A review on deep learning aided pilot decontamination in massive MIMO

Abstract

In multi-antenna systems, advanced techniques such as massive multiple-input multiple-output (MIMO), beamforming, and beam selection depend heavily on the accurate acquisition of the channel state. However, pilot contamination (PC) can be a major source of interference which degrades they are performance. Moreover, the severity of PC increases as more pilots are reused between users in the wireless systems. Researchers have shown that PC can be mitigated by using deep learning (DL) approaches. Nevertheless, when minimizing PC, the examination that identifies the applications and factors that distinguish these DL approaches is still limited. This paper reviews these DL approaches and the improvements needed to enhance their performance. Simulation results confirm that DL networks that learn to predict the channels directly have superior performance under PC.

Keywords:

• Pilot contamination
• channel estimation
• deep learning
• deep neural networks
• pilot assignment and design
• massive MIMO

REVIEWING EDITOR:

• Qingsong Ai, Wuhan University of Technology, Wuhan, China

Subjects:

• Artificial Intelligence
• Engineering Education
• Technology
• Electrical & Electronic Engineering
• Electromagnetics & Communication

1. Introduction

Massive MIMO is the technology that equips base stations (BS) with several antennas much larger than the number of active users (Ferrante et al., 2016). To boost the network capacity, it increases Spectral Efficiency (SE) by serving multiple single-antenna terminals over the same time-frequency resource (Boccardi et al., 2014). However, to make the users’ transmission orthogonal, the BS must assign orthogonal pilot sequences to users (Marzetta, 2010). Pilot sequences are utilized by BSs during the channel estimation phase which is followed by uplink data detection and downlink precoding respectively. Due to the lack of enough orthogonal pilots, the reuse of pilots in multicell systems is inevitable which causes PC. PC causes the BS to receive the pilot from an intended user terminal (UT) and other UTs who are reusing the same pilot. Thus, PC is one of the major sources of errors during CE and signal detection (Bjornson et al., 2016).

PC can be minimized via allocating pilots based on the angle of arrivals (AoAs) (Almamori & Mohan, 2017), pre-multiplying each UT pilot signal with a corresponding BS code (Alwakeel & Mehana, 2017), or prediction of covariance matrices (Almamori & Mohan, 2018; Cheng et al., 2016). Temporal correlation between channel vectors must be high to predict covariance matrices successfully. Another way of reducing PC is to carry out joint pilot allocation (Neumann et al., 2018). Approaches in (Almamori & Mohan, 2017; 2018; Cheng et al., 2016) and (Neumann et al., 2018) use pilots only for decreasing PC. In addition, a comparative examination of different pilot assignment schemes for PC mitigation is conducted in (Misso et al., 2020). There are also semi-blind (SB) and blind CE methods that can minimize the impact of PC. SB CE methods employ pilots and data for this. Blind CE methods make use of data only (Nayebi & Rao, 2018). SB proposals reduced PC by performing CE using the steepest descent (Alnajjar & Abdallah, 2016), robust independent component analysis (ICA) (Fatema et al., 2017), and the spatial repetition scheme (Alwakeel & Mehana, 2017). However, the complexity of the steepest descent was higher than that of the pilot-based method, robust ICA suffered from error accumulation and careful design for the block structure was vital for these proposals respectively (Alnajjar & Abdallah, 2016; Alwakeel & Mehana, 2017; Fatema et al., 2017).

Under blind CE methods (Chen et al., 2016), performed alternating projection and singular value decomposition (SVD) on the sample covariance matrix for estimating channels of all UTs. However, the BS consumed additional power for estimating out-of-cell channels. In (Mezghani & Swindlehurst, 2017), channel sparsity in the angular frequency domain allowed CE of all UTs by gradient descent. Nevertheless, the procedure was undermined ambiguities in terms of phase, time shifts, and user assignments (Mezghani & Swindlehurst, 2017). PC can also be decreased by blind signal detection (BSD) methods. BSD methods avoid PC effects by detecting the uplink data first followed by data-aided CE. This differentiates them from blind CE approaches which lower PC by performing CE first followed by data detection.

A BSD scheme that projected the received signal onto the signal subspace using SVD and ICA was proposed for data detection and least square (LS) based CE in (Amiri et al., 2017). PC decayed as the number of receiving antennas and the data length increased. However, it happened when the power of the UT of interest exceeded the power of the strongest interfering UT (Amiri et al., 2017). A group-blind receiver that doesn’t require BS cooperation and performs better under PC was developed by (Ferrante et al., 2017). It required second-order statistics which were estimated during black subframes. Blank subframes are a subset of symbols without transmissions from UTs of interest. Higher throughput was possible when SVD and BIG-AMP were deployed for BSD on the sparse channel. However, for all SNR values, the achievable rate was inferior to the case with perfect channel knowledge (Zhang et al., 2018). A detailed review of other state-of-the-art pilot decontamination techniques can be found in (Elijah et al., 2016). Performance of various uplink (UL) sounding references (SRSs) allocation strategies in practical 5 G deployments, to relieve neighboring BSs from PC is presented in (Giordano, 2018).

Previous works have provided various ways of reducing PC in massive MIMO. However, the review of approaches based on DL is still limited. This paper aims to provide a detailed review of the DL methods that have considered PC mitigation. Emphasis is on how DL is applied to tackle PC. Inputs and outputs processed by DL networks when lessening PCs are discussed. Moreover, unsupervised and supervised learning for PC alleviation with DL is covered. The contributions of this article are as follows.

1. The work demonstrates the use of 5G sounding reference signals (SRS) parameters for conducting channel estimation via pilots organized in a two-dimensional resource grid (Mathworks Inc, 2022, 2023). It establishes that the synchronization of pilot signals does not affect the quality of channel estimation under PC. In addition, it states that the desired user channel can be retrieved effectively by cascading two deniers in spatial-frequency and angle-delay domains (Hirose et al., 2021; Jiang et al., 2021).

2. The understanding of the pilot design networks which utilize two-layer neural networks (TNNs) or DNNs to minimize PC by searching for optimal non-orthogonal pilot signals is extended. These networks learn pilots as weights or labels however it is proposed to treat them as pilot allocation schemes because they provide another way of assigning pilots optimally (Chun et al., 2019; Lim et al., 2021).

