Christian Lameiro

Benefits of Improper Signaling for Underlay Cognitive Radio

In this letter we study the potential benefits of improper signaling for a secondary user (SU) in underlay cognitive radio networks. We consider a basic yet illustrative scenario in which the primary user (PU) always transmit proper Gaussian signals and has a minimum rate constraint. After parameterizing the SU transmit signal in terms of its power and circularity coefficient (which measures the degree of impropriety), we prove that the SU improves its rate by transmitting improper signals only when the ratio of the squared modulus between the SU-PU interference link and the SU direct link exceeds a given threshold. As a by-product of this analysis, we obtain the optimal circularity coefficient that must be used by the SU depending on its power budget. Some simulation results show that the SU benefits from the transmission of improper signals especially when the PU is not highly loaded.

A Quadratically Convergent Method for Interference Alignment in MIMO Interference Channels

Alternating minimization and steepest descent are commonly used strategies to obtain interference alignment (IA) solutions in the K-user multiple-input multiple-output (MIMO) interference channel (IC). Although these algorithms are shown to converge monotonically, they experience a poor convergence rate, requiring an enormous amount of iterations which substantially increases with the size of the scenario. To alleviate this drawback, in this letter we resort to the Gauss-Newton (GN) method, which is well-known to experience quadratic convergence when the iterates are sufficiently close to the optimum. We discuss the convergence properties of the proposed GN algorithm and provide several numerical examples showing that it always converges to the optimum with quadratic rate, reducing dramatically the required computation time in comparison to other algorithms, hence paving a new way for the design of IA algorithms.

Analysis of maximally improper signaling schemes for underlay cognitive radio networks

In this paper, the impact of improper Gaussian signaling is studied for an underlay cognitive radio (CR) scenario comprised of a primary user (PU), which has a rate constraint, and a secondary user (SU), both single-antenna. We first derive expressions for the achievable rate of the SU when it transmits proper and maximally improper Gaussian signals (assuming that the SU is solely limited by the CR constraint). These expressions depend on the channel gains to and from the SU through a single variable. Thereby, we observe that improper signaling is beneficial whenever the SU rate is below a threshold, which depends on the signal-to-noise ratio (SNR) and rate requirement of the PU. Furthermore, we provide bounds on the achievable gain that also depend only on the PU parameters. Then, the achievable rate is studied from a statistical viewpoint by deriving its cumulative distribution function considering a constant received SNR at the PU. In addition, we specialize this expression for the Z interference channel, for which the expected achievable rate is also derived. Numerical examples illustrate our claims and show that the SU may significantly benefit from using improper signaling.

Rate Region Boundary of the SISO Z-Interference Channel With Improper Signaling

This paper provides a complete characterization of the boundary of an achievable rate region, called the Pareto boundary, of the single-antenna Z interference channel (Z-IC), when interference is treated as noise and users transmit complex Gaussian signals that are allowed to be improper. By considering the augmented complex formulation, we derive a necessary and sufficient condition for improper signaling to be optimal. This condition is stated as a threshold on the interference channel coefficient, which is a function of the interfered user rate and which allows insightful interpretations into the behavior of the achievable rates in terms of the circularity coefficient (i.e., degree of impropriety). Furthermore, the optimal circularity coefficient is provided in closed form. The simplicity of the obtained characterization permits interesting insights into when and how improper signaling outperforms proper signaling in the single-antenna Z-IC. We also provide an in-depth discussion on the optimal strategies and the properties of the Pareto boundary.

An interference alignment algorithm for structured channels

In this paper we propose a new interference alignment (IA) algorithm specifically designed to work with structured channels (e.g., diagonal or block-diagonal). Multiple-input multiple-output (MIMO) structured channels arise when symbol extensions - either in time or frequency - are employed jointly with the spatial dimension in the design of the precoders. In this case, the rank constraint in the direct channels must explicitly be taken into account into the optimization problem to ensure that there is no degrees-of-freedom (DoF) loss. To this end, we propose an algorithm that minimizes the interference leakage while ensuring that the direct links are full rank and the transmitters satisfy a power constraint. The algorithm is based upon an alternating optimization procedure, which solves a generalized eigenvalue problem at each step. We show through simulations the advantages of the proposed algorithm in several scenarios that use symbols extensions or improper (a.k.a. asymmetric) signalling.

