This paper performs analysis of massive MIMO system having large number of base station antennas N and user terminals K with uplink and downlink of Time Divison Duplexing system. In this system model pathloss, pilot contamination and antenna correlation for each link is considered. In this work, estimation of achievable rates with several linear detectors like MF (Matched filter) and MMSE (Minimum Mean Square Error) are done. We simulated achievable rate versus number of base station antenna N for MF and MMSE. We observed that performance of MMSE detector is superior in terms of achievable rate compared to MF detector in massive MIMO system. Second, we analyze spectral efficiency and energy efficiency of massive MIMO system with imperfect CSI (Channel State Information measured from uplink pilots). In this analysis we have used MRC (Maximum Ratio Combining) detector and derived spectral efficiency and energy efficiency for different values of transmitted power. From simulation we can observe that as we increase transmitted power, spectral efficiency increased but at the cost of energy efficiency. So there is always trade off between spectral efficiency and energy efficiency. We also observed from simulation that as we increase number of base station antenna trade off curve shifts upwards.