Massive multiple input multiple output (MIMO) has become essential for the increase of capacity as the millimeter-wave (mmWave) communication is considered. Also, hybrid beamforming systems have been studied since full-digital beamforming is impractical due to high cost and power consumption of the radio frequency (RF) chains. This paper proposes a hybrid beamforming scheme to improve the spectral efficiency for multi-user MIMO (MU-MIMO) systems. In a frequency selective fading environment, hybrid beamforming schemes suffer from performance degradation since the analog precoder performs the same precoding for all subcarriers. To mitigate performance degradation, this paper uses the average channel covariance matrix for all subcarriers and considers an iterative algorithm to design analog precoder using approximation techniques. The analog precoder is iteratively updated for each column until it converges. The proposed scheme can reduce errors in the approximating process of the overall spectral efficiency. This scheme can be applied to fully-connected and partially-connected structures. The simulation results show that spectral efficiency performance for the proposed scheme is better than the conventional schemes. The proposed scheme can achieve similar performance with full-digital beamforming by using a sufficiently large number of RF chains. Also, this paper shows that the proposed scheme outperforms other schemes in the frequency selective fading environment. This performance improvement can be achieved in both structures.

Massive MIMO is the key solution in future 5G wireless networks to increase system capacity and data rates [

There are two structures of hybrid beamforming according to different mapping strategies from RF chains to antennas. Fully-connected structure can achieve high beamforming gain since each RF chain is connected to all antennas. However, this structure causes high hardware complexity and power consumption due to the large number of PS. To alleviate this problems, partially-connected structures were proposed in [

One of the main challenges in hybrid beamforming design is to achieve a similar spectral efficiency with the performance of full-digital beamforming. However, there are hardware constraints that degrade performance in a hybrid beamforming system. The optimization of analog precoder is considered as very hard problem with satisfying hardware constraints. Also, the frequency selective fading channel is more challenging since analog precoder is designed equally for the entire band. Hybrid precoding algorithms for wideband systems are very important issue in mmWave communication. Recently, several works have been studied to alleviate the performance degradation from frequency selectivity in [

For the performance improvement, this paper proposes an iterative hybrid precoding scheme that can be applied to both fully-connected and partially-connected structures. The proposed scheme derives an approximated upper-bound of spectral efficiency which is used as the objective function of analog precoding matrix optimization. To obtain a solution, proposed scheme divides the problem into a series of convex sub-problems that are updated iteratively until convergence is achieved. Digital precoder eliminates the inter-user interference (IUI) by using conventional ZF precoding for the effective channel. The schemes in [

This section expresses system model for conventional hybrid beamforming schemes. A block diagram of the system is given in

This paper considers mmWave multi-user massive MIMO hybrid beamforming system. Base station with _{t}_{s}_{u}_{s}_{u}

where _{u}

where

According to the mapping from RF chains to antennas, hybrid beamforming architectures can be categorized into fully-connected and partially-connected structures.

In a fully-connected structure, each RF chain is connected to all antennas using a network of PSs. Then, fully-connected structure can be expressed as follows:

where

Unlike the fully-connected structure, in a partially-connected structure, each of the

where each column vector

MmWave propagation is expected to have limited scattering. In this paper, mmWave propagation environment is modeled as a geometric channel with _{c}_{sc}

where _{t}

where

In this paper, the perfect channel state information (CSI) is assumed.

This paper considers the problem of the hybrid beamforming design to maximize the overall spectral efficiency under a constant modulus constraint

where

In this section, the design of digital and analog precoders for multi-user massive MIMO systems is considered. Then, the comparison between conventional schemes and proposed scheme is described.

In this paper, digital precoder is designed by using conventional ZF precoding to eliminate inter-user interference. The effective channel matrix for subcarrier

where

The proof of the

This paper proposes a scheme to design an analog precoder to maximize

where

where

Then, the column iterative algorithm is used to maximize the sub-objective function

The objective function

Input channel matrix

Generate random initial matrix

Calculate average channel covariance matrix for all subcarriers

Repeat the following process

Calculate positive semi-definite matrix

Set

Update

Go to Step 4 until

Repeat the following process

Calculate the digital precoder

Output analog and digital precoder

When partially-connected structures are considered, analog precoder

where

Then, the

For the partially-connected structure, the precoder design is performed through a similar procedure based on the aforementioned algorithm.

This subsection compares the proposed scheme and the conventional schemes. Conventional schemes in [

The optimal solution to maximize

Simulation results are presented to evaluate the performance of the proposed scheme for multi-user hybrid beamforming systems. In this section, the proposed scheme is compared with full-digital beamforming and conventional hybrid beamforming schemes. All simulations are performed for the MU-MIMO hybrid beamforming systems. The simulated mmWave channel adopts _{c}

_{t}_{u}

_{t}_{u}

_{t}_{u}

This paper proposes an enhanced hybrid beamforming method for multi-user massive MIMO systems. The proposed scheme can be applied to fully-connected and partially-connected structure. This scheme can improve performance by reducing approximation error in the process of approximating the system spectral efficiency. It is shown that the proposed scheme for both structures shows better performance compared to other schemes. Due to the limitations of the analog precoder, frequency selectivity causes significant performance degradation. Nevertheless, the proposed scheme achieves good performance in a frequency selective fading environment that the number of clusters increases. Also, the proposed scheme can achieve near full-digital beamforming performance using RF chains of half the number of transmitting antennas due to large beamforming gain.

The term

where the analog precoder typically satisfies _{t}

where

where