A distributed algorithm for two-way multiple-relay networks

In this paper we propose an efficient transmission strategy for the two-way relay channel (TWRC) with multiple relays, when these are multiple-input multiple-output (MIMO) transceivers that apply the amplify-and-forward (AF) protocol. Although the optimal beamforming strategy is known, it requires a central node, with channel state information (CSI) of the entire network, to compute all the beamforming matrices, which is impractical. To reduce the overhead, in this paper we present a distributed algorithm for the computation of the relay beamforming matrices. The proposed algorithm divides the problem in two stages. First, each relay computes its own beamforming matrix in parallel using only local CSI. Next, a distributed beamforming is applied to make the signals add up coherently at the nodes. Although the proposed algorithm is suboptimal, we show through simulations that it performs very close to the optimal achievable rate region.

Interference leakage minimization for convolutive MIMO interference channels

An alternating optimization algorithm was recently proposed for the K-user multiple-input multiple-output (MIMO) interference channel. For flat-fading channels and feasible problems, this algorithm successfully aligns the interfering signals exploiting the spatial dimensions. In this paper, we consider the case in which all pairwise MIMO channels are frequency-selective (convolutive), and the users transmit broadband signals using a single-carrier scheme. Unlike the flat-fading case, for frequency-selective channels it is necessary to add a spectral mask in the frequency response of the precoders and decoders to avoid trivial solutions. We show in the paper that each step of the alternating minimization algorithm can be reformulated as a convex optimization problem in which the autocorrelation function of the precoders or decoders is obtained. Upon convergence, a final spectral factorization stage must be applied to obtain the precoders and decoders from their autocorrelation functions. Simulation results are provided to illustrate the performance of the proposed algorithm.

Maximally improper interference in underlay cognitive radio networks

It is well-known that the use of improper signaling schemes can be beneficial in interference-limited networks. Here we consider an underlay cognitive radio scenario, where a multi-antenna primary user is protected by an interference temperature constraint that ensures a prescribed rate requirement. We study how the interference temperature threshold changes when the interference is constrained to be maximally improper. Since the spatial structure of the impropriety is an additional degree of freedom, we provide the maximum value of the interference threshold that ensures the rate requirement. We illustrate the potential payoffs of improper signaling with some numerical examples, which show that a secondary user can significantly improve its achievable rate with respect to the proper signaling case.

An experimental evaluation of broadband spatial IA for uncoordinated MIMO-OFDM systems

In this paper we present an experimental study on the performance of spatial Interference Alignment (IA) in broadband indoor wireless local area network scenarios that use Orthogonal Frequency Division Multiplexing (OFDM) according to the IEEE 802.11a physical-layer specifications. Experiments have been carried out using a wireless network testbed made up of six nodes equipped with Multiple-Input Multiple-Output (MIMO) radio interfaces. This setup allows the implementation of a 3-user MIMO interference channel. We have implemented different IA decoding schemes that operate either before or after the Fast Fourier Transform block. IA has been experimentally evaluated comparing both approaches to analyze its performance in synchronous and asynchronous transmissions. Our results indicate that spatial IA performs satisfactorily in practical broadband indoor scenarios in which wireless channels often exhibit relatively large coherence times.

Spatial interference shaping for underlay MIMO cognitive networks

Interference temperature (IT) is a widely-used approach for protecting primary users (PUs) from the secondary users (SUs) in underlay cognitive radio. H owever, when multiple antennas are available at the transmitters and receivers, the spatial structure of the interference comes into play, strongly affecting the performance of the primary network. In this work, we propose interference shaping constraints as an alternative to IT-based approaches. Spatial shaping constraints take account of the structure of interference and exploit it in benefit of the secondary network. Moreover, they can be designed dynamically based on the channel conditions and performance requirements of the PUs. We first show that spatial shaping constraints generalize IT, in that the latter can be expressed as a set of isotropic shaping constraints on each interference dimension. Then, we exemplary consider a PU that has a rate requirement, and propose an algorithm for obtaining suitable shaping matrices, which can be easily modified to include primary transmitter cooperation. This algorithm is performed at the primary receiver using only local channel state information. Afterwards, we address the transceiver optimization of the SU, modeled as a multiple-input multiple-output point-to-point link, and provide optimal and suboptimal transmit covariance designs under the proposed shaping constraints. HighlightsInterference shaping is proposed for multi-antenna underlay cognitive radio.Interference shaping is shown to generalize interference temperature.An efficient design of shaping matrices is proposed using local CSI.Significant performance improvements with respect to interference temperature are shown.