<figure><img src="image_12.png" /><figcaption>FIGURE 11. Proposed energy-based antenna selection with lens antenna array (a) Energy-based antenna selection at MT (b) Energy-based antenna selection at BS.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>FIGURE 12. Block diagram of the message passing method proposed in [157].</figcaption></figure>

its sparsity structure or its degree of sparsity. In addition, it is needed to estimate the sparsity ratio in each iteration. The expectation-maximization (EM) method is employed for that purpose. Actually, the cooperation between the LSE and SMP improves the performance of the estimation at each iteration, until the convergence of the algorithm is reached.

## CHANNEL ESTIMATION FOR 3-D LENS SYSTEMS

Most existing channel estimation methods are based on the 2D beamspace channel model. However, some papers consider the more general 3D nature of the beamspace [81], [82], [150]. In [150], the authors proposed an adaptive support detection (ASD)-based channel estimation scheme based on decomposing the 3D beamspace channel estimation problem into several sub-problems. For each sub-problem, the support of a sparse channel component is adaptively detected by exploiting the horizontal and vertical sparsity of the 3D beamspace channel. Then, the influence of each detected channel component is successfully removed before detecting the support of the following channel component. Finally, the non-zero elements of the 3D beamspace channel is estimated with low-complexity.

The structure of beamspace channel was further analyzed in [81] and it was demonstrated that the dominant entries of its matrix form a dual crossing (DC) shape. The authors proposed an iterative DC-based channel estimation scheme with the aim of refining the selection of dominant entries. This scheme outperforms the existing conventional CS algorithms and the above presented ASD. The performance of this scheme was further improved in [82] by mitigating some iterative steps and consequently the computational complexity was reduced.

## DEEP-LEARNING-BASED METHODS

The authors in [158] proposed a deep-learning-based channel estimator for mmWave massive MIMO systems based on learned denoising-based approximate message passing (LDAMP) network. The idea is to exploit a large set of training data to learn the channel structure in order to estimate it. The asymptotic performance of this channel estimation scheme was also analyzed. The LDAMP neural network was shown to provide better performance when compared to CS-based methods even when the receiver is equipped with a small number of RF chains. However, deep-learning-based methods have to be trained on real data in order to be capable of performing well when integrated in transceivers.

## TECHNIQUES FOR WIDEBAND SYSTEMS

The above works did not take into consideration the likely frequency-selective nature of the wideband mmWave channels, and their extension to this case is non-trivial. Indeed, the direction of beams tends to be varying with frequency as the bandwidth and the array size increase, this is called the *beam squint*. Hence, the supports of wideband beamspace channel depend on frequency which complicates their detection.
<figure><img src="image_12.png" /><figcaption>FIGURE 11. Proposed energy-based antenna selection with lens antenna array (a) Energy-based antenna selection at MT (b) Energy-based antenna selection at BS.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>FIGURE 12. Block diagram of the message passing method proposed in [157].</figcaption></figure>

its sparsity structure or its degree of sparsity. In addition, it is needed to estimate the sparsity ratio in each iteration. The expectation-maximization (EM) method is employed for that purpose. Actually, the cooperation between the LSE and SMP improves the performance of the estimation at each iteration, until the convergence of the algorithm is reached.

## CHANNEL ESTIMATION FOR 3-D LENS SYSTEMS

Most existing channel estimation methods are based on the 2D beamspace channel model. However, some papers consider the more general 3D nature of the beamspace [81], [82], [150]. In [150], the authors proposed an adaptive support detection (ASD)-based channel estimation scheme based on decomposing the 3D beamspace channel estimation problem into several sub-problems. For each sub-problem, the support of a sparse channel component is adaptively detected by exploiting the horizontal and vertical sparsity of the 3D beamspace channel. Then, the influence of each detected channel component is successfully removed before detecting the support of the following channel component. Finally, the non-zero elements of the 3D beamspace channel is estimated with low-complexity.

The structure of beamspace channel was further analyzed in [81] and it was demonstrated that the dominant entries of its matrix form a dual crossing (DC) shape. The authors proposed an iterative DC-based channel estimation scheme with the aim of refining the selection of dominant entries. This scheme outperforms the existing conventional CS algorithms and the above presented ASD. The performance of this scheme was further improved in [82] by mitigating some iterative steps and consequently the computational complexity was reduced.

## DEEP-LEARNING-BASED METHODS

The authors in [158] proposed a deep-learning-based channel estimator for mmWave massive MIMO systems based on learned denoising-based approximate message passing (LDAMP) network. The idea is to exploit a large set of training data to learn the channel structure in order to estimate it. The asymptotic performance of this channel estimation scheme was also analyzed. The LDAMP neural network was shown to provide better performance when compared to CS-based methods even when the receiver is equipped with a small number of RF chains. However, deep-learning-based methods have to be trained on real data in order to be capable of performing well when integrated in transceivers.

## TECHNIQUES FOR WIDEBAND SYSTEMS

The above works did not take into consideration the likely frequency-selective nature of the wideband mmWave channels, and their extension to this case is non-trivial. Indeed, the direction of beams tends to be varying with frequency as the bandwidth and the array size increase, this is called the *beam squint*. Hence, the supports of wideband beamspace channel depend on frequency which complicates their detection.
<table><caption>TABLE 5. A comparison among principal channel estimation techniques with lens antenna array.</caption><thead><tr><th>Reference</th><th>Year</th><th>Scenario</th><th>Array Model</th><th>Some Assumptions</th><th>Multiplexing Mode</th><th>2D/3D</th><th>Complexity</th><th>Description</th></tr></thead><tbody><tr><td>Gao et al. [83]</td><td>2017</td><td>U single-antenna users</td><td>DFT</td><td>Channel reciprocity, narrowband</td><td>TDD</td><td>2D</td><td>O(LQ(N<sub>B</sub> + N<sub>f</sub><sup>2</sup>))</td><td>Support detection scheme, only one sparse channel component is considered at each time</td></tr><tr><td>Yang et al. [86]</td><td>2018</td><td>Single-user with lens antenna array</td><td>approximate response</td><td>Path reciprocity, narrowband or wideband, block-fading channel</td><td>TDD or FDD</td><td>2D</td><td>O(N<sub>f</sub><sup>2</sup>)</td><td>Energy detector, then orthogonal training sequences and a correlation detector</td></tr><tr><td>Huang et al. [157]</td><td>2019</td><td>Single-user with lens antenna array</td><td>DFT</td><td>Sparsity ratio to be estimated</td><td>Not specified</td><td>2D</td><td>See section IV. 5 of [158]</td><td>Iterative message passing algorithm combined with least-square estimation</td></tr><tr><td>Gao et al. [150]</td><td>2016</td><td>U single-antenna users</td><td>DFT</td><td>Channel reciprocity, narrowband</td><td>TDD</td><td>3D</td><td>O(LN<sub>f</sub><sup>2</sup>)</td><td>Adaptive support detection then estimation of the non-zero elements</td></tr><tr><td>Gao et al. [84]</td><td>2018</td><td>U single-antenna users</td><td>DFT</td><td>Channel reciprocity, wideband, beam squint</td><td>TDD</td><td>2D</td><td>O(N<sub>B</sub>K<sub>s</sub>L + K<sub>s</sub>M<sub>B</sub>QL + K<sub>s</sub>M<sub>B</sub>QL<sup>2</sup>)</td><td>Successive support detection, the supports of each path at different frequencies are jointly estimated</td></tr><tr><td>Ma et al. [81]</td><td>2017</td><td>U single-antenna users</td><td>DFT</td><td>Channel reciprocity, narrowband</td><td>Not specified</td><td>3D</td><td>O(4QN<sub>f</sub> + 10N<sub>f</sub><sup>2</sup> + 2N<sub>f</sub>)</td><td>Iterative dual crossing method</td></tr><tr><td>Cheng et al. [82]</td><td>2018</td><td>U single-antenna users</td><td>DFT</td><td>Channel reciprocity, narrowband</td><td>TDD</td><td>3D</td><td>O(2QN<sub>f</sub> + 10N<sub>f</sub><sup>2</sup> + N<sub>f</sub>)</td><td>Low-complexity iterative dual crossing method</td></tr><tr><td>He et al. [158]</td><td>2018</td><td>Single-user with a single-antenna</td><td>DFT</td><td>Channel reciprocity, narrowband</td><td>Not specified</td><td>3D</td><td>Not specified</td><td>Learned denoising-based approximate message passing network</td></tr></tbody></table>