3. Computer simulations indicate that denoising approaches have the best channel estimation performance under PC. However, the DNN-based denoiser has a superior performance compared to the CNN-based denoiser (Hirose et al., 2021). This was because the channel gains at other symbol locations in the two-dimensional orthogonal frequency modulation (OFDM) grid were replicas of those at the first symbol. Therefore, the CNN-based denoiser did not benefit from learning the correlations of channel gains between OFDM symbols. Nevertheless, due to the abilities of CNNs to extract meaningful features from images denoisers based on CNNs can estimate the channel more accurately under PC effects well than the DNNs if pilots are transmitted by multiple OFDM carriers and symbols (Jiang et al., 2021; Lim et al., 2021).

4. It is shown that deep learning frameworks that perform power allocation in the uplink of massive MIMO have quite worse performance. The main reasons for this are shadowing effects and similar propagation conditions experienced by the pilot signals transmitted from different users because they force the algorithm to allocate comparable power levels to users which increases the severity of the PC. However, if distinct propagation conditions exist in the system power allocation can be a viable alternative (D’Andrea et al., 2019).

5. Although the labels for training the pilot and power allocation scheme were derived from solutions that maximize the signal-to-interference ratio (SINR) the performance of pilot allocation was way better than that of power allocation. This was caused by the fact that the considered 5G massive MIMO cellular system did not provide a substantial difference in propagation losses of users which allowed most of them to transmit pilots with the same powers. Without learning the channel of the user directly pilot allocation schemes showed a performance that is close to that of the CNN-based denoiser. Furthermore, pilot decontamination methods that use DNNs are faster in terms of training speed (D’Andrea et al., 2019; Kim et al., 2018).

The remainder of the paper is organized as follows. Section 2 establishes the system model which serves as the benchmark for discussing the DL approaches used to confront PC. Section 2 reviews different DL-based PC reduction techniques. Section 3 concludes the paper.

2. Pilot decontamination with deep learning

PC is an undesirable effect caused by inter-cell interference (ICI). ICI occurs when the UTs from unlike cells send the same pilot sequence to the corresponding BS on the uplink. ICI causes BSs to rely on an interference-limited received signal in the uplink which unavoidably infects the resulting channel estimate (Zhao et al., 2018). Due to PC, the BS in the $\mathit{\text{jth}}$ cell receives a signal which is the superposition of the pilot signals from the UTs in all the cells, and it is expressed as in Equation (1)(1) $$Y_j=\sum _{k=1}^K{h}_{\mathit{\text{jk}}}{S}_{\mathit{\text{jk}}}^H+\sum _{l\ne j}^L\sum _{k=1}^K{h}_{\mathit{\text{lk}}}{S}_{\mathit{\text{lk}}}^H+N_j$$(1) . The first term represents the signals of users in the $\mathit{\text{jth}}$ cell. The second term provides signals transmitted from other cells. The third term is the noise. (1) $$Y_j=\sum _{k=1}^K{h}_{\mathit{\text{jk}}}{S}_{\mathit{\text{jk}}}^H+\sum _{l\ne j}^L\sum _{k=1}^K{h}_{\mathit{\text{lk}}}{S}_{\mathit{\text{lk}}}^H+N_j$$(1)

Transmitted pilots from jth and lth cells are given as $S_{\mathit{\text{jk}}}=\sqrt{p_{\mathit{\text{jk}}}}{x}_{\mathit{\text{jk}}}^{ }$ and $S_{\mathit{\text{lk}}}=\sqrt{p_{\mathit{\text{lk}}}}{x}_{\mathit{\text{lk}}}$ respectively. Jth is a desired cell whilst all lth cells are causing inter-cell interference from their same pilot’s transmissions. $p_{\mathit{\text{jk}}}$ and $p_{\mathit{\text{lk}}}$ are desired and interfering UT pilot transmit powers respectively. $x_{\mathit{\text{jk}}}$ and $x_{\mathit{\text{lk}}}$ are actual pilots assigned to the UT in the jth and lth cells. If $\tau$ is the pilot length, it leads to $Y_j\in {\complement }^{M\times \tau }$ as the received signal. $N_j\in {\complement }^{M\times \tau }$ is the additive white Gaussian noise (AWGN) with zero mean and element-wise variance of ${\sigma }_n^2.$ $M$ is the number of receiving antennas. To perform channel estimation the jth BS uses least square (LS) estimation expressed by Equation (2)(2) $${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}=\frac{Y_j{S}_{\mathit{\text{jk}}}^{\mathrm{*}}}{\sqrt{p_{\mathit{\text{jk}}}}}$$(2) (Björnson et al., 2017). LS projects the received signal $Y_j$ on the transmitted pilot sequence $S_{\mathit{\text{jk}}}$ leading to kth UT channel estimate ${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}$ given as in Equation (3)(3) $${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}=h_{\mathit{\text{jk}}}+\sum _{l\ne j}^L\sqrt{\frac{p_{\mathit{\text{lk}}}}{p_{\mathit{\text{jk}}}}}{h}_{\mathit{\text{lk}}}{+}_{\mathrm{ }}^{\mathrm{ }}\frac{1}{\tau }\frac{N_j{S}_{\mathit{\text{jk}}}}{\sqrt{p_{\mathit{\text{jk}}}}}$$(3) . Also, LS channel estimation can be regarded as the correlation between the received signal $Y_j,$ and the pilot of the kth user. (2) $${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}=\frac{Y_j{S}_{\mathit{\text{jk}}}^{\mathrm{*}}}{\sqrt{p_{\mathit{\text{jk}}}}}$$(2) (3) $${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}=h_{\mathit{\text{jk}}}+\sum _{l\ne j}^L\sqrt{\frac{p_{\mathit{\text{lk}}}}{p_{\mathit{\text{jk}}}}}{h}_{\mathit{\text{lk}}}{+}_{\mathrm{ }}^{\mathrm{ }}\frac{1}{\tau }\frac{N_j{S}_{\mathit{\text{jk}}}}{\sqrt{p_{\mathit{\text{jk}}}}}$$(3)

