Joint Design of Beamforming and Antenna Selection in Short Blocklength Regime for URLLC in Cognitive Radio Networks

This paper considers the short blocklength regime for cognitive radio networks (CRNs) to deliver ultra-reliable and low-latency communications (URLLCs) promised for beyond 5G networks. The secondary system consists of a secondary transmitter (ST) and multiple secondary users, which are allowed to access the same spectrum of licensed users (i.e., the primary system). Adopting linear beamforming at ST, we formulate the optimization problem of the energy-efficient maximization for the secondary system under the power constraint at ST and interference power constraints at primary receivers. In the short blocklength regime, the rate function is more complex and computationally intractable than the traditional Shannon rate function, which makes the formulated problem more difficult to solve. By leveraging techniques from the Dinkelbach method and the inner approximation method, we first devise newly approximated functions to convexify nonconvex constraints, and the iterative algorithm is then developed to obtain at least a locally optimal solution. To further enhance the energy efficiency of the secondary system, we consider a joint optimization of beamforming and antenna selection at ST, where binary variables are introduced to establish the operation modes of transmit antennas. To solve the mixed-integer nonconvex problem, we incorporate the penalty function into the objective function to dealing with the uncertainty of binary variables. Numerical results are provided to demonstrate the fast convergence and merits of the proposed algorithms, as well as to confirm the role of antenna selection in improving energy efficiency.