The research work in [84] proposed an efficient successive support detection (SSD)-based beamspace channel estimation scheme which is similar to the classical successive interference cancellation for multi-user detection. For each path component of the wideband beamspace channel, a joint estimation of its supports at different frequencies is conducted before removing its contribution and then estimating the remained path components. Finally, a low complexity recovery of the wideband beamspace channel is applied.

**Conclusion:** Table 5 provides a list of existing channel estimation techniques for systems with lens antenna arrays. Most of existing techniques employed the DFT lens array model, the single-carrier transmission and the TDD scheme, and assumed the channel reciprocity and a scenario of multiple single-antenna MTs. In this context, it will be useful to further study the channel estimation problem for wideband communications with different waveforms, also to further explore the path reciprocity assumption for existing works, and finally to consider the more general case of multi-antenna multi-user system. The message passing methods seem promising and worth more extensive research.

## VII. CHANNEL ESTIMATION TECHNIQUES FOR SYSTEMS WITH FEW-BIT ADCS

It is well known that ADCs represent a high power consumption component of mmWave transceivers due to the large bandwidth [159], [160]. This is exacerbated for massive MIMO due to the large number of RF chains [161], where the power consumption of ADCs dominates the total power consumption of the whole RF chain [162]. Fortunately, the power consumption of ADCs is greatly reduced if the resolution is diminished to a few-bits - typically 1 to 4 bits-, hence the proposal for architectures with limited power consumption using low-resolution ADCs, known as few-bit ADCs architectures. An examination of lowering the ADCs's precision

on the system performance was elaborated in [163], and several efforts ushered out the feasibility and benefit of these few-bit ADCs on the system performance compared to high-resolution power-hungry ADCs [161], [164]. Owing to the fact that few-bit ADCs are a strong candidate against high-resolution ADCs for mmWave systems, various works provided the capacity analysis of such tools on mmWave systems [67], [165]. In addition, [166]–[168] delivered some research studies concerning the hybrid mmWave architecture with few-bit ADCs, answering many inquiries about the number of RF chains and the number of ADC's bits required, in which an energy-rate trade-off exists.

The research activity on mmWave channel estimation algorithms for few-bit ADCs architectures is quite recent, and we believe that such efforts are significant enough to be highlighted in this section. In fact, the prime research works on channel estimation for few-bit ADCs focused on the single-user case, yet some works which dealt with the multi-user case were also carried out and illustrated in this section. A pionnering work of Mo et al. focuses on architectures with one-bit ADCs [126]. Sparsity of the channel was exploited to formulate the channel estimation problem as a 1-bit compressive sensing problem which had been already investigated in [169]. Thus, the proposed estimation algorithm - along with much of the proposed estimation algorithms that follow - was guided by the capitalized knowledge on quantized CS techniques [170]–[175] as well as on non-mmWave MIMO channel estimation algorithms for low-resolution receivers [176]–[178].

In the forthcoming subsections, we will explain how channel estimation with few-bit ADCs is applicable for both narrowband and wideband mmWave systems by presenting the research works that have been proposed for this objective. Following that, channel estimation with few-bit ADCs but for non-mmWave systems will be rapidly reviewed to convey the
<table><caption>TABLE 5. A comparison among principal channel estimation techniques with lens antenna array.</caption><thead><tr><th>Reference</th><th>Year</th><th>Scenario</th><th>Array Model</th><th>Some Assumptions</th><th>Multiplexing Mode</th><th>2D/3D</th><th>Complexity</th><th>Description</th></tr></thead><tbody><tr><td>Gao et al. [83]</td><td>2017</td><td>U single-antenna users</td><td>DFT</td><td>Channel reciprocity, narrowband</td><td>TDD</td><td>2D</td><td>O(LQ(N<sub>B</sub> + N<sub>f</sub><sup>2</sup>))</td><td>Support detection scheme, only one sparse channel component is considered at each time</td></tr><tr><td>Yang et al. [86]</td><td>2018</td><td>Single-user with lens antenna array</td><td>approximate response</td><td>Path reciprocity, narrowband or wideband, block-fading channel</td><td>TDD or FDD</td><td>2D</td><td>O(N<sub>f</sub><sup>2</sup>)</td><td>Energy detector, then orthogonal training sequences and a correlation detector</td></tr><tr><td>Huang et al. [157]</td><td>2019</td><td>Single-user with lens antenna array</td><td>DFT</td><td>Sparsity ratio to be estimated</td><td>Not specified</td><td>2D</td><td>See section IV. 5 of [158]</td><td>Iterative message passing algorithm combined with least-square estimation</td></tr><tr><td>Gao et al. [150]</td><td>2016</td><td>U single-antenna users</td><td>DFT</td><td>Channel reciprocity, narrowband</td><td>TDD</td><td>3D</td><td>O(LN<sub>f</sub><sup>2</sup>)</td><td>Adaptive support detection then estimation of the non-zero elements</td></tr><tr><td>Gao et al. [84]</td><td>2018</td><td>U single-antenna users</td><td>DFT</td><td>Channel reciprocity, wideband, beam squint</td><td>TDD</td><td>2D</td><td>O(N<sub>B</sub>K<sub>s</sub>L + K<sub>s</sub>M<sub>B</sub>QL + K<sub>s</sub>M<sub>B</sub>QL<sup>2</sup>)</td><td>Successive support detection, the supports of each path at different frequencies are jointly estimated</td></tr><tr><td>Ma et al. [81]</td><td>2017</td><td>U single-antenna users</td><td>DFT</td><td>Channel reciprocity, narrowband</td><td>Not specified</td><td>3D</td><td>O(4QN<sub>f</sub> + 10N<sub>f</sub><sup>2</sup> + 2N<sub>f</sub>)</td><td>Iterative dual crossing method</td></tr><tr><td>Cheng et al. [82]</td><td>2018</td><td>U single-antenna users</td><td>DFT</td><td>Channel reciprocity, narrowband</td><td>TDD</td><td>3D</td><td>O(2QN<sub>f</sub> + 10N<sub>f</sub><sup>2</sup> + N<sub>f</sub>)</td><td>Low-complexity iterative dual crossing method</td></tr><tr><td>He et al. [158]</td><td>2018</td><td>Single-user with a single-antenna</td><td>DFT</td><td>Channel reciprocity, narrowband</td><td>Not specified</td><td>3D</td><td>Not specified</td><td>Learned denoising-based approximate message passing network</td></tr></tbody></table>

