Introduction. This paper presents optimization methods for the amplitude-phase distribution in a transmitting antenna array in a system with a common signal for multicast data transmission and radar sensing in a given sector of space. Two approaches are considered for the choice of an objective function for the optimization problem. The first approach involves minimizing the transmitted power for a given quality of user service and radar surveillance. The second approach involves optimizing the quality of service for the worst radar and communication channel under a given power budget. The value that determines the quality of service is the signal-to-noise ratio, for both communication and radar.Aim. Тo solve the optimization problem of spatial linear coding of signals in a joint multicast radar and communication system, which shares a common signal.Materials and methods. Optimization of spatial linear coding in a joint radio radar and communication system was carried out by the methods of statistical theory and optimization theory using the numerical solution of optimization problems. The performance characteristics of the system were analyzed by Monte Carlo simulation. Statistical simulation was performed in the MATLAB environment using standard tools, as well as the CVX package for the numerical solution of convex optimization problems.Results. Optimization problems were formulated based on the criteria of the minimum radiated power and the maximum signal-to-noise ratio in the worst channel. A limitation on the radiated power of individual antenna channels was used for both cases. Optimization problems were approximately reduced to convex problems with semidefinite constraints, which could be solved using the wellknown interior point algorithm with polynomial complexity. The performed statistical simulation produced optimal performance characteristics of a joint system, including the total power versus the threshold signal-to-noise ratio and the signal-to-noise ratio for the worst channel versus the power budget.Conclusion. The proposed numerical optimization methods for spatial linear coding in a transmitting antenna array can be recommended when designing joint radar communication systems.