CN112769462A - Millimeter wave MIMO broadband channel estimation method based on joint parameter learning - Google Patents

Millimeter wave MIMO broadband channel estimation method based on joint parameter learning Download PDF

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CN112769462A
CN112769462A CN202110016400.1A CN202110016400A CN112769462A CN 112769462 A CN112769462 A CN 112769462A CN 202110016400 A CN202110016400 A CN 202110016400A CN 112769462 A CN112769462 A CN 112769462A
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程龙
伍怡
岳光荣
李少谦
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University of Electronic Science and Technology of China
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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

Millimeter wave MIMO broadband channel estimation method based on joint parameter learning
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:
Figure BDA0002886845420000021
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:
Figure BDA0002886845420000022
wherein,
Figure BDA0002886845420000023
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:
Figure BDA0002886845420000024
wherein
Figure BDA0002886845420000025
Representing the equivalent channel gain.
The millimeter wave MIMO time domain channel for the nth antenna is represented as:
Figure BDA0002886845420000031
obtaining a frequency domain channel model of the nth antenna by utilizing Fourier transform
Figure BDA0002886845420000032
Suppose a MIMO-OFDM system has M subcarriers. The space-frequency channel model for all antennas can be expressed as:
Figure BDA0002886845420000033
wherein,
Figure BDA0002886845420000034
is a spatial guide vector that is a vector of the spatial orientation,
Figure BDA0002886845420000035
can be regarded as a frequency-oriented vector, the sign o denotes the hadamard product, fsIs the transmission bandwidth of the OFDM system,
Figure BDA0002886845420000036
can be thought of as a spatial broadband factor matrix, each of which
The items are:
Figure BDA0002886845420000037
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:
Figure BDA0002886845420000038
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:
Figure BDA0002886845420000039
s2, considering sparsity of the millimeter wave channel, expressing the linear spectrum estimation problem as:
Figure BDA0002886845420000041
wherein,
Figure BDA0002886845420000042
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:
Figure BDA0002886845420000043
wherein,
Figure BDA0002886845420000044
representing the estimated number of paths;
minimization function
Figure BDA0002886845420000045
Equal to:
Figure BDA0002886845420000046
wherein,
Figure BDA0002886845420000047
is the iterative function of the ith iteration, diagonal matrix D(i)：
Figure BDA0002886845420000048
S4 obtaining the optimal value by partial derivation
Figure BDA0002886845420000049
Figure BDA00028868454200000410
Obtaining:
Figure BDA00028868454200000411
where η is the regularization parameter;
s5, updating the regularization parameter by the following method:
Figure BDA00028868454200000412
where r is a constant proportionality parameter, ηmaxIndicating an initial parameter, ξ, that makes the problem well-conditioned(i)Is the noise variance:
Figure BDA0002886845420000051
each iteration is to estimate a new AOA so that the cost function is smaller; by using a gradient descent method, newly estimated
Figure BDA0002886845420000052
Comprises the following steps:
Figure BDA0002886845420000053
wherein γ represents a step size;
s6, obtained by iteration
Figure BDA0002886845420000054
The specific steps are as follows:
s61, S4 and S5
Figure BDA0002886845420000055
As an initial value, according to the formula
Figure BDA0002886845420000056
Calculating the value of eta;
s62, retrieve the function:
Figure BDA0002886845420000057
s63, according to the formula
Figure BDA0002886845420000058
Recalculation
Figure BDA0002886845420000059
S64, according to the formula
Figure BDA00028868454200000510
Recalculating new path gains
Figure BDA00028868454200000511
S65, repeating the process from S61 to S64 until
Figure BDA00028868454200000512
S7, mixing Y:,1、
Figure BDA00028868454200000513
Respectively change into
Figure BDA00028868454200000514
τ repeat the process from S1 to S5, from Y1,:To extract the obtained
Figure BDA00028868454200000515
S8, due to
Figure BDA00028868454200000516
And
Figure BDA00028868454200000517
all represent channel gains, only in different order, according to
Figure BDA00028868454200000518
And
Figure BDA00028868454200000519
in the same parameter, rearranging the vectors
Figure BDA00028868454200000520
The gain, angle, and delay of each path are aligned. (ii) a
S9、
Figure BDA00028868454200000521
Wherein
Figure BDA00028868454200000522
Representing the channel gain obtained in the last iteration,
Figure BDA00028868454200000523
representing the final angular vector obtained by iteration and sequential rearrangement,
Figure BDA00028868454200000524
the delay vector is also obtained through iteration and sequential rearrangement. (ii) a
S10, according to the formula
Figure BDA00028868454200000525
And three parameter vectors have been obtained
Figure BDA00028868454200000526
A 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,
Figure BDA0002886845420000061
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:
Figure BDA0002886845420000062
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:
Figure BDA0002886845420000063
s2, the linear spectrum estimation problem is expressed as:
Figure BDA0002886845420000064
wherein,
Figure BDA0002886845420000071
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:
Figure BDA0002886845420000072
wherein,
Figure BDA0002886845420000073
representing the estimated number of paths. Further, minimizing a function
Figure BDA0002886845420000074
Is equal to
Figure BDA0002886845420000075
Wherein,
Figure BDA0002886845420000076
is the iterative function of the ith iteration, diagonal matrix D(i)：
Figure BDA0002886845420000077
S4, obtaining the optimum through partial derivation
Figure BDA0002886845420000078
