CN112769462B - Millimeter wave MIMO broadband channel estimation method based on joint parameter learning - Google Patents
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Abstract
The invention belongs to the field of array signal processing in the communication technology, and particularly relates to a millimeter wave MIMO broadband channel estimation method based on joint parameter learning. The invention is based on a novel millimeter wave large-scale multiple-input multiple-output channel model, extracts channel information from a space domain and a frequency domain through part of received signals, and converts a channel estimation problem into a line spectrum estimation problem. Then, a joint parameter learning algorithm is proposed to estimate all channel parameters. Therefore, the channel can be finally recovered, and the method is a low-complexity and high-performance channel estimation method.
Description
Technical Field
The invention belongs to the field of array signal processing in the communication technology, and particularly relates to a millimeter wave MIMO broadband channel estimation method based on joint parameter learning.
Background
Large-scale multiple-input multiple-output (MIMO) and millimeter-wave (mmWave) are recognized as promising technologies for future fifth generation (5G) wireless communication. In one aspect, the millimeter wave spectrum is capable of providing transmission bandwidths of approximately 2 GHz. On the other hand, massive MIMO may provide high beamforming gain to compensate for path loss of the millimeter wave channel and improve spectrum and energy efficiency. Therefore, mmWave massive MIMO systems can achieve 1000 times the data traffic growth for future 5G cellular networks.
However, the practical implementation of mmWave massive MIMO may not be an easy task. One challenging problem is massive MIMO channel estimation due to the large number of antennas. The conventional solution is to set the beam codeword and then traverse all directions. Although these schemes are computationally inexpensive, they either require frequent feedback of training information or have a high training overhead. In the past few years, many effective channel estimation algorithms have been proposed, taking advantage of the sparse nature of mmWave channels. In particular, the channel estimation problem is translated into a sparse recovery problem using compressed sensing techniques. In addition, by modeling the received signal as a third order tensor, all channel parameters can be obtained based on a scheme of tensor decomposition. In fact, most of the existing research is based on conventional MIMO channel models, simply assuming that the channel size is large. However, if the number of antennas is large and the transmission bandwidth is very wide, different antenna elements will receive different symbols at the same sampling time. This phenomenon, known as beam squint in the field of array signal processing, produces a spatial broadband effect for mmWave massive MIMO systems. There are studies that propose a novel channel model in which the spatial broadband effect is taken into account. However, existing channel estimation schemes have high computational complexity and require sampling data from all antennas.
Disclosure of Invention
The invention aims to provide a millimeter wave MIMO low-complexity broadband channel estimation method based on joint parameter learning. The invention considers that a method with low complexity is designed to be suitable for engineering design, and meanwhile, the robustness of channel estimation needs to be improved on the basis of coping with the broadband effect.
The invention provides a millimeter wave MIMO low-complexity broadband channel estimation scheme based on joint parameter learning based on a novel millimeter wave large-scale MIMO channel model. In particular, by extracting channel information from the spatial and frequency domains. The channel estimation problem is converted into a line spectrum estimation problem. Then, a joint parameter learning algorithm is proposed to estimate all channel parameters. Therefore, the channel can be finally recovered, and the method is a low-complexity and high-performance channel estimation method.
The core idea of the invention is that the channel estimation problem is converted into a two-dimensional linear spectrum estimation problem, and channel parameters are extracted from the received signals by using a joint parameter learning algorithm.
For ease of understanding, the model used in the present invention is first introduced:
the method is used for the millimeter wave channel model considering the space broadband effect. In a millimeter-wave massive MIMO system with Uniform Linear Arrays (ULAs), a Base Station (BS) has N antennas, and a Mobile Station (MS) is equipped with 1 antenna. For each example, consider a millimeter wave orthogonal frequency division multiple access (OFDM) transmission scheme. Tau isk,nIndicating the k-th path from the MS to the n-th antenna of the BS. The baseband time domain signal received by the nth antenna can be represented as:
where K is the number of independent physical paths, αkRepresenting the complex gain of the k-th path, x (t) being the transmitted baseband signal, fcRepresenting the carrier frequency. Based on array signal theory, we have:
wherein,representing the time delay, tau, of adjacent antennask,1Can be regarded as a multipath time delay, abbreviated as tauk,θkIndicates the angle of arrival (AOA) of the kth path, d is the antenna spacing, and c indicates the speed of light.