In equation (3)(3) $${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}=h_{\mathit{\text{jk}}}+\sum _{l\ne j}^L\sqrt{\frac{p_{\mathit{\text{lk}}}}{p_{\mathit{\text{jk}}}}}{h}_{\mathit{\text{lk}}}{+}_{\mathrm{ }}^{\mathrm{ }}\frac{1}{\tau }\frac{N_j{S}_{\mathit{\text{jk}}}}{\sqrt{p_{\mathit{\text{jk}}}}}$$(3) , the first, second, and third terms represent the channel of UT of interest, PC from out-of-cell UTs, and noise respectively. $h_{\mathit{\text{jk}}}$ and $h_{\mathit{\text{lk}}}$ are channels for the desired and interfering UT respectively. The remaining part for the lth cells represents cases with $S_{\mathit{\text{lk}}}=S_{\mathit{\text{jk}}}$ for UTs in lth cells with the same pilot as a UT in the jth cell. Further, with a simple path loss model, the kth channel for each UT in the lth cell in can be modeled as in Equation (4)(4) $$h_{\mathit{\text{lk}}}={\sqrt{{\beta }_{\mathit{\text{lk}}}^{\mathrm{ }}}a}_{\mathit{\text{lk}}},l=1,\dots \dots j\dots \dots .,L,$$(4) . (4) $$h_{\mathit{\text{lk}}}={\sqrt{{\beta }_{\mathit{\text{lk}}}^{\mathrm{ }}}a}_{\mathit{\text{lk}}},l=1,\dots \dots j\dots \dots .,L,$$(4) ${\beta }_{\mathit{\text{lk}}}^{ }={\sigma }_{\mathit{\text{lk}}}^{ }{d}_{\mathit{\text{lk}}}^{-\alpha }$ is the large-scale fading coefficient that includes the path loss and the shadowing effect (Neumann et al., 2014). $a_{\mathit{\text{lk}}}^{ }$ comprises the fast fading variables which are i.i.d. complex Gaussian random variables with mean 0 and variance 1., ${\sigma }_{\mathit{\text{lk}}}^{}$ is the log-normal shadowing and $d_{\mathit{\text{lk}}}^{-\alpha }$ is the attenuation due to kth UT distance from the lth BS, and path loss exponent (Neumann et al., 2014).

If ${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}$ is employed for detecting uplink data and precoding of the downlink data. The precoding matrix used by the jth BS in a jth cell will be ruined (Jose et al., 2011). Because, according to Equation (3)(3) $${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}=h_{\mathit{\text{jk}}}+\sum _{l\ne j}^L\sqrt{\frac{p_{\mathit{\text{lk}}}}{p_{\mathit{\text{jk}}}}}{h}_{\mathit{\text{lk}}}{+}_{\mathrm{ }}^{\mathrm{ }}\frac{1}{\tau }\frac{N_j{S}_{\mathit{\text{jk}}}}{\sqrt{p_{\mathit{\text{jk}}}}}$$(3) , ${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}$ contains PC caused by the sum of the channels from other UTs using the same pilot signal. Also, signal detection performance will be undermined especially for signal detectors such as zero-forcing (ZF) and minimum mean square error (MMSE). Because ZF and MMSE assume perfect channel estimation (Biglieri et al., 2007). Moreover, both the uplink and downlink sum rates will be limited by the ICI imposed by pilot reuse (Zhao et al., 2018).

As shown by Equation (3)(3) $${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}=h_{\mathit{\text{jk}}}+\sum _{l\ne j}^L\sqrt{\frac{p_{\mathit{\text{lk}}}}{p_{\mathit{\text{jk}}}}}{h}_{\mathit{\text{lk}}}{+}_{\mathrm{ }}^{\mathrm{ }}\frac{1}{\tau }\frac{N_j{S}_{\mathit{\text{jk}}}}{\sqrt{p_{\mathit{\text{jk}}}}}$$(3) , PC can be controlled by: power allocation through $p_{\mathit{\text{lk}}}$ and $p_{\mathit{\text{jk}}};$ assignment of actual pilots $x_{\mathit{\text{jk}}}$ and $x_{\mathit{\text{lk}}};$ Denoising ${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}$ to get the desired channel $h_{\mathit{\text{jk}}}$ and designing the pilots $x_{\mathit{\text{jk}}}$ and $x_{\mathit{\text{lk}}}$ such that multicell interference is minimized. Concentrating on the kth UT in the jth cell. DL-based proposals that deploy deep neural networks (DNNs), convolutional neural networks (CNNs), recurrent neural networks (RNNs), and reinforcement learning networks (RLN) for remedying PC are reviewed (Goodfellow et al., 2016). All UTs from other lth cells that transmit the same pilot signal are considered to impair the reception of the target pilot signal.

2.1. Power allocation

Power allocation can either increase or decrease the transmission power of UT for interference management. Optimizing the transmission powers in the uplink is more difficult than in the downlink because the uplink powers affect the uplink data transmission and the quality of the channel estimates. In addition, uplink power control indirectly affects the precoding vectors (Björnson et al., 2017). Power allocation deep networks are those designed to learn the mapping between ${\beta }_{\mathit{\text{lk}}}$ and $p_{\mathit{\text{lk}}}.$ That is, the power of UTs with the same pilot sequence can be controlled based on large-scale coefficients. According to Equation (3)(3) $${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}=h_{\mathit{\text{jk}}}+\sum _{l\ne j}^L\sqrt{\frac{p_{\mathit{\text{lk}}}}{p_{\mathit{\text{jk}}}}}{h}_{\mathit{\text{lk}}}{+}_{\mathrm{ }}^{\mathrm{ }}\frac{1}{\tau }\frac{N_j{S}_{\mathit{\text{jk}}}}{\sqrt{p_{\mathit{\text{jk}}}}}$$(3) and Equation (4)(4) $$h_{\mathit{\text{lk}}}={\sqrt{{\beta }_{\mathit{\text{lk}}}^{\mathrm{ }}}a}_{\mathit{\text{lk}}},l=1,\dots \dots j\dots \dots .,L,$$(4) , if ${\beta }_{\mathit{\text{lk}}}$ is large decrease $p_{\mathit{\text{lk}}}$ to decrease ${\sum }_{l\ne j}^L\sqrt{\frac{p_{\mathit{\text{lk}}}}{p_{\mathit{\text{jk}}}}}{h}_{\mathit{\text{lk}}}$ which contaminates the LS estimation ${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}.$ Note that, $h_{\mathit{\text{lk}}}={\sqrt{{\beta }_{\mathit{\text{lk}}}^{ }}a}_{\mathit{\text{lk}}},$ so ${\beta }_{\mathit{\text{lk}}}$ and $p_{\mathit{\text{lk}}}$ can work in conjunction oppositely to control the level of PC interference. However, decreasing the power of other UTs for the sake of PC-affected UT will indirectly increase PC on them. Thus, power allocation must be conducted jointly based on a criterion such as uplink spectral efficiency (SE). Maximizing SE will be equivalent to PC minimization. If the SE expression is a function of the large-scale fading coefficient and power for each UT (Sanguinetti et al., 2018). Many criteria can be formulated. Nevertheless, these are the keys to designing supervised or unsupervised DL schemes.