The research work in [84] proposed an efficient successive support detection (SSD)-based beamspace channel estimation scheme which is similar to the classical successive interference cancellation for multi-user detection. For each path component of the wideband beamspace channel, a joint estimation of its supports at different frequencies is conducted before removing its contribution and then estimating the remained path components. Finally, a low complexity recovery of the wideband beamspace channel is applied.

**Conclusion:** Table 5 provides a list of existing channel estimation techniques for systems with lens antenna arrays. Most of existing techniques employed the DFT lens array model, the single-carrier transmission and the TDD scheme, and assumed the channel reciprocity and a scenario of multiple single-antenna MTs. In this context, it will be useful to further study the channel estimation problem for wideband communications with different waveforms, also to further explore the path reciprocity assumption for existing works, and finally to consider the more general case of multi-antenna multi-user system. The message passing methods seem promising and worth more extensive research.

## VII. CHANNEL ESTIMATION TECHNIQUES FOR SYSTEMS WITH FEW-BIT ADCS

It is well known that ADCs represent a high power consumption component of mmWave transceivers due to the large bandwidth [159], [160]. This is exacerbated for massive MIMO due to the large number of RF chains [161], where the power consumption of ADCs dominates the total power consumption of the whole RF chain [162]. Fortunately, the power consumption of ADCs is greatly reduced if the resolution is diminished to a few-bits - typically 1 to 4 bits-, hence the proposal for architectures with limited power consumption using low-resolution ADCs, known as few-bit ADCs architectures. An examination of lowering the ADCs's precision

on the system performance was elaborated in [163], and several efforts ushered out the feasibility and benefit of these few-bit ADCs on the system performance compared to high-resolution power-hungry ADCs [161], [164]. Owing to the fact that few-bit ADCs are a strong candidate against high-resolution ADCs for mmWave systems, various works provided the capacity analysis of such tools on mmWave systems [67], [165]. In addition, [166]–[168] delivered some research studies concerning the hybrid mmWave architecture with few-bit ADCs, answering many inquiries about the number of RF chains and the number of ADC's bits required, in which an energy-rate trade-off exists.

The research activity on mmWave channel estimation algorithms for few-bit ADCs architectures is quite recent, and we believe that such efforts are significant enough to be highlighted in this section. In fact, the prime research works on channel estimation for few-bit ADCs focused on the single-user case, yet some works which dealt with the multi-user case were also carried out and illustrated in this section. A pionnering work of Mo et al. focuses on architectures with one-bit ADCs [126]. Sparsity of the channel was exploited to formulate the channel estimation problem as a 1-bit compressive sensing problem which had been already investigated in [169]. Thus, the proposed estimation algorithm - along with much of the proposed estimation algorithms that follow - was guided by the capitalized knowledge on quantized CS techniques [170]–[175] as well as on non-mmWave MIMO channel estimation algorithms for low-resolution receivers [176]–[178].

In the forthcoming subsections, we will explain how channel estimation with few-bit ADCs is applicable for both narrowband and wideband mmWave systems by presenting the research works that have been proposed for this objective. Following that, channel estimation with few-bit ADCs but for non-mmWave systems will be rapidly reviewed to convey the
<figure><img src="image_14.png" /><figcaption>FIGURE 13. The SU mmWave system with coarse quantization at the receiver in [183].</figcaption></figure>

influence of low-resolution ADCs on channel estimation. In the end, we will present some other aspects of few-bit ADCs, such as capacity, performance under different beamforming schemes, and many more.

## TECHNIQUES FOR NARROWBAND SYSTEMS

Although not realistic for the mmWave channel, the narrow-band assumption can be considered as a starting point of research.

Traditionally, the channel estimation algorithms are based on a beamspace representation of the channel [75], [185] that takes advantage of the limited scattering of the mmWave environment and leads to a problem formulation that is adequate to compressive sensing techniques. In [126], some channel estimation algorithms are compared: The EM algorithm [176], [186], a modified version of EM that uses matching pursuit in lieu of maximum likelihood to exploit channel sparsity, and the generalized approximate message passing (GAMP) algorithm [39]. The latter was shown to have better performance in the low and medium SNR region. An adaptive one-bit CS scheme based on linear programming which does not require full optimization solving at each new measurement is proposed in [184]. New measurements are chosen adaptively with the aim of minimizing the region over which the final full optimization solving is done. However, the algorithm can not be extended to the case of few (> 1) bit ADCs. Furthermore, in this article, oversampling is proposed to improve the channel estimation at low SNRs. The authors in [183] were the first to consider an adaptive CS solution adapted to the mmWave channel with few but > 1 bit ADCs. The problem is formulated as a sparse recovery problem from quantized and noisy measurements, and a modification of the generalized expectation maximization (GEM) algorithm [172], which is a CS algorithm for quantized and noisy measurements, was proposed and shown to provide equivalent or even better (at high SNRs and for average length training sequences) mean square error than the classical CS approach with a fixed dictionary. Figure 13 depicts the SU mmWave system in [183] with coarse quantization at the RX, where the feedback link

is used to deliver the information about the selected training vectors to the TX where we have the codebook of the possible training vectors.

