CN108881074B - Broadband millimeter wave channel estimation method under low-precision hybrid architecture - Google Patents

Broadband millimeter wave channel estimation method under low-precision hybrid architecture Download PDF

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CN108881074B
CN108881074B CN201810434382.7A CN201810434382A CN108881074B CN 108881074 B CN108881074 B CN 108881074B CN 201810434382 A CN201810434382 A CN 201810434382A CN 108881074 B CN108881074 B CN 108881074B
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CN108881074A (en
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许威
王宇成
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Southeast University
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04L25/0224—Channel estimation using sounding signals
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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Abstract

The invention discloses a broadband millimeter wave channel estimation method under a low-precision hybrid architecture, which optimizes and designs the analog pre-coding and analog combiner of a full frequency band, and respectively optimizes and designs a digital combiner aiming at each subcarrier for broadband channel estimation. Firstly, designing an isotropic analog transceiver, wherein the analog transceiver adopts a fully-connected phase shifter network, and the phases of all phase shifters are uniformly distributed; and then optimally designing a digital combiner with frequency selectivity so as to obtain an optimal channel estimation result. Aiming at a millimeter wave channel with sparse multipath, before optimally designing a digital combiner, the method can find the element position corresponding to the main component of the channel by utilizing Orthogonal Matching Pursuit (OMP), thereby further reducing the complexity of channel estimation. The broadband channel estimator provided by the invention is suitable for a general channel model, and in a mixed-frame multi-antenna system adopting a low-precision analog-to-digital converter, the estimation precision of any channel is greatly improved compared with that of the traditional method.

Description

Broadband millimeter wave channel estimation method under low-precision hybrid architecture
Technical Field
The invention relates to the field of communication, in particular to a method for estimating a broadband millimeter wave channel under a low-precision hybrid architecture.
Background
In the next generation wireless networks, user data traffic will increase dramatically. However, the spectrum resources of the medium and low frequency bands are limited, and it is difficult to meet the user requirements. For this reason, millimeter wave band (mmWave) is being developed and has entered the next generation mobile communication standard, and its abundant spectrum resources have enabled a significant increase in system capacity. However, path loss and shadow fading of mmWave signals are more severe than those of the middle and low frequency bands, so that system capacity is limited by a lower received signal-to-noise ratio (SNR). Therefore, it is necessary to fully utilize the advantages of multi-antenna transmission and use large-scale antenna arrays to improve the system spectrum efficiency. On the other hand, the mmWave wavelength is shorter, and the space required by the large-scale antenna array is greatly saved. Therefore, the large-scale multi-antenna technology and the mmWave transmission technology should be used together, so that the system performance is obviously improved. The traditional large-scale multi-antenna technology requires a large number of radio frequency links to be equipped at the transmitting and receiving ends, and particularly in a broadband mmWave system, the cost and the power consumption are quite high. To reduce the cost and hardware complexity of mmWave large-scale multi-antenna technology systems, hybrid architectures using a small number of radio frequency links are attracting much attention.
In order to perform high performance transmission, channel estimation needs to be performed first. Channel estimation of conventional massive multi-antenna technology systems is itself a challenge. In a hybrid architecture massive multi-antenna technology system, channel estimation becomes more difficult due to the inability to perform pure digital operations. In wideband mmWave multiple antenna systems, high precision analog-to-digital converters (ADCs) are typically costly and power consuming. Therefore, a low-precision ADC needs to be introduced to reduce implementation complexity. However, when a quantization receiver using a low-precision ADC, the channel estimation precision is significantly degraded due to a highly nonlinear quantization operation. Therefore, high-precision channel estimation becomes a challenge in wideband mmWave large-scale multi-antenna technology systems using low-precision ADCs and hybrid architectures.
Disclosure of Invention
In order to solve the above problems, the present invention provides a general channel estimation method, which is used in a low-precision ADC and a hybrid-architecture wideband mmWave large-scale multi-antenna technology system. The method is suitable for any channel model by optimally designing the analog transceiver with flat frequency and the digital combiner with frequency selectivity, and the estimation precision is higher than that of the traditional method. If the prior information of sparse channel exists and can be obtained, the invention further reduces quantization noise caused by low-precision ADC by utilizing Orthogonal Matching Pursuit (OMP), thereby obtaining better channel estimation performance.
