Cell-free massive multiple-input multiple-output (CFMM) network is projected as the latest technology for the fifth-generation and beyond wireless networks. The recent research trend is to extensively study and analyse CFMM network for its advantages and bottlenecks. The CFMM network is strongly affected by pilot contamination (PC) which is one of the bottlenecks due to which quality of service (QoS) and accuracy of channel estimation gets impacted. Therefore, we address this problem by presenting a novel pilot assignment algorithm to mitigate PC and deep learning aided channel estimation for reducing channel estimation error for the CFMM systems to maximize spectral efficiency. We derive achievable UL and DL spectral efficiency (SE) expressions for the proposed system, and compared with Minimum Mean Square Error(MMSE) and Maximum Ratio (MR) combining techniques. The performance of cellular massive MIMO is derived for comparison. For the same cellular set up,the proposed CFMM system achieves higher SE than the cellular massive MIMO. Numerical results prove the efficacy of the proposed CFMM system to some of the existing schemes in this domain.