The authors in [182] and [181] presented an algorithm for estimating the AoAs and AoDs of the sparse channel. Instead of using a basis pursuit denoise (BPDN) approach that considers the 1-bit measurements as signals corrupted by noise, they adapted to complex-valued measurements of the binary iterative hard thresholding (BIHT) algorithm described in [187] that takes explicitly the 1-bit nature of the measurement. The algorithm was shown to provide similar performance to BPDN while having lesser complexity. Another channel estimation algorithm for hybrid architecture in the SU scenario was proposed in [180]. The method is based on a modified version of the EM algorithm combined with MMSE estimation and OMP. The results of the proposed algorithm showed a satisfactory estimation error when using the low-resolution ADCs, and that using the high-resolution ADCs doesn't provide that much reduction of MSE. In [125] a channel estimation algorithm for low-resolution mmWave system was provided based on GAMP [188]. The proposed algorithm was compared to other variants of GAMP algorithms like the algorithm in [189] and the EM algorithm in [190], where it was shown that the proposed one-bit GAMP algorithm provides the lowest estimation error compared to these algorithms. Moreover, it was illustrated that the three GAMP-based algorithms perform better than the LSE without quantization. In [124], a mmWave channel estimation algorithm for low-resolution ADCs was proposed, in which the CS formulated estimation of the channel was solved with the aid of the Stein's unbiased risk estimate (SURE) [191] within the GAMP framework and by employing the EM [190]. The resulting EM-SURE-GAMP algorithm was compared to the EM-GAMP algorithm and was shown to exhibit better MSE performance than the latter in the low and high SNR regions.

## TECHNIQUES FOR WIDEBAND SYSTEMS

The work presented so far concentrated on the narrow-band model, which is not a realistic assumption. However, over here we present the few works carried out for the wideband model. In [179] a channel estimation technique was proposed for SISO-OFDM mmWave system with low-resolution ADCs. The authors also developed an efficient data detection algorithm that achieves the Bayesian optimal design limits, and provided a power allocation scheme to reduce the symbol error rate. The results shown in the paper revealed that the proposed schemes perform similarly to an OFDM system with infinite-resolution ADCs. The work presented in [69] proposed a channel estimation algorithm with few-bit ADCs exploiting the sparsity of the channel in both the angle and delay domains. The estimation algorithm is based on the AMP algorithms. In particular, the authors proposed to use the GAMP algorithm detailed in [189] and the VAMP algorithms detailed in [192], [193],
<figure><img src="image_14.png" /><figcaption>FIGURE 13. The SU mmWave system with coarse quantization at the receiver in [183].</figcaption></figure>

influence of low-resolution ADCs on channel estimation. In the end, we will present some other aspects of few-bit ADCs, such as capacity, performance under different beamforming schemes, and many more.

## TECHNIQUES FOR NARROWBAND SYSTEMS

Although not realistic for the mmWave channel, the narrow-band assumption can be considered as a starting point of research.

Traditionally, the channel estimation algorithms are based on a beamspace representation of the channel [75], [185] that takes advantage of the limited scattering of the mmWave environment and leads to a problem formulation that is adequate to compressive sensing techniques. In [126], some channel estimation algorithms are compared: The EM algorithm [176], [186], a modified version of EM that uses matching pursuit in lieu of maximum likelihood to exploit channel sparsity, and the generalized approximate message passing (GAMP) algorithm [39]. The latter was shown to have better performance in the low and medium SNR region. An adaptive one-bit CS scheme based on linear programming which does not require full optimization solving at each new measurement is proposed in [184]. New measurements are chosen adaptively with the aim of minimizing the region over which the final full optimization solving is done. However, the algorithm can not be extended to the case of few (> 1) bit ADCs. Furthermore, in this article, oversampling is proposed to improve the channel estimation at low SNRs. The authors in [183] were the first to consider an adaptive CS solution adapted to the mmWave channel with few but > 1 bit ADCs. The problem is formulated as a sparse recovery problem from quantized and noisy measurements, and a modification of the generalized expectation maximization (GEM) algorithm [172], which is a CS algorithm for quantized and noisy measurements, was proposed and shown to provide equivalent or even better (at high SNRs and for average length training sequences) mean square error than the classical CS approach with a fixed dictionary. Figure 13 depicts the SU mmWave system in [183] with coarse quantization at the RX, where the feedback link

is used to deliver the information about the selected training vectors to the TX where we have the codebook of the possible training vectors.

The authors in [182] and [181] presented an algorithm for estimating the AoAs and AoDs of the sparse channel. Instead of using a basis pursuit denoise (BPDN) approach that considers the 1-bit measurements as signals corrupted by noise, they adapted to complex-valued measurements of the binary iterative hard thresholding (BIHT) algorithm described in [187] that takes explicitly the 1-bit nature of the measurement. The algorithm was shown to provide similar performance to BPDN while having lesser complexity. Another channel estimation algorithm for hybrid architecture in the SU scenario was proposed in [180]. The method is based on a modified version of the EM algorithm combined with MMSE estimation and OMP. The results of the proposed algorithm showed a satisfactory estimation error when using the low-resolution ADCs, and that using the high-resolution ADCs doesn't provide that much reduction of MSE. In [125] a channel estimation algorithm for low-resolution mmWave system was provided based on GAMP [188]. The proposed algorithm was compared to other variants of GAMP algorithms like the algorithm in [189] and the EM algorithm in [190], where it was shown that the proposed one-bit GAMP algorithm provides the lowest estimation error compared to these algorithms. Moreover, it was illustrated that the three GAMP-based algorithms perform better than the LSE without quantization. In [124], a mmWave channel estimation algorithm for low-resolution ADCs was proposed, in which the CS formulated estimation of the channel was solved with the aid of the Stein's unbiased risk estimate (SURE) [191] within the GAMP framework and by employing the EM [190]. The resulting EM-SURE-GAMP algorithm was compared to the EM-GAMP algorithm and was shown to exhibit better MSE performance than the latter in the low and high SNR regions.