In order to achieve the purpose, the invention provides the following technical scheme:
a method for estimating a broadband millimeter wave channel under a low-precision hybrid architecture comprises the following steps:
the transmitting end transmits a pilot signal to a receiver, wherein the transmitting and receiving ends use a small number of radio frequency links to match a large-scale antenna array, a mixed digital and analog transmitting and receiving technology is adopted, and the receiving end uses a low-precision ADC;
the hybrid digital and analog transceiving technology comprises analog radio frequency precoding, an analog radio frequency combiner and a digital baseband combiner, wherein the analog radio frequency combiner and the digital baseband combiner are connected by a radio frequency link;
the method is characterized in that: the channel estimation method based on the hardware architecture comprises the following steps:
(1) the transmitting terminal sends a pilot signal, and the pilot signal is optimally designedSimulating precoding and sending the precoding to a receiving end. Analog precoding FAmCalculated according to the following formula:
Figure BDA0001654260120000021
wherein, the [ alpha ], [ beta ]]ijElements representing the ith row and the jth column of the matrix; fAmWith a representation dimension of Nt×NRFtAnalog precoding matrix of, NtRepresenting the number of transmitting antennas, NRFtRepresenting the number of radio frequency links of a transmitting end;
Figure BDA0001654260120000022
the phase of the ith row and jth column element of the analog precoding matrix is represented.
(2) Receiving end optimization design simulation merging matrix WAm。WAmCalculated according to the following formula:
Figure BDA0001654260120000023
wherein, WAmWith a representation dimension of Nr×NRFrAnalog combining matrix of, NrRepresenting the number of receiving antennas, NRFrRepresenting the number of radio frequency links of a receiving end;
Figure BDA0001654260120000024
indicating the phase of the ith row and jth column element of the analog combining matrix.
(3) The receiving end selectively carries out the OMP process according to the prior information of whether the system has channel sparsity or not to obtain a selection matrix Pv[k]。
(4) Receiving end optimization design digital merging matrix corresponding to channel estimation on k sub-carrier
Figure BDA0001654260120000025
Detecting the received signal to obtain the channel estimation value
Figure BDA0001654260120000026
Further, the matrix P is selected in the step (3)v[k]Comprises the following steps:
Figure BDA0001654260120000027
wherein e isπ(i)(π(i)∈{1,2,…,NrNt}) represents a dimension of NrNtThe pi (i) -th element of x 1 is a vector of 1 and the remaining elements are 0.
Further, a matrix P is selectedv[k]The determination depends on whether a priori information of channel sparsity is present in the system. A priori information, i.e. parameter N, e.g. without channel sparsityv＝NrNtThen P isv[k]The values are as follows:
Figure BDA0001654260120000031
with a priori information about the sparsity of the channel, i.e. knowing Nv＜＜NrNtThen obtaining N using OMPvThe position of the non-zero channel coefficients. At this time, Pv[k]By
Figure BDA0001654260120000032
Is determined by the position of the non-zero element(s),
Figure BDA0001654260120000033
calculated by the following formula:
Figure BDA0001654260120000034
Figure BDA0001654260120000035
wherein,
Figure BDA0001654260120000036
with a representation dimension of NrNtSparse channel vector of x 1, | | | | non-woven voicel(l ═ 1,2) represents the vector l-norm; y [ k ]]With a representation dimension of MNRFrA received signal after a x 1 low precision ADC; and e represents the OMP algorithm stopping threshold, and the value can be taken as the variance value of the equivalent noise in the system.
Further, the optimal number merging matrix in the step (4)
Figure BDA0001654260120000037
The design criterion of (2) may be channel estimation mean square error minimization.
Further, if the minimum mean square error criterion is used,
Figure BDA0001654260120000038
it can be calculated as follows:
Figure BDA0001654260120000039
wherein K ∈ {1,2, …, K } denotes the kth subcarrier, K denotes the total number of subcarriers;
Figure BDA00016542601200000310
representing the dimension MN on the k sub-carrierRFr×NvM denotes the number of channel estimations in the method, NvRepresenting a dimension of N on the k-th subcarrierrNtVector component h of x 1 channel vector projected onto angular domainv[k]The number of medium non-zero elements; etabRepresents a distortion factor related to the ADC quantization bit number b; omega k]Denotes the dimension on the k sub-carrier as MNRFr×NvThe measurement matrix of (2);
Figure BDA00016542601200000311
representing the variance of each element of the equivalent noise vector;
Figure BDA00016542601200000312
represents the large scale fading coefficient of the channel;
Figure BDA00016542601200000316
with a representation dimension of Nv×NvThe identity matrix of (2).