An unsupervised learning scheme was proposed for power allocation among UTs based on the minimum sum of mean square error (MSE) of channel estimation as a criterion. Here, a multi-layer fully connected DNN was designed to optimize the power allocated to each sample in a pilot sequence. The sum MSE of channel estimation was derived based on the MMSE channel estimator (Xu et al., 2019). Subject to the total available power of each kth UT, the DNN was un-supervised and trained with ${\beta }_{\mathit{\text{lk}}}^{ }$ and $p_{\mathit{\text{lk}}}^{}$ as inputs and outputs. Sum MSE which had ${\beta }_{\mathit{\text{lk}}}^{ }$ and $p_{\mathit{\text{lk}}}^{}$ as parameters was the cost function. To facilitate power allocation for each cell under PC by the DNN. The input was formed as follows. Large-scale coefficients of users were column-aligned. Each column is a vector created by a large-scale coefficient of every receiving antenna. The output was also grabbed as follows. The powers of users were also column-aligned. Finally, each column consisted of a vector representing the power of every sample in a pilot sequence (Xu et al., 2019).

A supervised learning approach was developed that learns a mapping between either the users’ positions or the large-scale coefficients and the power allocation policy. A training sample was generated by either maximizing the system sum rate or maximizing the minimum of the users’ rate (D’Andrea et al., 2019). For the first case and second case, the inputs were (x, y) positions and the outputs were power allocated to each user. For the third case, the inputs were large-scale coefficients for all receiving antennas and the outputs were power allocated to each user. In all these cases the solution of two objectives was found by optimization methods found in (Alonzo et al., 2019; Buzzi & Zappone, 2017). The two objectives’ expressions had power and large coefficient variables. So, solving or learning them provided a DNN solution for PC mitigation (D’Andrea et al., 2019). Note that, as per Equation (4)(4) $$h_{\mathit{\text{lk}}}={\sqrt{{\beta }_{\mathit{\text{lk}}}^{\mathrm{ }}}a}_{\mathit{\text{lk}}},l=1,\dots \dots j\dots \dots .,L,$$(4) (x, y) positions for UTs can be used in place of large-scale coefficients.

DL-based power allocation schemes showed the best sum Minimum Square Error (MSE) performance with low complexity compared to other methods (Xu et al., 2019). In addition, the presence of a PC does not significantly influence the learning capabilities of the DNN. Instead, shadowing effects are the source of worse performance (D’Andrea et al., 2019). Finally, joint optimization of channel estimation (CE) and bit error (BER) rate ascended as a must to overcome the discrepancy between MSE and BER results (D’Andrea et al., 2019).

2.2. Pilot assignment

The pilot assignment task is the problem of optimally allocating pilots to UTs to minimize PC. The target is to allocate the pilot $x_{\mathit{\text{lk}}}^{}$ for each kth UT in every lth cell to minimize PC interference on every LS channel estimate ${\tilde{h}}_{\mathit{\text{lk}}}^{\mathit{\text{LS}}}.$ Whether supervised or unsupervised learning method is adopted. The pilot assignment task is carried out based on optimizing a criterion similar to power allocation. A supervised learning approach that generated training data by joint maximization of the uplink net capacity was proposed. The net capacity encompassed the entire massive MIMO system with all cells. BSs were assumed to know UT information for all UTs via Coordinated Multipoint (CoMP) transmission and reception (Kim et al., 2018). The inputs were (x, y) locations of all UTs from all cells. The labels were groups of matrices. In each matrix one row vector represented the pilot assignment for UTs in that cell. However, using the SoftMax output layer converted each label into stacked vectors. In each vector, the largest value was selected when the uplink net capacity reached maximum. Generation of the training set proceeded as follows. UTs were randomly dropped in a cell. Location information was sent to the BS. Finally, each UT was assigned a pilot to maximize the uplink net capacity to generate a training sample (Kim et al., 2018). The approach in (Kim et al., 2018), was constructed based on DNN by exploiting dropout to prevent overfitting. The DNN gave pilot assignments as outputs for all users in all cells with 99.38% normalized capacity gain and it only required 0.92 ms for computations.

Deep reinforcement learning (DRL) has also been employed for dealing with PC based on a cost function defined by AoAs of UTs. The cost function depicting the reward included PC interference emanating from UTs with AoA within that of the target UT. These were UTs that had the same pilot sequence as the target user in the massive MIMO system. Appropriate sets of states, sets of actions, and reward functions allowed the agent to learn the policy to minimize the cost function while allocating pilots. The deep residual network (ResNet) implemented the Q-neural network (QNN) which realized the aforementioned DRL. However, it was assumed that, the target user has an AoA within the pre-known AoA range and location (Omid et al., 2021).

The STATE SET was defined by the binary pilot assignment pattern for all UTs, pilot index and the cell index of the UTs with the maximum cost function in each cell, pilot index of the UT that action takes place on, cell index of the UT that action takes place on and the value of the maximum cost function in each cell. The ACTION SET selected a random UT in the adjacent cell and assigned the pilot of the target UT to that user. If the UT in the adjacent cell has the same pilot no action is pursued. Two thresholds were considered for defining the REWARD SET. As time progressed, the DRL algorithm was able to track the channel while learning the pilot assignment policy (Omid et al., 2021).

2.3. Denoisers

Denoisers are implemented to consume the PC-corrupted channel ${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}$ and produce the PC-free channel response $h_{\mathit{\text{jk}}}$ considering the kth UT in the jth cell. By mapping ${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}\to h_{\mathit{\text{jk}}},$ PC effects are minimized. However, the mapper must be designed to deal with PC interference from other cells ${\sum }_{l\ne j}^L\sqrt{\frac{p_{\mathit{\text{lk}}}}{p_{\mathit{\text{jk}}}}}{h}_{\mathit{\text{lk}}}$ and noise $\frac{1}{\tau }\frac{N_j{S}_{\mathit{\text{jk}}}}{\sqrt{p_{\mathit{\text{jk}}}}}$ which is still AWGN. Alternatively, ${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}$ can be replaced by $Y_j$ because they both contain PC interference. Cascading the DNN as a denoiser and LS estimation block allowed the retrieval of the desired channel from the PC-impaired channel in a study by (Balevi et al., 2020). Assuming the kth UT in the jth cell for the DNN, the input was $Y_j$ and the output was $Y_{\mathit{\text{jk}}}\mathrm{ }{=\sqrt{p_{\mathit{\text{jk}}}}h}_{\mathit{\text{jk}}}{S}_{\mathit{\text{jk}}}^H.$ So, training the DNN denoiser with $Y_j$ and $Y_{\mathit{\text{jk}}}$ as inputs and labels was equivalent to removing multi-cell interference caused by PC. The DNN parameters were fit online on the fly. Deploying the untrained DNN overcomes training overheads that hinder the implementation of DNNs for high dimensional channel estimation (Balevi et al., 2020). Finally, the LS estimation block projected the denoised signal $Y_{\mathit{\text{jk}}}$ on the transmitted pilot sequence $S_{\mathit{\text{jk}}}$ leading to kth UT channel estimate $h_{\mathit{\text{jk}}}$ (Balevi et al., 2020). This was possible because the deep image prior does not require training empowering it to evade the need for the training dataset (Ulyanov et al., 2018).