## TECHNIQUES FOR WIDEBAND SYSTEMS

The work presented so far concentrated on the narrow-band model, which is not a realistic assumption. However, over here we present the few works carried out for the wideband model. In [179] a channel estimation technique was proposed for SISO-OFDM mmWave system with low-resolution ADCs. The authors also developed an efficient data detection algorithm that achieves the Bayesian optimal design limits, and provided a power allocation scheme to reduce the symbol error rate. The results shown in the paper revealed that the proposed schemes perform similarly to an OFDM system with infinite-resolution ADCs. The work presented in [69] proposed a channel estimation algorithm with few-bit ADCs exploiting the sparsity of the channel in both the angle and delay domains. The estimation algorithm is based on the AMP algorithms. In particular, the authors proposed to use the GAMP algorithm detailed in [189] and the VAMP algorithms detailed in [192], [193],
<table><caption>TABLE 6. Channel estimation algorithms for mmWave systems with few-bit ADCs architectures.</caption><thead><tr><th>Reference</th><th>Year</th><th>Scenario</th><th>Some Assumptions</th><th>Architecture</th><th>UL/DL</th><th>2D/3D</th><th>Complexity</th><th>Description</th></tr></thead><tbody><tr><td>Kaushik et al. [124]</td><td>2018</td><td>Single-user</td><td>Narrowband</td><td>Hybrid</td><td>Not specified</td><td>2D</td><td>O((N<sub>T</sub>N<sub>B</sub>)<sup>2</sup>)</td><td>EM-SURE-GAMP</td></tr><tr><td>Sung et al. [125]</td><td>2018</td><td>Single-user</td><td>Narrowband</td><td>Hybrid</td><td>Not specified</td><td>2D</td><td>Not specified</td><td>1-bit GAMP, provided low estimation error</td></tr><tr><td>Mo et al. [69]</td><td>2018</td><td>Single-user</td><td>Wideband</td><td>Digital</td><td>Not specified</td><td>3D</td><td>O(N<sub>B</sub>N<sub>T</sub>D log(N<sub>B</sub>N<sub>T</sub>D))</td><td>AMP, showed that few-bit ADCs have a small amount of performance losses compared to infinite-precision ADCs</td></tr><tr><td>Wang et al. [179]</td><td>2017</td><td>Single-user or multi-user</td><td>Wideband</td><td>Digital</td><td>UL or DL</td><td>Not specified</td><td>O(K<sub>s</sub> log<sub>2</sub>(K<sub>s</sub>))</td><td>Performed similarly to an OFDM system with infinite-resolution ADCs</td></tr><tr><td>Rodriguezfernandez et al. [180]</td><td>2016</td><td>Single-user</td><td>Narrowband</td><td>Hybrid</td><td>Not specified</td><td>2D</td><td>Not specified</td><td>Modified EM, showed a satisfactory estimation error</td></tr><tr><td>Dong et al. [181]</td><td>2016</td><td>Single-user</td><td>Narrowband</td><td>Digital</td><td>UL</td><td>2D</td><td>Not specified</td><td>Complex BIHT</td></tr><tr><td>Stockle et al. [182]</td><td>2015</td><td>Not specified</td><td>Narrowband</td><td>Digital</td><td>Not specified</td><td>2D</td><td>O(N<sub>Qn</sub>)</td><td>Complex BIHT</td></tr><tr><td>Rusu et al. [183]</td><td>2015</td><td>Single-user</td><td>Narrowband</td><td>Digital</td><td>Not specified</td><td>2D</td><td>O(k log(n/k))</td><td>AGEM, provided equivalent mean square error compared to CS approach</td></tr><tr><td>Rusu et al. [184]</td><td>2015</td><td>Single-user</td><td>Narrowband</td><td>Digital</td><td>Not specified</td><td>2D</td><td>-</td><td>Adaptive 1-bit CS</td></tr><tr><td>Mo et al. [126]</td><td>2014</td><td>Single-user</td><td>Narrowband</td><td>Digital</td><td>Not specified</td><td>3D</td><td>Not specified</td><td>Modified EM and GAMP, GAMP was shown to have better performance in the low and medium SNR region</td></tr></tbody></table>

they also proposed a training sequence design and an FFT-based implementation that provides low complexity to the estimation process. The results of their paper [69] show that few-bit ADCs incur only small amount of performance losses compared to infinite-precision ADCs. It is worth noting that [69] is an extension of [126] in terms of ADCs precision and channel model, where a narrowband channel was assumed and one-bit ADCs were studied in [126]. Another work dealt with frequency selective channel estimation using 1-bit quantization for a multi-user uplink massive MIMO mmWave system was provided in [194]. A channel estimation algorithm was proposed based on the EM algorithm [176] combined with sparse recovery technique iterative hard thresholding (IHT) [106]. The proposed algorithm was shown to provide a good channel estimation performance through simulation results.

## NON-MMWAVE SYSTEMS

Under different conditions, some works dealt with the acquisition of channel information with the assumption of low-resolution ADCs but not for mmWave systems and channels. Some of these works include, [178] where a joint channel-and-data estimation algorithm for low-precision ADCs system was proposed based on the optimal Bayes estimator, and [195] where the bilinear generalized approximate message passing (BiG-AMP) technique was employed. A recent paper [196] studied channel estimation for multi-user uplink massive MIMO systems with 1-bit spatial sigma-delta ADCs. The authors explain the benefits of using the sigma-delta ADCs in reducing the noise on the signal, where it was shown through simulation results that the sigma-delta modulation reduces the quantization error of the low-resolution ADCs. The authors proposed to use the linear minimum mean squared estimator (LMMSE) to estimate the channel based on the Bussgang decomposition [197] which reformulates the non-linear quantizer model using an equivalent linear model plus quantization noise.

## OTHER ASPECTS OF FEW-BIT ADCS SYSTEMS

Many papers studied the effects of low-resolution ADCs on mmWave systems for different aspects rather than channel estimation, including achievable throughput, achievable capacity, beamforming schemes and types, spectral and

energy efficiency, codebook designs, and many more. One of these works is [198], where the authors studied the effects of low-resolution ADCs in two cases. First, they showed that the capacity of single-user SISO systems can be achieved by combining least-squares channel estimation with joint pilot and data symbols detection. Second, they showed that the use of maximum ratio combining jointly with least-squares channel estimation is adequate for the use of high-order constellation (example 16-QAM) in the case of multi-user uplink massive MIMO system. The authors in [199] provided a performance comparison between a system using hybrid beamforming and a system using digital beamforming, where the comparison was delivered for a multi-user scenario wideband mmWave system. Evaluations exhibited that for systems implementing low-resolution ADCs, the digital beamforming is more spectral and energy efficient than the hybrid one, and can convey a higher rate.

**Conclusion:** The high power cost of the RF chains in mmWave systems raises many questions mainly because a high power-hungry ADC is needed at each RF chain, this high power cost can be mitigated using few-bit ADCs. In this section we have presented the methods that have been proposed for mmWave channel estimation with few-bit ADCs. The popular ones are listed in Table 6. These works studied the narrowband and wideband systems. As we can see, all of them except [179] and [69] considered the narrowband case. Thus, more attention has to be appended for wideband case in the future. Thereafter, we have seen the importance of low-resolution ADCs for non-mmWave systems and some few other aspects of them.