Thus, the received signal can be described as:
The millimeter wave MIMO time domain channel for the nth antenna is represented as:
obtaining a frequency domain channel model of the nth antenna by utilizing Fourier transform
Suppose a MIMO-OFDM system has M subcarriers. The space-frequency channel model for all antennas can be expressed as:
can be regarded as a frequency-oriented vector, the sign o denotes the hadamard product, fsIs the transmission bandwidth of the OFDM system,can be thought of as a spatial broadband factor matrix, each of which
The items are:
the technical scheme of the invention is as follows:
a low-complexity broadband channel estimation method based on a combined parameter learning millimeter wave large-scale MIMO system is characterized in that a channel estimation problem is converted into a two-dimensional linear spectrum estimation problem, and a spatial broadband channel is finally recovered based on comprehensive perception of channel estimation, and comprises the following steps:
s1, acquiring the sample data from only the first antenna of the BS, and the MS transmits 1 to the BS, simplifying the received data to:
wherein, Y1,:A first row representing a received frequency domain signal, n being an additive white gaussian noise vector; the sampling data of the first subcarrier is as follows:
s2, considering sparsity of the millimeter wave channel, expressing the linear spectrum estimation problem as:
wherein,respectively, estimated channel gain and estimated spatial steering matrix, epsilon represents error tolerance;
s3, by substituting a logarithmic sum function and a data fitting term for l0Norm, further representing the problem of step S2 as an unconstrained optimization problem:
Obtaining:
where η is the regularization parameter;
s5, updating the regularization parameter by the following method:
where r is a constant proportionality parameter, ηmaxIndicating an initial parameter, ξ, that makes the problem well-conditioned(i)Is the noise variance:
each iteration is to estimate a new AOA so that the cost function is smaller; by using a gradient descent method, newly estimatedComprises the following steps:
wherein γ represents a step size;
S7, mixing Y:,1、Respectively change intoτ repeat the process from S1 to S5, from Y1,:To extract the obtained
S8, due toAndall represent channel gains, only in different order, according toAndin the same parameter, rearranging the vectorsThe gain, angle, and delay of each path are aligned. (ii) a
S9、WhereinRepresenting the channel gain obtained in the last iteration,representing the final angular vector obtained by iteration and sequential rearrangement,the delay vector is also obtained through iteration and sequential rearrangement. (ii) a
S10, according to the formulaAnd three parameter vectors have been obtainedA channel is constructed.
The invention has the beneficial effects that:
aiming at a novel channel model (considering space broadband influence), the method uses a joint parameter learning algorithm, only uses partial antenna receiving information to complete channel estimation, reduces algorithm complexity, and simultaneously improves system robustness in engineering application.
Drawings
FIG. 1 is a graph of Normalized Mean Square Error (NMSE) and computational complexity at different bandwidths;
figure 2 is a graph of normalized mean square error and computational complexity for different antenna numbers.
Detailed Description
The technical solution of the present invention is described in detail below with reference to the embodiments and the accompanying drawings.
Examples
Taking a millimeter wave broadband massive MIMO system as an example,M-N-128, K-3, carrier frequency fc60GHz, comprising the following steps:
s1, only the sampled data from the first antenna is considered, and the MS transmits 1 to the BS, then the received data can be simplified as:
wherein, Y1,:Representing the first row of the received frequency domain signal, n is an additive white gaussian noise vector. The sampling data of the first subcarrier is as follows:
s2, the linear spectrum estimation problem is expressed as:
wherein,respectively representing an estimated channel gain and an estimated space steering matrix, wherein epsilon represents error tolerance and is 0.05;
s3, by substituting a logarithmic sum function and a data fitting term for l0Norm, this problem can be further expressed as an unconstrained optimization problem:
This makes it possible to obtain:
where η is the regularization parameter.
S5, since the regularization parameter η is crucial to controlling the trade-off between sparsity and data fitting error, it can be updated in the following way
Wherein r is a constant proportionality parameter of 0.2, etamaxInitial parameters indicating that the problem was well-conditioned were 0.00008, ξ(i)Is the variance of the noise, i.e.
Each iteration is to estimate a new AOA so that the cost function is smaller. By using a gradient descent method, newly estimatedThis gives:
wherein gamma represents a step size, and the step size is 0.01;
S7, mixing Y:,1、Respectively change intoτ repeat the process from S1 to S5, from Y1,:Is extracted and found
The performance of the method of the invention will be analyzed to further verify the performance of the invention.
Two aspects are used to measure the effectiveness of the algorithm, one is to use a normalized mean square error plot to measure the accuracy of the channel estimate. Another is the complexity of the algorithm using a computational complexity curve metric.
Two scenarios are adopted to embody the superiority of the algorithm. One is the impact on the algorithm at different bandwidths and the other is the impact of different numbers of transmit antennas on the algorithm performance.
