This paper analyzes the performance of single-cell massive multiple-input multiple-output (MIMO) systems with non-orthogonal pilots. Specifically, closed-form expressions of the normalized channel estimation error and achievable uplink capacity are derived for both least squares (LS) and minimum mean square error (MMSE) estimation. Then a pilot reconstruction scheme based on orthogonal Procrustes principle (OPP) is provided to reduce the total normalized mean square error (NMSE) of channel estimations. With these reconstructed pilots, a two-step pilot assignment method is formulated by considering the correlation coefficient among pilots to reduce the maximum NMSE. Based on this assignment method, a step-by-step pilot power allocation scheme is further proposed to improve the average uplink signal-to-interference and noise ratio (SINR). At last, simulation results demonstrate the superiority of the proposed approaches.

In the Evolved UTRA (UMTS Terrestrial Radio Access) uplink, single-carrier frequency division multiple access (SC-FDMA) radio access was adopted owing to its advantageous low peak-to-average power ratio (PAPR) feature, which leads to wide coverage area provisioning with limited peak transmission power of user equipments. This paper proposes orthogonal pilot channel generation using the combination of FDMA and CDMA in the SC-FDMA-based Evolved UTRA uplink. In the proposed method, we employ distributed FDMA transmission for simultaneous accessing users with different transmission bandwidths, and employ CDMA transmission for simultaneous accessing users with identical transmission bandwidth. Moreover, we apply a code sequence with a good auto-correlation property such as a Constant Amplitude Zero Auto-Correlation (CAZAC) sequence employing a cyclic shift to increase the number of sequences. Simulation results show that the average packet error rate performance using an orthogonal pilot channel with the combination of FDMA and CDMA in a six-user environment, i.e., four users each with a 1.25-MHz transmission bandwidth and two users each with a 5-MHz transmission bandwidth, employing turbo coding with the coding rate of R = 1/2 and QPSK and 16QAM data modulation coincides well with that in a single-user environment with the same transmission bandwidth. We show that the proposed orthogonal pilot channel structure using the combination of distributed FDMA and CDMA transmissions and the application of the CAZAC sequence is effective in the SC-FDMA-based Evolved UTRA uplink.