Further, the minimum value of M is determined by the following formula:
Figure BDA00016542601200000313
wherein,
Figure BDA00016542601200000315
indicating rounding up.
Further, the channel vector component h projected onto the angular domainv[k]Calculated according to the following formula:
Figure BDA00016542601200000314
wherein A istWith a representation dimension of Nt×NtIs responsive to a transmit dictionary matrix formed of vectors,
Figure BDA0001654260120000041
representation matrix AtConjugation of (1);
Figure BDA0001654260120000042
represents the kronecker product; a. therWith a representation dimension of Nr×NrA receiving dictionary matrix composed of array response vectors; h [ k ]]Denotes the dimension N on the k sub-carrierr×NtVec (H [ k ]) of]) Is a matrix H [ k ]]The vectorization of (c).
Further, AtExpressed as:
Figure BDA0001654260120000043
wherein,
Figure BDA0001654260120000044
with a representation dimension of NtX 1 transmit array response vector, where
Figure BDA0001654260120000045
Further, ArExpressed as:
Figure BDA0001654260120000046
wherein,
Figure BDA0001654260120000047
with a representation dimension of NrX 1 transmit array response vector, where
Figure BDA0001654260120000048
Further, Ω [ k ] is represented as:
Figure BDA0001654260120000049
wherein, phi [ k]With a representation dimension of MNRFr×NrNtThe pilot correlation matrix of (a); pv[k]With a representation dimension of NrNt×NvThe selection matrix of (2).
Further, Φ [ k ] is represented as:
Figure BDA00016542601200000410
wherein s ism[k](M ∈ {1,2, …, M }) denotes the dimension N at the mth trainingRFrX 1 transmitted pilot vector.
Further, in the above-mentioned case,
Figure BDA00016542601200000411
calculated according to the following formula:
Figure BDA00016542601200000412
wherein,
Figure BDA00016542601200000413
represents an Additive White Gaussian Noise (AWGN) variance; p denotes a transmit pilot power.
Further, in the step (4)
Figure BDA00016542601200000414
Calculated according to the following formula:
Figure BDA00016542601200000415
wherein,
Figure BDA00016542601200000416
representation selection matrix
Figure BDA00016542601200000417
The reverse operation of (1).
Compared with the prior art, the invention has the following advantages and beneficial effects:
the method fully considers the influence of the quantization error of the low-precision ADC on the channel estimation precision, and converts the nonlinear estimation problem under the low-precision ADC into the linear estimation problem. For wideband channel estimation, the present invention uses OFDM modulation to perform frequency domain channel estimation on each narrowband subcarrier. Under a hybrid framework using a small number of RF links, the invention designs an analog pre-coding and hybrid digital/analog combiner, specifically designs the analog pre-coding and the analog combiner for full-band optimization, and designs the digital combiner for each subcarrier respectively, and particularly designs the digital combiner to realize the statistical characteristic based on equivalent noise, wherein the equivalent noise comprises low-precision ADC quantization noise and antenna end AWGN. The invention adopts a channel estimator with minimized mean square error, and is suitable for any channel model. If the prior information of sparse channels exists and can be obtained, before the digital combiner is optimally designed, OMP is used for reducing the dimension of the channel to be estimated, so that the estimation complexity is reduced, and meanwhile, the quantization error caused by low-precision ADC is reduced. Compared with the traditional method, the method has the advantage that the estimation precision of any channel is greatly improved.
Drawings
FIG. 1 is a block diagram of the system of the present invention;
fig. 2 is a graph of Normalized Mean Square Error (NMSE) of channel estimates versus SNR for 3-bit ADC quantization at the receiving end.
Fig. 3 is a graph of channel estimate NMSE versus ADC accuracy for a fixed SNR.
Detailed Description
The technical solutions provided by the present invention will be described in detail below with reference to specific examples, and it should be understood that the following specific embodiments are only illustrative of the present invention and are not intended to limit the scope of the present invention.
