can operate 1.39 dB lower than the traditional coded modulation capacity at the bit error rate (BER) level around 10–6.