Hybrid precoding is a promising technology for massive multiple-input multiple-output (MIMO) systems. It can reduce the number of radio frequency (RF) chains. However, the power consumption is still very high owing to the large-scale antenna array. In this paper, we propose an energy-efficient precoding scheme based on antenna selection technology. The precoding scheme greatly increases the energy efficiency (EE) of the system. In the first step, we derive an exact closed-form expression of EE. Meanwhile, we further study the relationship between the number of transmit antennas and EE on the basis of the exact closed-form expression of EE. We prove that there exists an optimal value. When the number of transmit antennas equals to the value, the EE of the system can reach the maximum by a proper hybrid precoding scheme. Then, we propose an antenna selection algorithm to select antennas from the transmit antennas. And the number of selected antennas equals to the optimal value. Subsequently, we design the analog precoder based on a codebook to maximize the equivalent channel gain. At last, we further improve the EE by baseband digital precoding. The precoding algorithm we proposed offers a compromise between spectral efficiency (SE) and EE in millimeter wave (mmWave) massive MIMO systems. Finally, simulation results validate our theoretical analysis and show that a substantial EE gain can be obtained over the precoding scheme we proposed without large performance loss.
Millimeter wave band communication recently acquires more and more attention owing to its great advantages [
The contributions existing in this paper are summarized as follows:
An exact closed-form expression of In previous precoding schemes, all the antennas are activated. In this paper, not all the transmit antennas are activated (an antenna is activated, which means the antenna is used to transmit message). Based on channel state information and the exact closed-form expression of In the prior hybrid precoding scheme, we design the analog precoder and the digital precoder according to the channel state information An energy-efficient hybrid precoding scheme for a single user in mmWave systems is developed in this paper. First, we calculate the optimal number of transmit antennas and then the antenna selection algorithm is used to select the subset of transmit antennas. Then, we use the analog precoding scheme to maximize the gain of the equivalent channel between BS and objective users. Furthermore, we use the digital precoding scheme to maximize the
The rest of this paper is organized as follows: Section
Notations: we use the following notation throughout the paper.
In this paper, we consider a downlink SU-MIMO mmWave system where a base station (BS) is equipped with
First,
A mmWave single-user MIMO system.
Since mmWave channels have high free-space path loss, the mmWave propagation can be perfectly characterized by a clustered channel model [
In this paper, we adopt a uniform square planar array with
This section discusses the power consumption model of the downlink single-user MIMO mmWave system. The power consumption model of the system [
First, we consider the relationship between system capacity and signal-to-noise ratio. According to Shannon’s theorem, the relationship between system capacity and SNR can be expressed by the following formula:
Once the antenna set is determined, the corresponding channel matrix is determined. We can define the channel matrix as
The objective of this paper is to select the transmit antenna subset according to channel state information and design the hybrid precoders to maximize the
At first, we would briefly introduce the
Suppose there exists a communication system.
Thus,
Next, we will analyze the effects of the number of transmitted antennas on the EE.
If the power consumption of the mmWave MIMO system can be modeled as the addition of the transmit power
We can take the first derivative of
Then, we take the first derivative of
It is obvious that
We do not know whether
We take the first derivative of (
As mentioned earlier in this paper, if if
That is to say, there exists an optimal number of antenna
Based on the system model and power consumption model that we proposed,
Denote the selected transmit antenna subset as
At first, as we know, there exists an optimal value
Then, an analog precoder is designed to maximize the gains of the equivalent channel, where the equivalent channel
The design of digital precoder will become an easily solved optimization problem with a single variable after the analog precoding. The digital precoding matrix will be designed based on the maximized
The proposed antenna select algorithm and hybrid precoding scheme will be discussed in the next section.
1: 2: Calculate: 3: Update 4: 5: 6: Sort 7: Setting 8: Setting 9: Sort 10: 11:
In this section, a low-complexity antenna select algorithm is proposed which enables the BS to reduce the number of transmit antennas and without large performance loss. The antenna selection algorithm is described as below.
As discussed above,
The pseudocode of the proposed antenna selection algorithm is summarized in Algorithm
In this section, we will discuss the design of the hybrid precoder for the mmWave massive MIMO system under the condition that the transmit antenna subset
As the antenna selection process effectively reduces the number of transmit antennas, the power consumption of the system is reduced. After the antenna subset has been obtained, analog precoding and base band digital precoding will be utilized to improve the
At first, an analog precoding algorithm is proposed to maximize the power of the received signal for the objective user [
Firstly, an analog precoder is designed that is aimed at maximizing the equivalent channel gain and assuming that the base-band precoding matrix
After the analog precoding matrix is obtained, the original optimization problem (
Then, the optimal baseband precoding matrix
In this section, we will discuss the optimal analog precoding matrix
The gain of the equivalent channel can be expressed as
We aim to find an analog precoding matrix
The pseudocode of the proposed analog precoding algorithm is summarized in Algorithm
1: 2: 3: User feed back the index of codebook vector 4: 5: 6: 7:
At the beginning, we set
Then,
The procedure is repeated until
In this section, we discuss the design of digital beamformer to further improve the
There exist many approaches to solve this classical fractional programming problem [
1: 2: 3: Solve the problem ( 4: update 5: If 6: 7:
In Algorithm
According to the knowledge of the determinant, it is obvious that
The problem in (
By solving the KKT conditions of (
1: 2: 3: calculate 4: update 5: if 6: otherwise 7: 8: 9: 10: Calculate 11:
In this section, we present simulation results to evaluate the performance of the proposed algorithm in terms of
Simulation parameters.
Parameters | Value |
---|---|
Number of antennas | 0~180 |
Channel model | IEEE 802.11ad living room |
Number of users | 1 |
Carrier frequency (GHz) | 60 |
Bandwidth | 2.56 |
Power amplifier efficiency |
26 |
Modulation coding scheme | 16PSK, 1/2 turbo codes |
Simulation frames | 20000 |
Number of RF chains | 2~20 |
Figure
SE comparison of different precoding algorithms under different SNRs.
Figure
Figure
The
Figure
Figure
SE comparison of the energy-efficient precoding scheme under different radio frequency chains.
In this paper, an energy-efficient hybrid precoding scheme for single-user mmWave massive MIMO systems was considered. First, we calculate the optimal number of transmit antennas according to the channel state information and then design an antenna selection algorithm to select the antenna to maximize the channel gain. Finally, the
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
This paper is sponsored by the National Natural Science Foundation of China under Grant 61871321, National Science and Technology Major Project under Grant 2016ZX03001016, and Innovation Team Project of Shaanxi Province under Grant 2017KCT-30-02.