The low-complexity DNN-based denoiser proposed by (Balevi et al., 2020) outperformed the more complex MMSE estimator. It even came close to the Genie-Aided MMSE with a perfectly known channel statistic. Deep residual learning (DRL) that consisted of the neural network with noise estimator and denoiser was adopted to suppress PC. Considering the kth UT in a jth cell the adopted DRL structure was as in Figure 1. $h_{\mathit{\text{jk}}}={\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}-Z_{\mathit{\text{jk}}}$ and $h_{\mathit{\text{jk}}}={\alpha }_{\mathit{\text{jk}}}\circ {\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}+{\gamma }_{\mathit{\text{jk}}}.$ $Z_{\mathit{\text{jk}}}$ computed the distortion noise due to PC interference from other cells and the AWGN (Lim et al., 2021). The deep residual network was trained offline for channel estimation in the presence of a PC. The input was the LS estimate ${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}$ and large-scale coefficient ${\beta }_{\mathit{\text{lk}}}.$ The output label was the channel estimate $h_{\mathit{\text{jk}}}.$ Together these provided the training data set for kth UT in the jth cell. ${\alpha }_{\mathit{\text{jk}}}$ and ${\gamma }_{\mathit{\text{jk}}}$ were also learnable parameters. The advantage of this method was the ability of each BS to independently perform channel estimation based on its data (Lim et al., 2021).

Figure 1. DRL based channel denoiser (Lim et al., 2021).

As in Equation (3)(3) $${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}=h_{\mathit{\text{jk}}}+\sum _{l\ne j}^L\sqrt{\frac{p_{\mathit{\text{lk}}}}{p_{\mathit{\text{jk}}}}}{h}_{\mathit{\text{lk}}}{+}_{\mathrm{ }}^{\mathrm{ }}\frac{1}{\tau }\frac{N_j{S}_{\mathit{\text{jk}}}}{\sqrt{p_{\mathit{\text{jk}}}}}$$(3) , the LS estimated channel comprises the sum of the channels for all UTs using the same pilot signal. This motivated strategy is expressed as $h_{\mathit{\text{jk}}}=f({\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}),$ where $f$ denoted a mapping from the LS estimated channel to the desired channel (Hirose et al., 2021). The strategy employed two DL structures. First, the DNN was considered. However, the DNN could not exploit spatial local correlation. Therefore, CNN was brought on board because it eradicates the problem using sliding convolutional filters. The CNN performance was better compared to the DNN. Because CNN filters had the power to learn the information related to the channel covariance matrix such as AoAs and magnitude of signals. LS estimated channel was a perfect candidate for the input as it contains information about AoAs and the magnitude of signals (Hirose et al., 2021).

Three cases were considered: perfect timing, imperfect timing, and channel aging. Investigation under perfect and imperfect timing synchronization was motivated by the difficulties of achieving timing synchronization throughout the multi-cellular network (Pitarokoilis et al., 2017). Channel aging was for channel changes over time because of UT movements. However, the strategy assumed that the large-scale coefficient of the target UT is often larger than the UTs of the other cells (Hirose et al., 2021).

Two CNN denoisers in spatial-frequency (SF) and angle-delay (AD) were cascaded to retrieve the desired channel $h_{\mathit{\text{jk}}}$ from the LS estimated channel ${\tilde{h}}_{\mathit{\text{jk}}}^{\mathit{\text{LS}}}$ under the massive MIMO-OFDM system. Discrete Fourier Transform (DFT) transformed the output of the SF-CNN into the AD domain which served as the input to the AD-CNN. In the end, the output of the AD-CNN was transformed back by Inverse DFT (Jiang et al., 2021). The denoiser was called a dual CNN. It enabled the CNNs to ease interference in the SF domain. Simultaneously, it handled most of the white noise due to channel sparsity found in the AD domain. Moreover, correlation in the SF domain decreased the noise power in the AD domain so that the CNN is less confused when differentiating the channel and noise.

The dual CNN had better performance and robustness than estimation in a single domain under PC. However, the supremacy of CNN in the SF domain was key because PC interference spreads over the SF domain well. Therefore, CNN in the SF domain could cover these corrupted areas due to the correlation of adjacent areas (Jiang et al., 2021). This design was an attempt to combine CNN and expert knowledge in wireless communications. It is exemplified by the introduction of the DFT and IDFT to make CNN learn from different domains.

2.4. Pilot design

Pilot design approaches attempt to minimize PC by searching for optimal non-orthogonal pilot sequences. Pilot designers aim to jointly optimize the needed pilots ${\left\{x_{\mathit{\text{jk}}}\right\}}_{k=1}^K$ of the K users and the channel estimator of the jth BS to minimize the discrepancy of the estimated channel ${\tilde{h}}_{\mathit{\text{jk}}}$ from the desired channel $h_{\mathit{\text{jk}}}.$ Two techniques are available for designing pilots. Pilots can be collected at the output of the DNN (Lim et al., 2021) or pilots can be learned as weights of the Two-layer Neural Network (TNN) (Chun et al., 2019). For the TNN approach, separate TNNs each learning the mapping $h_{\mathit{\text{jk}}}\to Y_{\mathit{\text{jk}}}$ for each kth UT in a jth cell are trained jointly and each weight stands for the pilot sample from the pilot sequence $x_{\mathit{\text{jk}}}.$ The design of non-orthogonal pilots can proceed by jointly optimizing TNNs for all UTs in all cells to minimize PC. Zero bias vectors and unit activation functions must be used in TNNS for the weights to be direct representatives of pilot samples (Chun et al., 2019).