## VIII. DISCUSSION AND OPEN DIRECTIONS OF RESEARCH

In this article, we have provided a comprehensive overview of the state-of-the-art of channel estimation techniques for mmWave systems. A lot of work in this domain was conducted in the past few years as we have seen in the above sections. Existing techniques for hybrid architecture systems, for ones with lens antenna array and for ones with few-bit ADCs are respectively summarized in Tables 2 and 4, 5 and 6. However, a lot of work also remains to be done in order to develop efficient channel estimation techniques for mmWave cellular systems. We list in the following some identified future research directions.
<table><caption>TABLE 6. Channel estimation algorithms for mmWave systems with few-bit ADCs architectures.</caption><thead><tr><th>Reference</th><th>Year</th><th>Scenario</th><th>Some Assumptions</th><th>Architecture</th><th>UL/DL</th><th>2D/3D</th><th>Complexity</th><th>Description</th></tr></thead><tbody><tr><td>Kaushik et al. [124]</td><td>2018</td><td>Single-user</td><td>Narrowband</td><td>Hybrid</td><td>Not specified</td><td>2D</td><td>O((N<sub>T</sub>N<sub>B</sub>)<sup>2</sup>)</td><td>EM-SURE-GAMP</td></tr><tr><td>Sung et al. [125]</td><td>2018</td><td>Single-user</td><td>Narrowband</td><td>Hybrid</td><td>Not specified</td><td>2D</td><td>Not specified</td><td>1-bit GAMP, provided low estimation error</td></tr><tr><td>Mo et al. [69]</td><td>2018</td><td>Single-user</td><td>Wideband</td><td>Digital</td><td>Not specified</td><td>3D</td><td>O(N<sub>B</sub>N<sub>T</sub>D log(N<sub>B</sub>N<sub>T</sub>D))</td><td>AMP, showed that few-bit ADCs have a small amount of performance losses compared to infinite-precision ADCs</td></tr><tr><td>Wang et al. [179]</td><td>2017</td><td>Single-user or multi-user</td><td>Wideband</td><td>Digital</td><td>UL or DL</td><td>Not specified</td><td>O(K<sub>s</sub> log<sub>2</sub>(K<sub>s</sub>))</td><td>Performed similarly to an OFDM system with infinite-resolution ADCs</td></tr><tr><td>Rodriguezfernandez et al. [180]</td><td>2016</td><td>Single-user</td><td>Narrowband</td><td>Hybrid</td><td>Not specified</td><td>2D</td><td>Not specified</td><td>Modified EM, showed a satisfactory estimation error</td></tr><tr><td>Dong et al. [181]</td><td>2016</td><td>Single-user</td><td>Narrowband</td><td>Digital</td><td>UL</td><td>2D</td><td>Not specified</td><td>Complex BIHT</td></tr><tr><td>Stockle et al. [182]</td><td>2015</td><td>Not specified</td><td>Narrowband</td><td>Digital</td><td>Not specified</td><td>2D</td><td>O(N<sub>Qn</sub>)</td><td>Complex BIHT</td></tr><tr><td>Rusu et al. [183]</td><td>2015</td><td>Single-user</td><td>Narrowband</td><td>Digital</td><td>Not specified</td><td>2D</td><td>O(k log(n/k))</td><td>AGEM, provided equivalent mean square error compared to CS approach</td></tr><tr><td>Rusu et al. [184]</td><td>2015</td><td>Single-user</td><td>Narrowband</td><td>Digital</td><td>Not specified</td><td>2D</td><td>-</td><td>Adaptive 1-bit CS</td></tr><tr><td>Mo et al. [126]</td><td>2014</td><td>Single-user</td><td>Narrowband</td><td>Digital</td><td>Not specified</td><td>3D</td><td>Not specified</td><td>Modified EM and GAMP, GAMP was shown to have better performance in the low and medium SNR region</td></tr></tbody></table>

they also proposed a training sequence design and an FFT-based implementation that provides low complexity to the estimation process. The results of their paper [69] show that few-bit ADCs incur only small amount of performance losses compared to infinite-precision ADCs. It is worth noting that [69] is an extension of [126] in terms of ADCs precision and channel model, where a narrowband channel was assumed and one-bit ADCs were studied in [126]. Another work dealt with frequency selective channel estimation using 1-bit quantization for a multi-user uplink massive MIMO mmWave system was provided in [194]. A channel estimation algorithm was proposed based on the EM algorithm [176] combined with sparse recovery technique iterative hard thresholding (IHT) [106]. The proposed algorithm was shown to provide a good channel estimation performance through simulation results.

## NON-MMWAVE SYSTEMS

Under different conditions, some works dealt with the acquisition of channel information with the assumption of low-resolution ADCs but not for mmWave systems and channels. Some of these works include, [178] where a joint channel-and-data estimation algorithm for low-precision ADCs system was proposed based on the optimal Bayes estimator, and [195] where the bilinear generalized approximate message passing (BiG-AMP) technique was employed. A recent paper [196] studied channel estimation for multi-user uplink massive MIMO systems with 1-bit spatial sigma-delta ADCs. The authors explain the benefits of using the sigma-delta ADCs in reducing the noise on the signal, where it was shown through simulation results that the sigma-delta modulation reduces the quantization error of the low-resolution ADCs. The authors proposed to use the linear minimum mean squared estimator (LMMSE) to estimate the channel based on the Bussgang decomposition [197] which reformulates the non-linear quantizer model using an equivalent linear model plus quantization noise.

## OTHER ASPECTS OF FEW-BIT ADCS SYSTEMS

Many papers studied the effects of low-resolution ADCs on mmWave systems for different aspects rather than channel estimation, including achievable throughput, achievable capacity, beamforming schemes and types, spectral and

energy efficiency, codebook designs, and many more. One of these works is [198], where the authors studied the effects of low-resolution ADCs in two cases. First, they showed that the capacity of single-user SISO systems can be achieved by combining least-squares channel estimation with joint pilot and data symbols detection. Second, they showed that the use of maximum ratio combining jointly with least-squares channel estimation is adequate for the use of high-order constellation (example 16-QAM) in the case of multi-user uplink massive MIMO system. The authors in [199] provided a performance comparison between a system using hybrid beamforming and a system using digital beamforming, where the comparison was delivered for a multi-user scenario wideband mmWave system. Evaluations exhibited that for systems implementing low-resolution ADCs, the digital beamforming is more spectral and energy efficient than the hybrid one, and can convey a higher rate.

**Conclusion:** The high power cost of the RF chains in mmWave systems raises many questions mainly because a high power-hungry ADC is needed at each RF chain, this high power cost can be mitigated using few-bit ADCs. In this section we have presented the methods that have been proposed for mmWave channel estimation with few-bit ADCs. The popular ones are listed in Table 6. These works studied the narrowband and wideband systems. As we can see, all of them except [179] and [69] considered the narrowband case. Thus, more attention has to be appended for wideband case in the future. Thereafter, we have seen the importance of low-resolution ADCs for non-mmWave systems and some few other aspects of them.