The invention provides a broadband millimeter wave channel estimation method under a low-precision hybrid architecture.A transmitting end transmits a pilot signal to a receiving end, wherein the transmitting end and the receiving end both use a small number of radio frequency links to match a large-scale antenna array, so that a hybrid digital and analog transmitting and receiving technology is required to be adopted, and the receiving end uses a low-precision ADC. The hybrid digital and analog transceiving technology comprises an analog radio frequency pre-coding, an analog radio frequency combiner and a digital baseband combiner, wherein the analog radio frequency combiner and the digital baseband combiner are connected by a radio frequency link.
In order to improve the channel estimation precision, the invention optimally designs the analog pre-coding and the analog combiner of the full frequency band, and respectively optimally designs the digital combiner aiming at each subcarrier for the broadband channel estimation. Firstly, designing an isotropic analog transceiver, wherein the analog transceiver adopts a fully-connected phase shifter network, and the phases of all phase shifters are uniformly distributed; and then optimally designing a digital combiner with frequency selectivity so as to obtain an optimal channel estimation result. Aiming at the millimeter wave channel with multipath sparsity, before optimally designing the digital combiner, the invention can find the element position corresponding to the main component of the channel by utilizing OMP (object-to-performance processor), thereby further reducing the complexity of channel estimation. The broadband channel estimator provided by the invention is suitable for a general channel model, and in a mixed-frame multi-antenna system adopting a low-precision ADC, the estimation precision of any channel is greatly improved compared with that of the traditional method.
As shown in fig. 1, the transceiving end is a hybrid architecture, and the transmitting end is designed to perform analog precoding first, so that the pilot signal is transmitted omni-directionally when the channel directivity information is unknown. The receiving end firstly designs an analog combiner, and selects to receive the received signal in an omnidirectional way when the directional information of the channel is unknown. And then, determining whether OMP needs to be carried out or not according to the prior information of whether the system has channel sparsity or not. If the system has prior information of channel sparsity, OMP is performed after the low-precision ADC to reduce quantization noise and reduce channel estimation complexity. And finally, optimally designing a digital combiner to obtain a channel estimation value. By optimally designing the analog transceiving weight with flat frequency and the digital combining weight with frequency selectivity and fully considering the possible sparse characteristic of a millimeter wave channel, the channel estimator provided by the invention can greatly reduce the estimation error caused by the quantization noise of the low-precision ADC, and can obtain good estimation precision for any channel model.
The channel estimation method provided by the invention comprises the following steps:
(1) the transmitting end sends a pilot signal, optimally designs analog precoding for the pilot signal and sends the pilot signal to the receiving end. Analog precoding FAmCalculated according to the following formula:
Figure BDA0001654260120000061
wherein, the [ alpha ], [ beta ]]ijElements representing the ith row and the jth column of the matrix; fAmWith a representation dimension of Nt×NRFtAnalog precoding matrix of, NtRepresenting the number of transmitting antennas, NRFtRepresenting the number of radio frequency links of a transmitting end;
Figure BDA0001654260120000062
i row and j column representing analog precoding matrixThe phase of the element.
(2) Receiving end optimization design simulation merging matrix WAm。WAmCalculated according to the following formula:
Figure BDA0001654260120000063
wherein, WAmWith a representation dimension of Nr×NRFrAnalog combining matrix of, NrRepresenting the number of receiving antennas, NRFrRepresenting the number of radio frequency links of a receiving end;
Figure BDA0001654260120000064
indicating the phase of the ith row and jth column element of the analog combining matrix.
(3) The receiving end selectively carries out the OMP process according to the prior information of whether the system has channel sparsity or not to obtain a selection matrix Pv[k]：
Figure BDA0001654260120000065
Wherein e isπ(i)(π(i)∈{1,2,…,NrNt}) represents a dimension of NrNtThe pi (i) -th element of x 1 is a vector of 1 and the remaining elements are 0. Selection matrix Pv[k]The form of (c) depends on whether a priori information on channel sparsity is available in the system. A priori information, i.e. parameter N, e.g. without channel sparsityv＝NrNtThen P isv[k]The values are as follows:
Figure BDA0001654260120000071
if the system possesses a priori information of channel sparsity, i.e. N is knownv＜＜NrNtThen obtaining N using OMPvThe position of the non-zero channel coefficients. At this time, Pv[k]By
Figure BDA0001654260120000072
Is determined by the position of the non-zero element(s),
Figure BDA0001654260120000073
calculated by the following formula:
Figure BDA0001654260120000074
Figure BDA0001654260120000075
wherein,
Figure BDA0001654260120000076
with a representation dimension of NrNtSparse channel vector of x 1, | | | | non-woven voicel(l ═ 1,2) represents the vector l-norm; y [ k ]]With a representation dimension of MNRFrA received signal after a x 1 low precision ADC; and e represents the OMP algorithm stopping threshold, and the value can be taken as the variance value of the equivalent noise in the system.