Figure BDA0002886845420000079
This makes it possible to obtain:
Figure BDA00028868454200000710
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
Figure BDA00028868454200000711
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.
Figure BDA0002886845420000081
Each iteration is to estimate a new AOA so that the cost function is smaller. By using a gradient descent method, newly estimated
Figure BDA0002886845420000082
This gives:
Figure BDA0002886845420000083
wherein gamma represents a step size, and the step size is 0.01;
s6, obtained by iteration
Figure BDA0002886845420000084
The specific steps are as follows;
s61, S4 and S5
Figure BDA0002886845420000085
As an initial value, according to the formula
Figure BDA0002886845420000086
Calculating the value of eta;
s62, retrieve the function:
Figure BDA0002886845420000087
s63, according to the formula
Figure BDA0002886845420000088
Recalculation
Figure BDA0002886845420000089
S64, according to the formula
Figure BDA00028868454200000810
Recalculating new path gains
Figure BDA00028868454200000811
S65, repeating the process from S61 to S64 until
Figure BDA00028868454200000812
S7, mixing Y:,1、
Figure BDA00028868454200000813
Respectively change into
Figure BDA00028868454200000814
τ repeat the process from S1 to S5, from Y1,:Is extracted and found
Figure BDA00028868454200000815
S8, according to
Figure BDA00028868454200000816
And
Figure BDA00028868454200000817
in the same parameter, rearranging the vectors
Figure BDA00028868454200000818
The order of (a);
S9、
Figure BDA00028868454200000819
s10, according to the formula
Figure BDA00028868454200000820
A channel is constructed.
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,
Figure BDA0002886845420000091
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,
Figure BDA0002886845420000092
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 remains less complex than the beam space approachAnd (4) degree. This may be due to the present invention making use of unaliased information in the beam space domain.
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:
Figure FDA0002886845410000011
wherein,
Figure FDA0002886845410000012
representing the equivalent channel gain, αkComplex 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,
Figure FDA0002886845410000013
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:
Figure FDA0002886845410000014
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:
Figure FDA0002886845410000015
wherein,
Figure FDA0002886845410000016
is a spatial guide vector that is a vector of the spatial orientation,
Figure FDA0002886845410000017
is a frequency-oriented vector, symbol
Figure FDA00028868454100000111
Representing the Hadamard product, fsIs the transmission bandwidth of the system and,
Figure FDA0002886845410000018
however, the spatial wideband factor matrix, each of its terms is:
Figure FDA0002886845410000019
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:
Figure FDA00028868454100000110
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:
Figure FDA0002886845410000021
s2, considering sparsity of the millimeter wave channel, expressing the linear spectrum estimation problem as:
Figure FDA0002886845410000022
wherein,
Figure FDA0002886845410000023
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:
Figure FDA0002886845410000024
wherein,
Figure FDA0002886845410000025
representing the estimated number of paths;
minimization function
Figure FDA0002886845410000026
Equal to:
Figure FDA0002886845410000027
wherein,
Figure FDA0002886845410000028
is the iterative function of the ith iteration, diagonal matrix D(i)：
Figure FDA0002886845410000029
S4 obtaining the optimal value by partial derivation
Figure FDA00028868454100000210
Figure FDA00028868454100000211
Obtaining:
Figure FDA0002886845410000031
where η is the regularization parameter;
s5, updating the regularization parameter by the following method:
Figure FDA0002886845410000032
where r is a constant proportionality parameter, ηmaxIndicating an initial parameter, ξ, that makes the problem well-conditioned(i)Is the noise variance:
Figure FDA0002886845410000033
each iteration is to estimate a new AOA so that the cost function is smaller; by using a gradient descent method, newly estimated
Figure FDA0002886845410000034
Comprises the following steps:
Figure FDA0002886845410000035
wherein γ represents a step size;
s6, obtained by iteration
Figure FDA0002886845410000036
The specific steps are as follows:
s61, S4 and S5
Figure FDA0002886845410000037
As an initial value, according to the formula
Figure FDA0002886845410000038
Calculating the value of eta;
s62, retrieve the function:
Figure FDA0002886845410000039
s63, according to the formula
Figure FDA00028868454100000310
Recalculation
Figure FDA00028868454100000311
S64, according to the formula
Figure FDA00028868454100000312
Recalculating new path gains
Figure FDA00028868454100000313
S65, repeating the process from S61 to S64 until
Figure FDA00028868454100000314
S7, mixing Y:,1、
Figure FDA00028868454100000315
Respectively change into
Figure FDA00028868454100000316
τ repeat the process from S1 to S5, from Y1,:To extract the obtained
Figure FDA00028868454100000317
S8, due to
Figure FDA00028868454100000318
And
Figure FDA00028868454100000319
all represent channel gains, only in different order, according to
Figure FDA00028868454100000320
And
Figure FDA00028868454100000321
in the same parameter, rearranging the vectors
Figure FDA0002886845410000041
Aligning the gain, angle, and delay of each path;
S9、
Figure FDA0002886845410000042
wherein
Figure FDA0002886845410000043
Representing the channel gain obtained in the last iteration,
Figure FDA0002886845410000044
representing the angle vector obtained through the last iteration and the sequential rearrangement,
Figure FDA0002886845410000045
is a delay vector obtained through iteration and sequential rearrangement;
s10, according to the formula
Figure FDA0002886845410000046
And three parameter vectors that have been obtained
Figure FDA0002886845410000047
A channel is constructed.
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