## VIII. DISCUSSION AND OPEN DIRECTIONS OF RESEARCH

In this article, we have provided a comprehensive overview of the state-of-the-art of channel estimation techniques for mmWave systems. A lot of work in this domain was conducted in the past few years as we have seen in the above sections. Existing techniques for hybrid architecture systems, for ones with lens antenna array and for ones with few-bit ADCs are respectively summarized in Tables 2 and 4, 5 and 6. However, a lot of work also remains to be done in order to develop efficient channel estimation techniques for mmWave cellular systems. We list in the following some identified future research directions.
* Duplexing techniques: At this stage the TDD is considered to be the best choice for mmWave systems. Recently, the FDD have gained more attention thanks to the huge available bandwidth in the mmWave frequency bands. Most of existing channel estimation methods assume that the employed duplexing technique is TDD. To the best of our knowledge, the only exception is the solution proposed in [86] for systems with lens antenna array. Thus it will be useful to come up with solutions that adapt to the FDD case for the three aforementioned system architectures.

* Wideband frequency-selective channels: The wide bandwidth available in the mmWave bands leads inevitably to frequency-selective channels since the different frequency components will experience independent fadings. This problem is traditionally solved by employing appropriate waveforms such as OFDM, filter bank multi-carrier (FBMC) or universal filtered multi-carrier (UFMC), among others, refer to [12] for more details. The channel estimation for wideband problem has been mainly studied for hybrid architecture with OFDM. This area must be further explored to cover all the architectures and all the waveforms in order to propose tailored channel estimation solutions and to try to keep up with the latest advances in this domain.

* Multi-user scenario: The application of mmWave communications to cellular systems implies to consider multi-user communications. This also requires to employ some multiple access scheme such as orthogonal frequency-division multiplexing access, semi-orthogonal multiple access scheme [200], or non-orthogonal multiple access [201]. Most of the above presented works either consider a single-user or several users with single-antenna per user, which is not realistic. The employed multiple access scheme must be taken into consideration in the design of channel estimation techniques. Furthermore, an additional effort must be dedicated to the pilot contamination problem which could limit the number of scheduled users and degrades the channel estimation accuracy.

* Graphical models: The channel estimation problem can be reformulated such as it can be represented in factor graph models which allows to employ the message passing algorithms as a powerful solution. This approach was exploited in the literature especially for the systems with few-bit ADCs where the GAMP is mainly used. It is promising to extend this effort to the other mmWave system architectures, and to other variations of message passing algorithms such as expectation-propagation algorithms and belief-propagation algorithms and their different approximations.

* Machine learning: It is not complicated to collect a large amount of wireless communications data which makes worth investigating if machine learning tools are capable to inspect the structure of the received signal and hence to estimate the mmWave channel.

This idea becomes more legitimate with the recent advances in machine learning fields especially the deep learning which proposes several efficient tools such as deep convolutional neural networks, recurrent neural Networks, and Bayesian neural networks, and their different variations. For the time being, this axe of research was rarely studied, that is why it is deemed as promising and attractive.

* 3D: A 3D channel estimation means that neither the elevation scattering nor the horizontal scattering is neglected. Indeed, it is more practical to know the AoAs and the AoDs in both the horizontal and the vertical plans. A quick look on Tables 2, 4, 5 and 6, shows that few papers studied the 3D channels estimation for mmWave systems with lens antennas arrays. Even in these papers, the 3D estimation was not combined with other assumptions like FDD, wideband channels, different waveforms, path reciprocity, multiple-antenna terminals. This issue must be fixed by introducing new 3D estimation solutions for the hybrid architectures and the ones with few-bit ADCs, and by including other realistic assumptions.

* Antenna array design: Beamforming gains are enabled by antenna arrays which are composed of several antenna elements that can be distributed via different geometrical configuration (linear, planar, circular) [202] and array layouts (uniform and non-uniform) [203]. All existing channels estimation works for hybrid architectures and the ones with few-bit ADCs assume a uniform linear planar geometry of the antenna array. It will be useful to adapt the channel estimation techniques according to the employed array configuration.

* High mobility: Accurate alignment of narrow beams of mmWave transmission is essential to avoid a significant loss in received power in the high mobility scenarios, such as vehicular mmWave systems, since the high mobility will increase the beam training and alignment overhead. In order to establish a stable link between the BS and the MT, the channel estimation, and hence the beam alignment, must be completed or joined with a beam tracking scheme in order to track the variations in AoDs/AoAs at the receiver. Despite the efforts deployed in this area [204], [205], some extensive research is needed to develop practical and fast estimation/tracking algorithms for mmWave channels.

* Quantization errors: In the literature, the beam steering directions are assumed to be quantized, i.e., the AoAs/AoDs are considered discrete against continuous ones in practice, which leads to quantization errors in channel estimation algorithms. The impact of this quantization errors on the performance of existing algorithms must be evaluated and new improved ones must be proposed if necessary.

* Cognitive radio: One solution to increase the spectral efficiency and to reply to the increasing traffic demand
* Duplexing techniques: At this stage the TDD is considered to be the best choice for mmWave systems. Recently, the FDD have gained more attention thanks to the huge available bandwidth in the mmWave frequency bands. Most of existing channel estimation methods assume that the employed duplexing technique is TDD. To the best of our knowledge, the only exception is the solution proposed in [86] for systems with lens antenna array. Thus it will be useful to come up with solutions that adapt to the FDD case for the three aforementioned system architectures.

* Wideband frequency-selective channels: The wide bandwidth available in the mmWave bands leads inevitably to frequency-selective channels since the different frequency components will experience independent fadings. This problem is traditionally solved by employing appropriate waveforms such as OFDM, filter bank multi-carrier (FBMC) or universal filtered multi-carrier (UFMC), among others, refer to [12] for more details. The channel estimation for wideband problem has been mainly studied for hybrid architecture with OFDM. This area must be further explored to cover all the architectures and all the waveforms in order to propose tailored channel estimation solutions and to try to keep up with the latest advances in this domain.

* Multi-user scenario: The application of mmWave communications to cellular systems implies to consider multi-user communications. This also requires to employ some multiple access scheme such as orthogonal frequency-division multiplexing access, semi-orthogonal multiple access scheme [200], or non-orthogonal multiple access [201]. Most of the above presented works either consider a single-user or several users with single-antenna per user, which is not realistic. The employed multiple access scheme must be taken into consideration in the design of channel estimation techniques. Furthermore, an additional effort must be dedicated to the pilot contamination problem which could limit the number of scheduled users and degrades the channel estimation accuracy.

* Graphical models: The channel estimation problem can be reformulated such as it can be represented in factor graph models which allows to employ the message passing algorithms as a powerful solution. This approach was exploited in the literature especially for the systems with few-bit ADCs where the GAMP is mainly used. It is promising to extend this effort to the other mmWave system architectures, and to other variations of message passing algorithms such as expectation-propagation algorithms and belief-propagation algorithms and their different approximations.