(4) Receiving end optimization design digital merging matrix corresponding to channel estimation on k sub-carrier
Figure BDA0001654260120000077
Detecting the received signal to obtain the channel estimation value
Figure BDA0001654260120000078
Figure BDA0001654260120000079
The design criterion of (2) may be channel estimation mean square error minimization. If the minimum mean square error criterion is used,
Figure BDA00016542601200000710
it can be calculated as follows:
Figure BDA00016542601200000711
wherein K ∈ {1,2, …, K } denotes the kth subcarrier, K denotes the total number of subcarriers;
Figure BDA00016542601200000712
representing the dimension MN on the k sub-carrierRFr×NvM denotes the number of channel estimations in the method, NvDenotes the dimension N on the k sub-carrierrNtVector component h of x 1 channel vector projected onto angular domainv[k]The number of medium and non-zero elements; etabRepresents a distortion factor related to the ADC quantization bit number b; omega k]Denotes the dimension on the k sub-carrier as MNRFr×NvThe measurement matrix of (2);
Figure BDA00016542601200000713
representing the variance of each element of the equivalent noise vector;
Figure BDA00016542601200000714
represents the large scale fading coefficient of the channel;
Figure BDA00016542601200000715
with a representation dimension of Nv×NvThe identity matrix of (2). The minimum value of M is determined by the following equation:
Figure BDA00016542601200000716
wherein,
Figure BDA00016542601200000717
indicating rounding up. Channel vector component h projected onto the angular domainv[k]Calculated according to the following formula:
Figure BDA00016542601200000718
wherein A istWith a representation dimension of Nt×NtArray loudspeakerThe transmit dictionary matrix should be composed of vectors,
Figure BDA00016542601200000719
representation matrix AtConjugation of (1);
Figure BDA00016542601200000720
represents the kronecker product; a. therWith a representation dimension of Nr×NrA receiving dictionary matrix composed of array response vectors; h [ k ]]Denotes the dimension N on the k sub-carrierr×NtVec (H [ k ]) of]) Is a matrix H [ k ]]The vectorization of (c). A. thetThe definition is as follows:
Figure BDA0001654260120000081
wherein,
Figure BDA0001654260120000082
with a representation dimension of NtX 1 transmit array response vector, where
Figure BDA0001654260120000083
ArThe definition is as follows:
Figure BDA0001654260120000084
wherein,
Figure BDA0001654260120000085
with a representation dimension of NrX 1 transmit array response vector, where
Figure BDA0001654260120000086
Ω[k]Calculated according to the following formula:
Figure BDA0001654260120000087
wherein, phi [ k]With a representation dimension of MNRFr×NrNtThe pilot correlation matrix of (a); pv[k]With a representation dimension of NrNt×NvThe selection matrix of (2). Phi k]Calculated according to the following formula:
Figure BDA0001654260120000088
wherein s ism[k](M ∈ {1,2, …, M }) denotes the dimension N at the mth trainingRFrX 1 transmitted pilot vector.
Figure BDA0001654260120000089
Calculated according to the following formula:
Figure BDA00016542601200000810
wherein,
Figure BDA00016542601200000811
represents an Additive White Gaussian Noise (AWGN) variance; p denotes a transmit pilot power.
Figure BDA00016542601200000812
Calculated according to the following formula:
Figure BDA00016542601200000813
wherein,
Figure BDA00016542601200000814
representation selection matrix
Figure BDA00016542601200000815
The reverse operation of (1).
As shown in fig. 2, under rayleigh channels, the channel estimation method proposed by the present invention is more accurate than the LMMSE estimator, especially under high SNR. Under a sparse channel, the invention provides the use of OMP, and further improves the channel estimation precision.
