# Low-Complexity Channel Estimation in 5G Massive MIMO-OFDM Systems
## 1 Introduction  
A massive multi-input multi-output (MIMO) system utilizes a large number of transmitting antennas on the base station and simultaneously serves multiple single receiver antenna users [1]. Therefore, massive MIMO shows good anti-noise and anti-narrowband fading ability, so as to make better use of increasingly precious spectrum and energy resources, and is poised to become the key technology for the future development of 5G [2, 3]. In massive MIMO systems, accurate channel state information (CSI) is required for signal detection, beamforming, resource allocation, and channel allocation. Therefore, the channel estimation scheme with outstanding performance has become the supporting technology for massive MIMO. Pilot contamination, on the other hand, is considered as a bottleneck as the pilot sequence is limited and it is reused in massive MIMO and varies with the numberof antennas [1; 2]. Therefore, such pilot signal reuse causes contamination which reduces the accuracy of CSI. Moreover, pilot contamination puts asymptotic limits on the spectral efficiency, creates coherent interference, and also results from many users using the pilot signals in different cells in massive MIMO systems [3]. At present, most of the research on massive MIMO is carried out in time division duplex (TDD) mode, with the aim of utilizing the reciprocity of uplink and downlink channels. The CSI of the downlink channel is obtained by channel estimation for the uplink [4]. However, the frequency division duplex (FDD) mode has lower latency and higher communication efficiency than the TDD mode, and the current cellular systems in most countries in the world use FDD mode [5]. Therefore, research on channel estimation for massive MIMO in FDD mode has far-reaching significance. However, in FDD mode, an accurate estimation of the downlink is very difficult [6]. A large number of antennas are distributed on the base station, and these transmissions are simultaneously sent to the user. Therefore, the data requires the user side to accurately estimate the CSI formed by each of the transmitting antennas and the single receiving antenna on the user side. It is also very difficult to satisfy both high accuracy and low pilot overhead. OFDM systems have many advantages, such as higher spectrum utilization, good resistance to multipath interference, and the ability to resist narrowband fading [7]. In today's surge in wireless communication users, more system capacity needs to be upgraded. Therefore, the OFDM system is combined with massive MIMO systems to achieve antenna diversity and spatial multiplexing [7]. In the current communication environment, the available wireless bandwidth is becoming more and more scarce. Combining the two systems can greatly improve the utilization of the spectrum resource, and can also effectively deal with the selective fading environment of the wireless channel frequency. In the typical broadband wireless transmission environment, frequency-selective fading occurs. Therefore, in order to solve this problem, we use massive MIMO in combination with OFDM systems to establish a massive MIMO-OFDM system [8]. In a massive MIMO-OFDM transmission environment, a large number of scatters are distributed to form a Rayleigh multipath transmission channel, and most of the energy of the wireless channel is concentrated on the very small component of the channel impulse response (CIR) [9], so that the CSI formed by the user side and the base station naturally exhibit sparsity [10; 11]. Based on the sparsity of the channel, the channel can be estimated using compressed sensing (CS) [12]. However, in the actual environment, the sparseness of the wireless channel is unknown as in the above literature. Then, the algorithms itself cannot estimate the channel without knowing the sparsity [13]. Therefore, this paper proposes the structured sparse adaptive coding sampling matching pursuit (SSA-CoSaMP) algorithm.