This paper presents a method for designing linear precoders for fixed multiple input multiple output (MIMO) receivers using conic optimization. The authors consider two design criteria: minimizing transmitted power under SINR constraints and maximizing the worst-case SINR under a power constraint. Both problems are shown to be solvable using standard conic optimization packages. The paper also develops conditions for the optimal precoder and proposes fixed point iterations to find solutions that satisfy these conditions. The approach is general and can handle rank-deficient channels, unlike many existing precoders. Simulation results show that the proposed precoders outperform existing linear precoders in multiuser systems. The paper also explores the relationship between the proposed method and the well-known downlink-uplink duality in joint downlink beamforming and power control. The authors show that their precoder design can achieve the performance of minimum mean squared error (MMSE) receivers in symmetric channels while using simple matched filter (MF) receivers. The paper also discusses the use of conic optimization in solving the power optimization problem, and provides a detailed analysis of the optimality conditions for the precoder design. The results show that the proposed method is efficient and robust, and can be applied to a wide range of MIMO systems.This paper presents a method for designing linear precoders for fixed multiple input multiple output (MIMO) receivers using conic optimization. The authors consider two design criteria: minimizing transmitted power under SINR constraints and maximizing the worst-case SINR under a power constraint. Both problems are shown to be solvable using standard conic optimization packages. The paper also develops conditions for the optimal precoder and proposes fixed point iterations to find solutions that satisfy these conditions. The approach is general and can handle rank-deficient channels, unlike many existing precoders. Simulation results show that the proposed precoders outperform existing linear precoders in multiuser systems. The paper also explores the relationship between the proposed method and the well-known downlink-uplink duality in joint downlink beamforming and power control. The authors show that their precoder design can achieve the performance of minimum mean squared error (MMSE) receivers in symmetric channels while using simple matched filter (MF) receivers. The paper also discusses the use of conic optimization in solving the power optimization problem, and provides a detailed analysis of the optimality conditions for the precoder design. The results show that the proposed method is efficient and robust, and can be applied to a wide range of MIMO systems.