As shown in fig. 3, the NMSE decreases monotonically with ADC quantization accuracy for different channels and different estimation methods. Under Rayleigh channels and sparse channels, the precision of the channel estimation method provided by the invention is higher than that of the traditional channel estimation method. In addition, the NMSE of the channel estimation method provided by the invention has different variation trends along with the ADC precision under different channels: under a Rayleigh channel, when the ADC precision is more than 4 bits, the channel estimation error tends to be unchanged; in sparse channels, when the ADC accuracy is greater than 2 bits, the channel estimation accuracy tends to be fixed.
The technical means disclosed in the invention scheme are not limited to the technical means disclosed in the above embodiments, but also include the technical scheme formed by any combination of the above technical features. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and such improvements and modifications are also considered to be within the scope of the present invention.

Claims (10)

1. A broadband millimeter wave channel estimation method under a low-precision hybrid architecture is characterized by comprising the following steps: (1) the transmitting end sends pilot signals, pilot signals are optimally designed to simulate pre-coding and sent to the receiving end, and the simulated pre-coding FAmCalculated according to the following formula:
Figure FDA0002695684610000011
wherein, the [ alpha ], [ beta ]]ijElements representing the ith row and the jth column of the matrix; fAmWith a representation dimension of Nt×NRFtAnalog precoding matrix of, NtRepresenting the number of transmitting antennas, NRFtRepresenting the number of radio frequency links of a transmitting end;
Figure FDA0002695684610000015
representing the phase of the ith row and jth column element of the analog precoding matrix;
(2) receiving end optimization design simulation merging matrix WAm，WAmCalculated according to the following formula:
Figure FDA0002695684610000012
wherein, WAmWith a representation dimension of Nr×NRFrAnalog combining matrix of, NrRepresenting the number of receiving antennas, NRFrRepresenting the number of radio frequency links of a receiving end;
Figure FDA0002695684610000016
representing the phase of the ith row and jth column element of the simulation merging matrix;
(3) the receiving end selectively carries out Orthogonal Matching Pursuit (OMP) process according to the prior information of whether the system has channel sparsity or not to obtain a selection matrix Pv[k]；
(4) Receiving end optimization design digital merging matrix corresponding to channel estimation on k sub-carrier
Figure FDA0002695684610000013
Detecting the received signal to obtain the channel estimation value
Figure FDA0002695684610000014
2. The method for estimating the broadband millimeter wave channel under the low-precision hybrid architecture according to claim 1,
selecting a matrix P in the step (3)v[k]Comprises the following steps:
Figure FDA0002695684610000017
wherein e isπ(i)(π(i)∈{1，2，...，NrNt}) represents a dimension of NrNtThe pi (i) -th element of x 1 is a vector of 1 and the remaining elements are 0.
3. The method for estimating the broadband millimeter wave channel under the low-precision hybrid architecture according to claim 2,
selection matrix Pv[k]The determination depends on whether the system possesses a priori information of channel sparsity, such as no channel sparsity, i.e. parameter Nv＝NrNtThen P isv[k]The values are as follows:
Figure FDA00026956846100000214
with a priori information about the sparsity of the channel, i.e. knowing Nv＜＜NrNtThen obtaining N using OMPvA position of a non-zero channel coefficient, in this case, Pv[k]By
Figure FDA0002695684610000021
Is determined by the position of the non-zero element(s),
Figure FDA0002695684610000022
calculated by the following formula:
Figure FDA0002695684610000023
Figure FDA00026956846100000213
wherein,
Figure FDA0002695684610000024
with a representation dimension of NrNtSparse channel vector of x 1, | | | | non-woven voicel(l ═ 1,2) represents the vector l-norm; y [ k ]]With a representation dimension of MNRFrA received signal after a x 1 low precision ADC; e represents orthogonal matching pursuit OMP algorithm stopping thresholdThe variance value of the equivalent noise in the system can be taken as the value;
m represents the number of channel estimates, η, in the methodbRepresents a distortion factor related to the ADC quantization bit number b;
Φ[k]with a representation dimension of MNRFr×NrNtThe pilot correlation matrix of (a); a. thetWith a representation dimension of Nt×NtIs responsive to a transmit dictionary matrix formed of vectors,
Figure FDA0002695684610000025
representation matrix AtConjugation of (1).
