Spectrum sensing is a key component of the cognitive radio paradigm. Primary signals are typically detected with uncalibrated receivers at signal-to-noise ratios (SNRs) well below decodability levels. Multiantenna detectors exploit spatial independence of receiver thermal noise to boost detection performance and robustness. We study the problem of detecting a Gaussian signal with rank-P unknown spatial covariance matrix in spatially uncorrelated Gaussian noise with unknown covariance using multiple antennas. The generalized likelihood ratio test (GLRT) is derived for two scenarios. In the first one, the noises at all antennas are assumed to have the same (unknown) variance, whereas in the second, a generic diagonal noise covariance matrix is allowed in order to accommodate calibration uncertainties in the different antenna frontends. In the latter case, the GLRT statistic must be obtained numerically, for which an efficient method is presented. Furthermore, for asymptotically low SNR, it is shown that the GLRT does admit a closed form, and the resulting detector performs well in practice. Extensions are presented in order to account for unknown temporal correlation in both signal and noise, as well as frequency-selective channels.

We recently proposed the dynamic spectrum leasing (DSL) paradigm for dynamic spectrum access in cognitive radio networks. In this paper, we formalize this concept by developing a general game-theoretic framework for the DSL and by carefully identifying requirements for the coexistence of primary and secondary systems via spectrum leasing. In contrast to hierarchical spectrum access, spectrum owners in proposed DSL networks, which are denoted as primary users, dynamically adjust the amount of secondary interference that they are willing to tolerate in response to the demand from secondary transmitters. The secondary transmitters, in turn, opportunistically attempt to achieve maximum possible throughput, or another suitably defined reward, while not violating the interference limit that is set by the primary users. The new game-theoretic model, however, allows the secondary users to encourage the spectrum owners to push the interference cap upward based on demand. We have proposed a general structure for the utility functions of primary users and secondary users that allows the primary users to control the price and the demand for spectrum access based on their required quality of service (QoS). We establish that, with these utility functions, the DSL game has a unique Nash equilibrium to which the best response adaptation finally converges. Moreover, it is shown that the proposed coexistence and best response adaptations can be achieved with no significant interaction between the two systems. In fact, it is shown that the only requirement is that the primary system periodically broadcasts two parameter values. We use several examples to illustrate the system behavior at the equilibrium and use the performance at the equilibrium to identify suitable system design parameters.

Spectrum sensing is a key ingredient of the dynamic spectrum access paradigm, but it needs powerful detectors operating at SNRs well below the decodability levels of primary signals. Noise uncertainty poses a significant challenge to the development of such schemes, requiring some degree of diversity (spatial, temporal, or in distribution) for identifiability of the noise level. Multiantenna detectors exploit spatial independence of receiver thermal noise. We review this class of schemes and propose a novel detector trading off performance and complexity. However, most of these methods assume that the noise power, though unknown, is the same at all antennas. As it turns out, calibration errors have a substantial impact on these detectors. Another novel detector is proposed, based on an approximation to the Generalized Likelihood Ratio, outperforming previous schemes for uncalibrated multiantenna receivers.

In recent years, the derivation of nonasymptotic converse and achievability bounds on the maximum coding rate as a function of the error probability and blocklength has gained attention in the information theory literature. While these bounds are accurate for many scenarios of interest, they need to be evaluated numerically for most wireless channels of practical interest, and their evaluation is computationally demanding. This paper presents saddlepoint approximations of state-of-the-art converse and achievability bounds for noncoherent, single-antenna, Rayleigh block-fading channels. These approximations can be calculated efficiently and are shown to be accurate for SNR values as small as 0 dB and blocklengths of 168 channel uses or more.

Saddlepoint approximations of the meta-converse and random-coding union bounds are derived. These bounds accurately characterize the channel coding minimum error probability for symmetric memoryless channels in a wide range of system parameters. The proposed approximations are simple to compute and yield a unified analysis of both hypothesis-testing lower bounds and random-coding upper bounds.

Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy et al.; the second expression is a function of an information-spectrum measure and implies the tightness of a generalized Verdú-Han lower bound. The formulas characterize the minimum error probability of several problems in information theory and help to identify the steps where existing converse bounds are loose.