To accurately model the computation $h_{\mathit{\text{jk}}}{x}_{\mathit{\text{jk}}}\to Y_{\mathit{\text{jk}}}$ with a TNN. Weights that cannot be mapped to pilot samples must be set to zero because all weights do not contribute to the received pilot signal in a TNN. It is known that optimal pilot sequences are influenced by changes in the fading characteristics of large-scale coefficients of UTs. Therefore, the second technique uses a DNN to allow cells to generate pilot sequences using the large-scale coefficient ${\beta }_{\mathit{\text{lk}}}^{ }$ of UTs. By using a DNN, large-scale coefficients are fed as inputs to get optimal pilots for UTs at the output. If the orthogonality of pilot sequences for UTs with close large-scale coefficients is maintained by the DNN. PC can be reduced at the stage of channel estimation (Lim et al., 2021). However, usefulness would require knowing the large-scale coefficients for all UTs in all cells at the BSs.

2.5. Analysis

First, the use of assumed channel models may compromise the performance of DL networks on the real massive MIMO system. The reason is that the assumed channel may inaccurately reflect the actual channel. In addition, assumptions about a channel bias the learned weights, widening the discrepancy between the assumed and the actual channel (Ye et al., 2018). Online training can rescue the situation by fine-tuning the networks at the BS after offline training. However, networks can be trained from pure observations alone without any model of the massive MIMO channel via policy learning techniques to evade the drawback (Aoudia & Hoydis, 2018). Policy learning can be implemented by deep reinforcement networks (DRN) to enable the participation of the transmitter and receiver when decreasing PC. Using DRNs is also known as end-to-end learning (O’Shea & Hoydis, 2017).

Second, PC can be removed if the power received from UT within the cell of interest is larger than the power received from UTs in other cells. However, this is subject to irregularities caused by multicell systems and propagation environments. For instance, the target UT inside the building may require more power which can reach maximum without avoiding PC. If the interfering UT has a line of sight to the target BS (Müller et al., 2014). Power control may not be feasible in dense small-cell networks and for a fraction of UTs that experience similar channel conditions to more than a single BS (Ferrante et al., 2017; Müller et al., 2014). Moreover, its more complicated for hyperdense small‐cells installed in homes and are user controlled (Rodriguez, 2015). Power attenuation on interfering UTs is created for free by shadowing and path loss for the UT of interest. Power attenuation on these UTs reduces PC. However, shadowing and path loss might not help for interfering UTs found at the cell edges. Semi-blind and blind techniques have been developed to counteract this effect. Remedy of PC via DL designs centered on these techniques can be handy (Chen et al., 2016; Fatema et al., 2017).

Third, variability found in the data dimensions is a challenge for realizability. As an example, for five UTs, the DNN input dimension varied from 10 to 150 when the input labels changed from (x, y) positions to large-scale coefficients for 30 BS antennas (D’Andrea et al., 2019). Additionally, the performance of the dual CNN was evaluated for 32, 48, and 64 BS antennas. Implying that, the input dimension was changing in the spatial domain (Jiang et al., 2021). Variables such as these have an impact on the size of data processed by DL networks. This can be solved by designing adaptive schemes. For instance, instead of training different networks for different input sizes the same network can be trained to process data of different sizes (Orhan & Bastanlar, 2018; Sekou et al., 2019).

3. Performance evaluation

In simulation experiments, the 5 G massive MIMO system operating at a carrier frequency of $f_c=4$ GHz is used to compare the deep learning based pilot decontamination techniques. The pilots are derived from uplink-sounding reference signals (SRSs) for uplink channel estimation. The SRS parameters and the transmission process are shown in Figure 2. As shown in Figure 2, a frame is made up of 10 subframes and each subframe has 10 slots. Within one slot 14 OFDM symbols arranged in a two-dimensional resource grid of size $N_{\mathit{\text{sc}}}\times N_{\mathit{\text{symbols}}}^{\mathit{\text{Slot}}}$ are communicated from a user to the BS. $N_{\mathit{\text{sc}}}$ and $N_{\mathit{\text{symbols}}}^{\mathit{\text{Slot}}}$ represent the number of subcarriers and symbols per slot in frequency and time dimensions respectively. Every resource grid has $N_{\mathit{\text{sc}}}{N}_{\mathit{\text{symbols}}}^{\mathit{\text{Slot}}}$ resource elements. Figure 2 shows 4 resource elements whereby 2 are designated for carrying the SRS samples. However, for the evaluations, a 5 G massive MIMO system with $N_{\mathit{\text{sc}}}=52\times 12=624$ carriers and $N_{\mathit{\text{symbols}}}^{\mathit{\text{Slot}}}=14$ symbols giving $624\times 14=8736$ resource elements has been considered (Mathworks Inc, 2022). In the experiments, slots and resource elements containing SRS pilots only are considered during channel estimation. An example of the SRS resource grids achieved by the parameters in Figure 2 is shown in Figure 3. It can be seen that out of 14 OFDM symbols in the slot the SRS pilots can be transmitted using one or multiple symbols.

Figure 2. Sounding reference signal parameters and transmission process.

Figure 3. Sounding reference signal resource grid generated by parameters (symbol start, number of SRS symbols): (a) (0, 1) (b) (0, 4) (c) (7, 1) (d) (7, 4).

The impact of PC is measured by considering users dropped randomly in 7 hexagonal cells located in the urban microenvironment (UMi) (ETSI, 2017). A drop is an instant where each user sends the SRS signal in the allocated slot to its BS. Each user terminal has one transmitting antenna. The BSses are equipped with 128 receiving antennas. To realize the received SRS signal, an SRS signal is filtered by a tapped delay line (TDL) fading channel. Then, the AWGN is added at various signal-to-noise ratios (SNRs) (3GPP, 2020). Given a received SRS OFDM grid, PC happens when non-orthogonal SRSs that occupy the same time and frequency elements in an OFDM resource grid are transmitted from different users (Mathworks Inc, 2023). This is because multiplexed SRSses interfere with each other for identical resource elements with non-orthogonal SRS samples. When channel estimation is conducted by correlating the received SRS signal with a pre-known SRS signal PC affects the quality of the estimated channel gains for the user under consideration. It has already been pointed out that PC can be mitigated by power control, pilot (or SRS) allocation, pilot design, and denoising method respectively.