4. The method for estimating the broadband millimeter wave channel under the low-precision hybrid architecture according to claim 3,
the optimal digit merging matrix in the step (4)
Figure FDA0002695684610000026
The design criterion of (2) may be channel estimation mean square error minimization;
if the minimum mean square error criterion is used,
Figure FDA0002695684610000027
it can be calculated as follows:
Figure FDA0002695684610000028
wherein K belongs to {1, 2.,. K } represents the kth subcarrier, and K represents the total number of subcarriers;
Figure FDA0002695684610000029
representing the dimension MN on the k sub-carrierRFr×NvM denotes the number of channel estimations in the method, NvRepresenting a dimension of N on the k-th subcarrierrNtVector component of x 1 channel vector projection onto angular domainAmount hv[k]The number of medium non-zero elements; etabRepresents a distortion factor related to the ADC quantization bit number b; omega k]Denotes the dimension on the k sub-carrier as MNRFr×NvThe measurement matrix of (2);
Figure FDA00026956846100000210
representing the variance of each element of the equivalent noise vector;
Figure FDA00026956846100000211
represents the large scale fading coefficient of the channel;
Figure FDA00026956846100000212
with a representation dimension of Nv×NvThe identity matrix of (2).
5. The method for estimating the broadband millimeter wave channel under the low-precision hybrid architecture according to claim 4,
the minimum value of M is determined by the following equation:
Figure FDA0002695684610000031
wherein,
Figure FDA0002695684610000032
represents rounding up;
channel vector component h projected onto the angular domainv[k]Calculated according to the following formula:
Figure FDA0002695684610000033
wherein A istWith a representation dimension of Nt×NtIs responsive to a transmit dictionary matrix formed of vectors,
Figure FDA0002695684610000034
representation matrix AtConjugation of (1);
Figure FDA0002695684610000035
represents the kronecker product; a. therWith a representation dimension of Nr×NrA receiving dictionary matrix composed of array response vectors; h [ k ]]Denotes the dimension N on the k sub-carrierr×NtVec (H [ k ]) of]) Is a matrix H [ k ]]The vectorization of (c).
6. The method for estimating the wideband millimeter wave channel under the low-precision hybrid architecture according to claim 5, wherein the transmission dictionary matrix is defined as follows:
Atexpressed as:
Figure FDA0002695684610000036
wherein,
Figure FDA0002695684610000037
with a representation dimension of NtX 1 transmit array response vector, where
Figure FDA0002695684610000038
The receiving dictionary matrix is defined as follows:
Arexpressed as:
Figure FDA0002695684610000039
wherein,
Figure FDA00026956846100000310
with a representation dimension of NrX 1 transmit array response vector, where
Figure FDA00026956846100000311
7. The method for estimating the wideband millimeter wave channel under the low-precision hybrid architecture according to claim 6, wherein the measurement matrix Ω [ k ] is represented as:
Figure FDA00026956846100000312
wherein, phi [ k]With a representation dimension of MNRFr×NrNtThe pilot correlation matrix of (a); pv[k]With a representation dimension of NrNt×NvThe selection matrix of (2).
8. The method for estimating the wideband millimeter wave channel under the low-precision hybrid architecture according to claim 7, wherein the pilot correlation matrix Φ [ k ] is represented as:
Figure FDA0002695684610000041
wherein s ism[k](M ∈ {1, 2.., M }) denotes that the dimension at the time of the mth training is NRFrX 1 transmitted pilot vector.
9. The method according to claim 8, wherein the variance of each element of the equivalent noise vector is calculated according to the following formula:
Figure FDA0002695684610000042
calculated according to the following formula:
Figure FDA0002695684610000043
wherein,
Figure FDA0002695684610000044
represents an Additive White Gaussian Noise (AWGN) variance; p denotes a transmit pilot power.
10. The method according to claim 9, wherein the channel estimation value in step (4) is the channel estimation value in the broadband millimeter wave channel under the low-precision hybrid architecture
Figure FDA0002695684610000045
Calculated according to the following formula:
Figure FDA0002695684610000046
wherein,
Figure FDA0002695684610000047
representation selection matrix
Figure FDA0002695684610000048
The reverse operation of (1).
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