This paper investigates the impact of uplink training on the performance of multi-cell multiple antenna systems with precoding. It focuses on time division duplex (TDD) systems, where channel state information (CSI) is obtained through uplink training and the reciprocity of the wireless medium. The paper shows that non-orthogonal training sequences lead to pilot contamination, where the channel estimate at one base station becomes corrupted by users in other cells. This problem is analyzed and a new multi-cell MMSE-based precoding method is developed to mitigate it. The method has a simple closed-form expression and is shown to provide significant performance gains compared to popular single-cell precoding methods. The paper also discusses the implications of pilot contamination in multi-cell systems and the importance of considering training sequence allocation when designing precoding methods. Numerical results demonstrate the effectiveness of the proposed method in improving system performance.This paper investigates the impact of uplink training on the performance of multi-cell multiple antenna systems with precoding. It focuses on time division duplex (TDD) systems, where channel state information (CSI) is obtained through uplink training and the reciprocity of the wireless medium. The paper shows that non-orthogonal training sequences lead to pilot contamination, where the channel estimate at one base station becomes corrupted by users in other cells. This problem is analyzed and a new multi-cell MMSE-based precoding method is developed to mitigate it. The method has a simple closed-form expression and is shown to provide significant performance gains compared to popular single-cell precoding methods. The paper also discusses the implications of pilot contamination in multi-cell systems and the importance of considering training sequence allocation when designing precoding methods. Numerical results demonstrate the effectiveness of the proposed method in improving system performance.