For the pilot allocation method, SRS pilots were generated by using different cyclic shifts (Mathworks Inc, 2022). For power control, each user selected an optimum power level for its transmission. Sgnal-to-interference plus noise (SINR) was an optimization criterion for power control and pilot allocation (Kim et al., 2018). However, the SINR of the entire 5 G massive MIMO cellular system expressed by Equation (5)(5) $${\mathit{\text{SINR}}}_{\mathit{\text{net}}}=\sum _{l=1}^L\sum _{k=1}^{K_l}\frac{p_k{\beta }_k^2{x}_k^{\mathrm{ }}{x}_k^{\mathrm{*}}\mathrm{ }}{\sum _{m=1}^{K_l}\mathrm{ }\sum _{\begin{array}{c}n=1\\ n\ne k\end{array}}^{K_l}{\sqrt{p_m{p}_n}\beta }_m{\beta }_n{x}_m^{\mathrm{ }}{x}_n^{\mathrm{*}}}\mathrm{ }$$(5) was considered. $K_l$ is the number of users in the lth cell. $\beta ,p,$ and $x$ give the propagation loss, power, and SRS pilot for each user respectively. (5) $${\mathit{\text{SINR}}}_{\mathit{\text{net}}}=\sum _{l=1}^L\sum _{k=1}^{K_l}\frac{p_k{\beta }_k^2{x}_k^{\mathrm{ }}{x}_k^{\mathrm{*}}\mathrm{ }}{\sum _{m=1}^{K_l}\mathrm{ }\sum _{\begin{array}{c}n=1\\ n\ne k\end{array}}^{K_l}{\sqrt{p_m{p}_n}\beta }_m{\beta }_n{x}_m^{\mathrm{ }}{x}_n^{\mathrm{*}}}\mathrm{ }$$(5)

Propagation losses ${\beta }_{ }$ required for SINR computations were gathered using Equations (6(6) $$d_{3D}=\sqrt{{(x_{\mathit{\text{UT}}}-x_{\mathit{\text{BS}}})}^2+{(y_{\mathit{\text{UT}}}-y_{\mathit{\text{BS}}})}^2+{(h_{\mathit{\text{UT}}}-h_{\mathit{\text{BS}}})}^2}$$(6) ,7)(7) $${\beta }_{\mathrm{ }}=35.3\mathrm{ }{\mathrm{\text{log}}}_{10}{(d}_{3D})+22.4+21.3{\mathrm{\text{log}}}_{10}{(f}_c)+{0.3\left(h_{\mathit{\text{UT}}}-1.5\right)+\sigma }_{\mathit{\text{SF}}}$$(7) . $d_{3D}$ is the three-dimensional distance between the user and the BS. ${\sigma }_{\mathit{\text{SF}}}=4$ dB is the shadow fading standard deviation for non-line of sight (NLOS) propagation. The antenna height $h_{\mathit{\text{UT}}}$ and $h_{\mathit{\text{BS}}},$ at the user and BS, are 1.5 m and 35 m respectively. User and BS two-dimensional positions are given as $(x_{\mathit{\text{UT}}},y_{\mathit{\text{UT}}})$ and $(x_{\mathit{\text{BS}}},y_{\mathit{\text{BS}}})$ respectively. Note that positions are determined by randomly dropping users in the cell while for each BS a cell center determines its position (ETSI, 2017). (6) $$d_{3D}=\sqrt{{(x_{\mathit{\text{UT}}}-x_{\mathit{\text{BS}}})}^2+{(y_{\mathit{\text{UT}}}-y_{\mathit{\text{BS}}})}^2+{(h_{\mathit{\text{UT}}}-h_{\mathit{\text{BS}}})}^2}$$(6) (7) $${\beta }_{\mathrm{ }}=35.3\mathrm{ }{\mathrm{\text{log}}}_{10}{(d}_{3D})+22.4+21.3{\mathrm{\text{log}}}_{10}{(f}_c)+{0.3\left(h_{\mathit{\text{UT}}}-1.5\right)+\sigma }_{\mathit{\text{SF}}}$$(7)

In reality, pilot design by learning non-orthogonal pilots as weights from a TNN (Chun et al., 2019) or collecting them at the output of the DNN (Lim et al., 2021) is another way of allocating pilots to users. Therefore, pilot design has been regarded as pilot allocation in the evaluations. For power control, the neural network was trained by using the positions of the user and optimal power allocations (D’Andrea et al., 2019). A pilot allocation neural network adopted positions and pilot identifiers as inputs and labels during training (Kim et al., 2018). Denoising neural networks were structured to learn the actual channel $H$ given the LS channel estimate ${\tilde{H}}_{ }^{\mathit{\text{LS}}}.$ The semi-blind channel estimator was utilized to compute the actual channel $H$ (Alnajjar & Abdallah, 2016). Neural networks were built in MATLAB based on a deep learning toolbox. A computer with GeForce 930MX NVIDIA GPU and intel core i5-7200U [email protected] GHz was used for simulation experiments. Adam optimizer was selected as a learning algorithm. For denoising a DNN that applied fully connected layers for mapping LS estimates, ${\tilde{H}}_{ }^{\mathit{\text{LS}}}$ to actual channel $H$ (Wang & Xu, 2020). A CNN used deep residual learning to perform denoising of LS estimates, ${\tilde{H}}_{ }^{\mathit{\text{LS}}}$ to give the actual channel $H$ (Lim et al., 2021). Average and normalized mean square error (MSE) were exploited as indicators of performance. Equation (8)(8) $$\mathit{\text{Average MSE}}=\frac{1}{S}\sum _{i=1}^S{\left|\right|H-\widehat{H}\left|\right|}_{\mathrm{ }}^2$$(8) and Equation (9)(9) $$\mathit{\text{NMSE}}=\frac{1}{S}\sum _{i=1}^S\frac{{\left|\right|H-\widehat{H}||}_{ }^2}{{\left|\right|H\left|\right|}_{ }^2}$$(9) provide the average MSE and normalized MSE (NMSE) with $H$ and $\widehat{H}$ as the actual and estimated channel. (8) $$\mathit{\text{Average MSE}}=\frac{1}{S}\sum _{i=1}^S{\left|\right|H-\widehat{H}\left|\right|}_{\mathrm{ }}^2$$(8) (9) $$\mathit{\text{NMSE}}=\frac{1}{S}\sum _{i=1}^S\frac{{\left|\right|H-\widehat{H}||}_{ }^2}{{\left|\right|H\left|\right|}_{ }^2}$$(9)

In Equation (8)(8) $$\mathit{\text{Average MSE}}=\frac{1}{S}\sum _{i=1}^S{\left|\right|H-\widehat{H}\left|\right|}_{\mathrm{ }}^2$$(8) s stands for all samples while s is the total samples per SNR in Equation (9)(9) $$\mathit{\text{NMSE}}=\frac{1}{S}\sum _{i=1}^S\frac{{\left|\right|H-\widehat{H}||}_{ }^2}{{\left|\right|H\left|\right|}_{ }^2}$$(9) . For power control users sent the same SRS using power levels assigned by a neural network (D’Andrea et al., 2019). Under pilot allocation users sent SRSs assigned by a neural network at the same power level. Then, for the user under consideration, channel estimation was conducted by correlating the received SRS signal with the pre-known SRS signal. For denoising users sent the same SRS using equal power level then the DNN and CNN denoisers predicted the actual channel given the LS channel estimate (Lim et al., 2021; Wang & Xu, 2020). Finally, the channel estimate of each method was compared with the actual channel to get the average MSE and NMSE (Alnajjar & Abdallah, 2016).

