Multiple-input multiple-output (MIMO) spatial multiplexing is known to increase the transmission rate without bandwidth expansion. However, in cellular networks (CNs), the transmission rate of a user close to the cell edge significantly degrades because the received signal-to-interference plus noise power ratio (SINR) degrades due to the presence of strong co-channel interference (CCI) from neighboring cells. Distributed antenna network (DAN), in which many antennas are spatially distributed over the cell, is suitable for MIMO spatial multiplexing because the received SINR improves over the entire cell. In this paper, assuming block transmission with cyclic prefix (CP) insertion, we theoretically derive an expression for the downlink spectral efficiency of DAN-MIMO spatial multiplexing in a multi-cell environment. Then, we propose the optimal and suboptimal transmit power allocation schemes for DAN-MIMO spatial multiplexing. We evaluate the spectral efficiency distribution by Monte Carlo numerical computation method to show that DAN allows single frequency reuse and achieves higher spectral efficiency compared to CN.