* Machine learning: It is not complicated to collect a large amount of wireless communications data which makes worth investigating if machine learning tools are capable to inspect the structure of the received signal and hence to estimate the mmWave channel.

This idea becomes more legitimate with the recent advances in machine learning fields especially the deep learning which proposes several efficient tools such as deep convolutional neural networks, recurrent neural Networks, and Bayesian neural networks, and their different variations. For the time being, this axe of research was rarely studied, that is why it is deemed as promising and attractive.

* 3D: A 3D channel estimation means that neither the elevation scattering nor the horizontal scattering is neglected. Indeed, it is more practical to know the AoAs and the AoDs in both the horizontal and the vertical plans. A quick look on Tables 2, 4, 5 and 6, shows that few papers studied the 3D channels estimation for mmWave systems with lens antennas arrays. Even in these papers, the 3D estimation was not combined with other assumptions like FDD, wideband channels, different waveforms, path reciprocity, multiple-antenna terminals. This issue must be fixed by introducing new 3D estimation solutions for the hybrid architectures and the ones with few-bit ADCs, and by including other realistic assumptions.

* Antenna array design: Beamforming gains are enabled by antenna arrays which are composed of several antenna elements that can be distributed via different geometrical configuration (linear, planar, circular) [202] and array layouts (uniform and non-uniform) [203]. All existing channels estimation works for hybrid architectures and the ones with few-bit ADCs assume a uniform linear planar geometry of the antenna array. It will be useful to adapt the channel estimation techniques according to the employed array configuration.

* High mobility: Accurate alignment of narrow beams of mmWave transmission is essential to avoid a significant loss in received power in the high mobility scenarios, such as vehicular mmWave systems, since the high mobility will increase the beam training and alignment overhead. In order to establish a stable link between the BS and the MT, the channel estimation, and hence the beam alignment, must be completed or joined with a beam tracking scheme in order to track the variations in AoDs/AoAs at the receiver. Despite the efforts deployed in this area [204], [205], some extensive research is needed to develop practical and fast estimation/tracking algorithms for mmWave channels.

* Quantization errors: In the literature, the beam steering directions are assumed to be quantized, i.e., the AoAs/AoDs are considered discrete against continuous ones in practice, which leads to quantization errors in channel estimation algorithms. The impact of this quantization errors on the performance of existing algorithms must be evaluated and new improved ones must be proposed if necessary.

* Cognitive radio: One solution to increase the spectral efficiency and to reply to the increasing traffic demand
is to combine cognitive radio and mmWave communica-
tions, this perspective had been studied in several recent
research works [206]–[208]. In this context, the problem
of joint channel estimation and spectrum sensing for
the secondary and the primary users must be further
investigated.

IX. CONCLUSION

This survey will serve as a useful review of the state-of-the-
art of channel estimation techniques for mmWave massive
MIMO communication systems. The systems design and the
channel characteristics to be taken into consideration were
first explained. Afterwards, we treated with a casual and
non-analytical way the principal channel estimation meth-
ods so as to provide an essential knowledge on each one
among them. This treatment was applied to the three main
mmWave system architectures namely the hybrid architec-
ture, the lens antenna array one, and the one with few-bit
ADCs. However, the reader is recommended to further dig
for more understanding of the details of each method.

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[25] *Deutsche Telekom and Huawei Complete World's First 5G High mmWave Technology over-the-air Field Tests*, Huawei, Shenzhen, China, Feb. 2018. [Online]. Available: https://www.huawei.com/en/press-events/news/2018/2/DectschTelcko m-5G-High-mmWave-Technology*

[26] M. Marcus and B. Pattan, "Millimeter wave propagation: Spectrum management implications," *IEEE Microw. Mag.*, vol. 6, no. 2, pp. 54–62, Jun. 2005.

[27] X. Zhang and J. G. Andrews, "Downlink cellular network analysis with multi-slope path loss models," *IEEE Trans. Commun.*, vol. 63, no. 5, pp. 1881–1894, May 2015.

[28] S. Sun, G. R. MacCartney, and T. S. Rappaport, "Millimeter-wave distance-dependent large-scale propagation measurements and path loss models for outdoor and indoor 5G systems," in *Proc. 10th Eur. Conf. Antennas Propag. (EuCAP)*, Davos, Switzerland, 2016, pp. 1–5.

[29] M. R. Akdeniz et al., "Millimeter wave channel modeling and cellular capacity evaluation," *IEEE J. Sel. Areas Commun.*, vol. 32, no. 6, pp. 1164–1179, Jun. 2014.

[30] T. S. Rappaport, G. R. MacCartney, M. K. Samimi, and S. Sun, "Wideband millimeter-wave propagation measurements and channel models for future wireless communication system design," *IEEE Trans. Commun.*, vol. 63, no. 9, pp. 3029–3056, Sep. 2015.

[31] Y. Banday, G. Mohammad Rather, and G. R. Begh, "Effect of atmospheric absorption on millimetre wave frequencies for 5G cellular networks," *IET Commun.*, vol. 13, no. 3, pp. 265–270, Feb. 2019.

[32] D. Nandi and A. Maitra, "Study of rain attenuation effects for 5G Mm-wave cellular communication in tropical location," *IET Microw. Antennas Propag.*, vol. 12, no. 9, pp. 1504–1507, Jul. 2018.

[33] H. Zhao et al., "28 GHz millimeter wave cellular communication measurements for reflection and penetration loss in and around buildings in New York City," in *Proc. IEEE Int. Conf. Commun. (ICC)*, Budapest, Hungary, 2013, pp. 5163–5167.

[34] Z. Pi and F. Khan, "An introduction to millimeter-wave mobile broadband systems," *IEEE Commun. Mag.*, vol. 49, no. 6, pp. 101–107, Jun. 2011.

[35] "5G spectrum public policy position," Huawei Technol., Shenzhen, China, Rep., 2017.
is to combine cognitive radio and mmWave communica-
tions, this perspective had been studied in several recent
research works [206]–[208]. In this context, the problem
of joint channel estimation and spectrum sensing for
the secondary and the primary users must be further
investigated.

IX. CONCLUSION

This survey will serve as a useful review of the state-of-the-
art of channel estimation techniques for mmWave massive
MIMO communication systems. The systems design and the
channel characteristics to be taken into consideration were
first explained. Afterwards, we treated with a casual and
non-analytical way the principal channel estimation meth-
ods so as to provide an essential knowledge on each one
among them. This treatment was applied to the three main
mmWave system architectures namely the hybrid architec-
ture, the lens antenna array one, and the one with few-bit
ADCs. However, the reader is recommended to further dig
for more understanding of the details of each method.

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