# A Low Complexity Channel Estimation and Detection for Massive MIMO Using SC-FDE
## 1 Introduction
Channel estimation can be performed making use of pilots multiplexed with data [14]. Nevertheless, this means that a part of the spectrum is dedicated to such estimate, which degrades the efficiency. An alternative channel estimate technique makes use of superimposed pilots (also referred to as implicit pilots) [15]. In this case, pilots are added to the data [16], but a problem of interference between pilots and data exists: the detection of data is degraded due to the existence of overlapping pilots, and the channel estimate obtained with the pilots is degraded due to the existence of the overlapping data. This can be overcome through the implementation of an iterative receiver, where the channel estimate and data detection take place in different iterations of the receiver, while subtracting the non-desired signal of such iteration (i.e., subtracting the data from the pilots or the pilots from the data). Most of the work that has been done in the area of iterative receivers performing joint detection and channel estimation for massive MIMO is based on OFDM [17, 18]. This article focusses on SC-FDE, using an iterative receiver specific of this transmission technique. The receiver of a communication system employing MIMO should be able to separate different data streams, translating in an increase of complexity. Knowing that the computation requirements tends to increase with the number of antennas, such computation tends to be extremely high in the case of m-MIMO. Therefore, using a low complexity receiver, one can decrease such complexity. The Zero Forcing (ZF) algorithm corresponds to a certain complexity [19], as it requires the computation of the pseudo-inverse of the channel matrix, for each frequency component of the channel. In that context, we propose a simplified receiver for m-MIMO, based on either the Maximum Ratio Combiner(MRC) [15] or on the Equal Gain Combiner (EGC) [10], and therefore, the computation requirements are kept at a lower level. The advantage of these algorithms relies on the fact that the computation of the pseudo-inverse of the channel is overcome, reducing the complexity. Nevertheless, since such algorithms are non-optimum, a certain interference is generated in the detection process. This is mitigated by incorporating an iterative receiver that performs the following functions:  
1. Channel Estimation using superimposed pilots;
2. Data Detection;
3. Interference Mitigation generated in the data detection process, using an Iterative Block--Decision Feedback Equalization technique (IB-DFE) [20]. This article presents and studies an iterative receiver based on MRC/EGC algorithms, that jointly perform channel estimation and data detection (including interference mitigation), optimized for m-MIMO and using SC-FDE signals. This article is organized as follows: Section 2 describes the system and signal characterization for m-MIMO using SC-FDE transmissions; Section 3 describes the channel estimation using multiplexed or superimposed pilots; Section 4 analyzes the performance results and Section 5 concludes the article.