Figure 4 shows the average mean square error (MSE) on channel estimates for each pilot decontamination method. It can be observed that by benchmarking on the power control method the denoising schemes have the lowest average MSE. Specifically, the DNN denoiser shows superior performance improvement by a factor of 3.5949 compared to the CNN denoiser which has a factor of 2.3886. This was caused by the fact that the channel gains for the remaining symbol were assumed to be the same as the channel gains of the first symbol when training the CNN denoiser. It was done this way because the SRS was transmitted in the first OFDM symbol only. Therefore, the CNN architecture did not benefit from learning correlations of channel gains between symbols. If SRS parameters are changed to place SRS samples in multiple symbols as in Figure 3(b,d), channel estimation would become an image-to-image regression task. In this case, the CNN denoiser would perform better than the DNN denoiser because CNNs are better when learning features from images. Although the labels of power control and pilot allocation methods were derived from the solutions that maximize the SINR in Equation (5)(5) $${\mathit{\text{SINR}}}_{\mathit{\text{net}}}=\sum _{l=1}^L\sum _{k=1}^{K_l}\frac{p_k{\beta }_k^2{x}_k^{\mathrm{ }}{x}_k^{\mathrm{*}}\mathrm{ }}{\sum _{m=1}^{K_l}\mathrm{ }\sum _{\begin{array}{c}n=1\\ n\ne k\end{array}}^{K_l}{\sqrt{p_m{p}_n}\beta }_m{\beta }_n{x}_m^{\mathrm{ }}{x}_n^{\mathrm{*}}}\mathrm{ }$$(5) , the average MSE of the pilot allocation method is much better by a factor of 2.0455 than that of power control. Moreover, without learning the channel gains directly pilot allocation performance improvement is close to that of CNN denoising.

Figure 4. Average mean square error on channel estimates for each pilot decontamination method.

The performance of pilot decontamination versus SNR is provided in Figure 5 by using the NMSE as a metric for each pilot decontamination method. As the SNR increases the NMSE decreases for each method. The NMSE for the DNN denoising scheme is the lowest. It is revealed that the NMSE of the pilot allocation method follows closely that of the CNN denoising scheme. For pilot allocation, DNN and CNN denoising the difference in NMSE diminishes as the SNR tends to the highest value. The NMSE difference between power control and pilot allocation stays almost the same as the SNR increases. Power control has the highest NMSE because the 5 G massive MIMO cellular system provided similar propagation conditions to SRSes transmitted from different users. This forced the power control scheme to assign comparable power levels to users. In turn, it led to large deviations when channel estimation was performed for the intended user. However, in real propagation environments, distinguishable propagation conditions exist allowing power-controlled SRSs to give channel estimates with less error. Repeated experiments at SNR above 10 did not show a clear trend on NMSE versus SNR because for high SNR the SRS are PC-limited. The study proposes to investigate NMSE against SINR under high SNR conditions.

Figure 5. Normalized mean square error versus signal-to-noise ratio performance.

4. Conclusion

In this paper, deep learning-based schemes that lessen pilot contamination in massive MIMO have been discussed. It has been shown that pilot contamination can be decreased by pilot assignment, power allocation, denoising the least square channel estimation and design of non-orthogonal pilots. Pilot design and pilot assignment schemes do not differ because they attempt to search for optimal pilots that can be used by users. Performance evaluation with average MSE and NMSE as indicators showed that denoisers are superior because the channel of users can be learned directly. Power allocation schemes have a performance that depends on propagation conditions experienced by each user. If it is not possible to train the neural network to predict the channels, pilot assignment schemes promise optimal performance at less complexity and computational time. This is because DNNs that have fast learning speed can be exploited for pilot allocation. In the future, the study of the deep learning-based pilot decontamination under a massive MIMO system based on reflective surfaces is essential. Research on the development of deep learning frameworks for channel estimation with real 5 G measurement data is also very important. Extension of the deep learning techniques for end-to-end joint pilot decontamination and beamforming using reinforcement learning or conditional generative adversarial net is another area for future investigations.

Disclosure statement

The authors report there are no competing interests to declare.

Additional information

Funding

This work did not receive any funding.

Notes on contributors

Crallet M. Victor

Crallet M. Victor received the B.Sc. and M.Sc. degrees in Telecommunications engineering from the University of Dar es Salaam, Tanzania in 2009 and the University of Dodoma, Tanzania in 2012 respectively. Currently, he is a PhD student in Telecommunications Engineering at the Department of Electronics and Telecommunications Engineering, College of Informatics and Virtual Education, University of Dodoma, Dodoma, Tanzania. He is also a Lecturer in the Department of Electronics and Telecommunications Engineering, College of Informatics and Virtual Education, University of Dodoma, Dodoma, Tanzania. His research interest includes wireless communication, deep learning for communication systems, multimedia systems, and electronics engineering. Email: [email protected], [email protected]

Alloys N. Mvuma

Aloys N. Mvuma received a BSc in Electrical Engineering degree from the University of Dar es Salaam in 1994, an MSc in Information Science from Shimane University, Japan, and a Doctor of Engineering (Systems Engineering) from Hiroshima University, Japan in 2003. He is currently an Associate Professor at Mbeya University of Science and Technology. His research interests include adaptive signal processing, digital communication systems, and information communication technologies for development. He has published over 20 IEEE conference papers and various journal papers. He is a registered member of the Engineers Registration Board (ERB) and the Institute of Electrical and Electronic Engineers (IEEE). Email: [email protected]

Salehe I. Mrutu

Salehe I. Mrutu received his B.Sc. and M.Sc. degrees in Computer Science from the International University of Africa (IUA) in 2003 and the University of Gezira in 2006 respectively. In 2014, He obtained his PhD in Information and Communication Science and Engineering from the Nelson Mandela African Institution of Science and Technology (NM-AIST) in Arusha, Tanzania. He is currently serving as a lecturer at The University of Dodoma (UDOM) under the College of Informatics and Virtual Education. His research interests include signal processing, artificial intelligence, forward error correction (FEC) codes, quality-of-service provisioning, and resource management for multimedia communications networks. Email: [email protected]