Fig. 1 is a graph of Normalized Mean Square Error (NMSE) and computational complexity at different bandwidths, where SNR is 10dB,in the case of P10, the algorithm proposed by the present invention compares the normalized mean square error and the computational complexity with different algorithms. Although the algorithm NMSE provided by the invention is slightly higher than the algorithm based on the beam space, the complexity can be reduced by 88%. When the transmission band is large, conventional compressed sensing-based algorithms such as Orthogonal Matching Pursuit (OMP) do not perform well. Compared with the beam space algorithm, the algorithm can realize 88% complexity reduction and has considerable performance improvement. The result shows that the invention skillfully utilizes the information of space and frequency dimensions and reduces the calculation complexity. Furthermore, when data is sampled from partial antennas (e.g., 100 antennas and 80 antennas), the present algorithm can still effectively estimate the channel, while other algorithms cannot. In addition, in an actual millimeter wave system, the special advantage of the algorithm can be used for reducing the power consumption of the system;
fig. 2 is a graph of normalized mean square error and computational complexity for different antenna counts, where SNR is 10dB,P=10,fsin the case of 1GHz, as the number of antennas increases, the normalized mean square error of the algorithm based on compressed sensing increases rapidly, while the complexity of the algorithm based on beam space increases rapidly, whereas the normalized mean square error of the algorithm of the present invention may even decrease, and the computational complexity increases only slightly. As the number of antennas increases, the performance of the conventional compressed sensing-based algorithm decreases, and the complexity of the beam space algorithm increases rapidly. However, the algorithm of the present invention still remains less complex compared to the beam space approach. This may be due to the invention making use ofUnaliased information in the beam space domain is obtained.
In summary, the present invention provides a new low-complexity wideband channel estimation scheme for the millimeter wave spatial wideband channel model. Simulation results show that compared with the beam space algorithm of a new channel model, the method can reduce the complexity by 88% and has less performance loss. Furthermore, our method can effectively estimate new channels when sampling data from partial antennas, which has a significant advantage in practical millimeter-wave massive MIMO systems.
Claims (1)
1. A millimeter wave MIMO broadband channel estimation method based on joint parameter learning is used for a millimeter wave large-scale MIMO system, wherein a base station BS in the system is provided with N antennas, a mobile station MS is provided with 1 antenna, and the received signal of the nth antenna of the BS is as follows:
wherein,representing equivalent channel gain, x (t) being the transmitted baseband signal, alphakComplex gain, f, of k path representing the n antenna from MS to BScRepresenting the carrier frequency, τk,nDenotes the K-th path from the MS to the n-th antenna of the BS, K being the number of independent physical paths, τkIs the time delay of the multi-path,representing the time delay of adjacent antennas, d is the antenna spacing, c represents the speed of light, thetakRepresenting the arrival angle of the kth path, and lambda is the signal wavelength;
the millimeter wave MIMO time domain channel for the nth antenna of the BS is represented as:
where δ (t) is the impulse function, assuming that the system has M subcarriers, the space-frequency channel model for all antennas is expressed as:
wherein,is a spatial guide vector that is a vector of the spatial orientation,is a frequency-oriented vector, symbolRepresenting the Hadamard product, fsIs the transmission bandwidth of the system and,however, the spatial wideband factor matrix, each of its terms is:
the channel estimation method is characterized by comprising the following steps:
s1, acquiring the sample data from only the first antenna of the BS, and the MS transmits 1 to the BS, simplifying the received data to:
wherein, Y1,:A first row representing a received frequency domain signal, n being an additive white gaussian noise vector; the sampling data of the first subcarrier is as follows:
s2, considering sparsity of the millimeter wave channel, expressing the linear spectrum estimation problem as:
wherein,respectively, estimated channel gain and estimated spatial steering matrix, epsilon represents error tolerance;
s3, by substituting a logarithmic sum function and a data fitting term for l0Norm, further representing the problem of step S2 as an unconstrained optimization problem:
Obtaining:
where η is the regularization parameter;
s5, updating the regularization parameter by the following method:
where r is a constant proportionality parameter, ηmaxIndicating an initial parameter, ξ, that makes the problem well-conditioned(i)Is the noise variance:
each iteration is to estimate a new AOA so that the cost function is smaller; by using a gradient descent method, newly estimatedComprises the following steps:
wherein γ represents a step size;
S7, mixing Y:,1、Respectively change intoτ repeat the process from S1 to S5, from Y1,:To extract the obtained
S8, due toAndall represent channel gains, only in different order, according toAndin the same parameter, rearranging the vectorsAligning the gain, angle, and delay of each path;
S9、 whereinRepresenting the channel gain obtained in the last iteration,indicating a final pass through the stackThe angle vectors obtained by the generation and sequential rearrangement,is a delay vector obtained through iteration and sequential rearrangement;
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