Energy-Efficient Power and Bandwidth Allocation in an Integrated Sub-6 GHz -- Millimeter Wave System

In mobile millimeter wave (mmWave) systems, energy is a scarce resource due to the large losses in the channel and high energy usage by analog-to-digital converters (ADC), which scales with bandwidth. In this paper, we consider a communication architecture that integrates the sub-6 GHz and mmWave technologies in 5G cellular systems. In order to mitigate the energy scarcity in mmWave systems, we investigate the rate-optimal and energy-efficient physical layer resource allocation jointly across the sub-6 GHz and mmWave interfaces. First, we formulate an optimization problem in which the objective is to maximize the achievable sum rate under power constraints at the transmitter and receiver. Our formulation explicitly takes into account the energy consumption in integrated-circuit components, and assigns the optimal power and bandwidth across the interfaces. We consider the settings with no channel state information and partial channel state information at the transmitter and under high and low SNR scenarios. Second, we investigate the energy efficiency (EE) defined as the ratio between the amount of data transmitted and the corresponding incurred cost in terms of power. We use fractional programming and Dinkelbach's algorithm to solve the EE optimization problem. Our results prove that despite the availability of huge bandwidths at the mmWave interface, it may be optimal (in terms of achievable sum rate and energy efficiency) to utilize it partially. Moreover, depending on the sub-6 GHz and mmWave channel conditions and total power budget, it may be optimal to activate only one of the interfaces.Comment: A shorter version to appear in Asilomar Conference on Signals, Systems, and Computer

Fundamental Limits of Covert Communication over MIMO AWGN Channel

Fundamental limits of covert communication have been studied in literature for different models of scalar channels. It was shown that, over $n$ independent channel uses, $\mathcal{O}(\sqrt{n})$ bits can transmitted reliably over a public channel while achieving an arbitrarily low probability of detection (LPD) by other stations. This result is well known as square-root law and even to achieve this diminishing rate of covert communication, some form of shared secret is needed between the transmitter and the receiver. In this paper, we establish the limits of LPD communication over the MIMO AWGN channel. We define the notion of $\epsilon$-probability of detection ($\epsilon$-PD) and provide a formulation to evaluate the maximum achievable rate under the $\epsilon$-PD constraint. We first show that the capacity-achieving input distribution is the zero-mean Gaussian distribution. Then, assuming channel state information (CSI) on only the main channel at the transmitter, we derive the optimal input covariance matrix, hence, establishing the $\epsilon$-PD capacity. We evaluate $\epsilon$-PD rates in the limiting regimes for the number of channel uses (asymptotic block length) and the number of antennas (massive MIMO). We show that, in the asymptotic block-length regime, while the SRL still holds for the MIMO AWGN, the number of bits that can be transmitted covertly scales exponentially with the number of transmitting antennas. Further, we derive the $\epsilon$-PD capacity \textit{with no shared secret}. For that scenario, in the massive MIMO limit, higher covert rate up to the non LPD constrained capacity still can be achieved, yet, with much slower scaling compared to the scenario with shared secret. The practical implication of our result is that, MIMO has the potential to provide a substantial increase in the file sizes that can be covertly communicated subject to a reasonably low delay.Comment: Submitted to IEEE Transactions on Information Theor