# Compressive Sensing-Based Sparsity Adaptive Channel Estimation for 5G Massive MIMO Systems
## 1 Introduction  
Massive MIMO (multiple-input multiple-output) technology is one of the key technologies of next-generation mobile cellular networks, which can form a massive antenna array by providing a large number of antennas at the cell base station. It will greatly improve the channel capacity and spectrum utilization and has become a hotspot in the field of wireless communications in recent years [1]. In a massive MIMO system, a precise channel state information (CSI) is critical, which is directly related to the system signal detection, beamforming, resource allocation and so on. The number of base station antennas in massive MIMO systems has reached hundreds of thousands, which greatly deepens the complexity of system data processing. Therefore, in order to make full use of the potential advantages of massive MIMO technology, the more efficient and low complexity channel estimation algorithms are worthy of further study. Massive MIMO has various merits over the conventional MIMO. First, it uses a large number of antennas at the BS due to which the simplest coherent-combiner and linear-precoder can be used for signal processing such MF or ZF. Second, increasing the number of antennas increases the system capacity substantially using the channel-reciprocity features and without increasing feedback-overhead. Third, the reduced power benefits in the uplink/downlink (UL/DL) provide the feasibility to shrink the cell-size, which can be used in micro and pico-cells. The massive multi-input multi-output (MIMO) system has doubled the capacity of the communication system without increasing the signal bandwidth and signal transmission power and is regarded as the core technology of 5G wireless communication. Channel estimation is the keytechnology in the physical layer of massive MIMO systems. Its accuracy directly affects the system performance under fading channels. In massive MIMO systems, accurate Channel State Information (CSI) is required to utilize the full potential of MIMO systems [2; 3]. However, such accurate CSI is not available in real communication environment [4]. With the increasing number of antennas, the receiver has to estimate more channel coefficients, which effectively increases the pilot overhead, computational complexity and reduces the overall throughput of the system [5]. This is a challenging issue which has been addressed in [3; 4; 5; 6]. Literature [7; 8; 9; 10; 11; 12; 13; 14; 15] shows that the massive MIMO channel has sparse characteristics which can be utilized for computationally-efficient channel estimation. Classical channel estimation methods include least-square (LS) algorithm [16], minimum mean-squared error (MMSE) algorithm [17], linear minimum mean square error (LMMSE) [18] and so on. The actual radio channel has a certain multi-sparseness [19]. In recent years, a large number of researchers applied compressive sensing to the pilot-aided channel estimation, e.g., in [20; 21]. Research shows that compressed channel estimation achieves better performance based on the same number of pilots in sparse channels. Compressed sensing channel estimation algorithms orthogonal matching pursuit (OMP) [22], regularization orthogonal matching pursuit (ROMP) [23], and subspace pursuit (SP) [24] are currently used. The above algorithms need to predict the channel sparsity. However, the channel sparsity in the actual communication environment is usually unknown, which greatly limits the application of the above algorithm. The sparsity adaptive matching pursuit (SAMP) algorithm can recover sparsity-unknown channels [25], but the algorithm has a high dependence on the iterative steps, resulting in the pursuit of high performance and at the same time, greater computational complexity. Massive MIMO systems need to deal with a huge amount of data, and the traditional compression-aware channel estimation algorithm is difficult to strike a balance between estimation performance and computational complexity.