# A Low Complexity Channel Estimation and Detection for Massive MIMO Using SC-FDE
## 1 Introduction  
Massive Multiple-Input-Multiple-Output (MIMO), alongside with millimeter-wave communications (mm-Wave), are two key techniques that will support the improvements of 5G (Fifth Generation) communications, such as improved spectral efficiency and network capacity [1, 2]. Such a combination of massive MIMO (m-MIMO) with mm-Wave [3] is being utilized by other systems, such as IEEE 802.11 ad [4], using bands around 60 GHz [5]. For small cells, dedicated to increasing the capacity in a small geographic area of 5G communications, mm-Wave communications will be used [6]. Under these conditions, the area throughput will be augmented by increasing the bandwidth of the communication channels. However, it is well known that there is a very large path loss in the mm-Wave spectrum. Therefore, in order to mitigate such path loss, MIMO techniques such as beamforming will be implemented to guarantee a large array gain at the reception, so that the signal-to-noise ratio (SNR) of the received signal is acceptable. It should also be noted that due to the large path-loss in mm-Wave, the interference is lower, and the cell density can be increased by reducing the inter-base station distance, which leads to capacity gains. Regarding large-cells, commonly responsible for the coverage and mobility tiers, there is no available bandwidth to increase the capacity. Therefore, massive MIMO techniques will be employed since they allow for huge gains in spectral efficiency [7, 8, 9]. These gains come from the use of appropriate precoding/decoding schemes that can take advantage of the tens or even hundreds of antennas and yield very large array and multiplexing gains. This technique is also known as multi-user MIMO and it enables more users to be multiplexed in a given time-frequency resource, which leads to higher area throughputs. One difference of 5G communications relating to all previous generations is the possibility of allowing direct mobile-to-mobile communications, based on the IP protocol (Internet of Things), in addition to the traditional communication through base stations. This direct mode of operation uses frequencies of the order of 60 GHz, to the detriment of the traditional carriers between 2 and 3 GHz (centimeter waves), presenting a much higher channel coherence bandwidth. Moreover, the implementation of m-MIMO is facilitated with mm-Wave due to the very low wavelength and small antenna size. It is worth noting that the distance between antenna elements is such that the signals in adjacent elements are uncorrelated, which requires a minimum distance of 3 to 5 wavelengths (depending on the propagation scenario). Intersymbol Interference is the most severe problem of wireless communications [10]. One technique that can be employed to mitigate this limitation is using a block transmission technique, such as Orthogonal Frequency Division Multiplexing (OFDM) or Single-Carrier with Frequency-Domain Equalization (SC-FDE) [11]. By combining a block transmission technique with m-MIMO, results in a system that tends to be very agile, resistant to intersymbol interference and able to face the requirements of future wireless systems. OFDM signals comprise the transmission of a sum of many independent and parallel sub-carriers, which leads to signals with a high peak-to-average power ratio (PAPR), translated in a reduced amplification efficiency [12] (a similar effect occurs with the transmission of high order modulations in single-carrier systems). An alternative block transmission technique that mitigates this limitation is the SC-FDE scheme. This presents lower envelope fluctuations of signals, translating in lower-complexity and more efficient power amplification [13], being well suited for the uplink of a cellular system, where the mobile terminal has limitations in terms of dynamic range. The post-processing of block transmission techniques and m-MIMO comprises, among other specificities, the equalization process. This requires an accurate channel estimate by the receiver.