CN112953864B - Honeycomb-free hybrid large-scale MIMO system channel estimation method for protecting privacy - Google Patents
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Abstract
The invention discloses a method for estimating a channel of a honeycomb-free hybrid large-scale MIMO system for protecting privacy, which is suitable for the field of communication. Each AP obtains an incomplete baseband signal sampling matrix for channel estimation by establishing an uplink signal transmission model and a mixed structure sampling model; designing a privacy protection matrix completion algorithm, taking an incomplete baseband signal sampling matrix obtained by each AP as input, and outputting a complete matrix by each AP while protecting the position privacy of a user; each AP carries out channel estimation according to the output complete matrix and the known pilot frequency matrix, thereby achieving the best channel estimation performance while effectively protecting the privacy of the single-antenna user position. The method can well protect the position privacy of the user and simultaneously obtain good channel estimation performance.
Description
Technical Field
The invention relates to the technical field of wireless communication, in particular to a method for estimating a channel of a non-cellular hybrid large-scale MIMO system for protecting privacy.
Background
A non-cellular hybrid large-scale Multiple Input Multiple Output (MIMO) system usually has a large number of Access Points (APs) distributed in a region, and uses the same time-frequency resources to cooperatively serve users. To reduce the high cost associated with equipping each antenna with a Radio Frequency (RF) chain containing a high resolution analog-to-digital converter, systems typically employ a hybrid analog/digital architecture, in which the antennas are typically randomly connected to a small number of RF chains in an analog combination based on switches or phase shifters.
In order to implement a large-scale MIMO system without cellular mixing, it is important to acquire Channel State Information (CSI). In order to obtain a better channel estimation result, each AP needs to send the received signal observed by each AP to a Central Processing Unit (CPU) for uniform processing, and the CPU performs channel estimation and data detection on all users. However, this is highly likely to cause the positional information of the user to leak to the CPU. Since large-scale fading in CSI highly depends on the distance between a user and an AP, and the AP location is generally fixed, theoretically, a CPU has the capability of estimating the user location after obtaining CSI between a certain user and three or more APs, and thus leakage of user location information may occur. Therefore, how to provide accurate channel estimation under the premise of protecting the privacy of the user position is a crucial problem, and no suitable solution exists in the prior art.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the defects of the prior art, the invention provides a privacy-protecting channel estimation method of a honeycomb-free hybrid large-scale MIMO system, which can effectively protect the position privacy of a user, aims to estimate a channel and protect the position privacy of the user,
The technical scheme is as follows: in order to achieve the technical purpose, the invention provides a method for estimating a channel of a non-cellular hybrid massive MIMO system for protecting privacy, which comprises the following steps:
s1, establishing an uplink signal transmission model and a mixed structure sampling model of a non-cellular mixed large-scale MIMO system, and obtaining an incomplete baseband signal sampling matrix for channel estimation by each AP;
s2, designing a privacy protection matrix completion algorithm, wherein the algorithm takes an incomplete baseband signal sampling matrix obtained by each AP as input, and each AP outputs a complete matrix while protecting the position privacy of a user;
and S3, each AP carries out channel estimation according to the output complete matrix and the known pilot frequency matrix, so that the privacy of the position of the single-antenna user is effectively protected and the optimal channel estimation performance is achieved.
The step S1 specifically includes:
by using
Representing a set of APs, utilizing
Representing a set of single antenna users; within the coherence intervalThe set of time slots is represented as
Wherein front τ is p One slot is used for uplink channel estimation and is represented as
The rest of tau d ＝τ c -τ p One time slot is used for uplink data transmission and is represented as
Using s [ t ]]A vector of transmitted signals representing K single-antenna users in time slot t, wherein
Time s [ t ]]Represents a pilot signal used to estimate the channel when
Time s [ t ]]Representing data symbols containing information; by using
Representing channel vectors of the m-th AP to the k-th single-antenna user, wherein
Representing a complex field;
n on mth AP a Received signal vector of root antenna in time slot t
Expressed as:
wherein
Channel matrix for mth AP to all users, n m [t]Is the noise received by the mth AP at time slot t, subject to mean 0 and variance σ 2 Circularly symmetric complex gaussian distribution of (a);
defining the following matrix
In the formula: r m Represents N at the mth AP a Root antenna at c Received signal matrix of one time slot, N m Represents N at the mth AP a Root antenna at c A received noise matrix of one time slot, P denotes the front tau p Pilot matrix sent by user in one time slot, D represents rear tau d The matrix of data transmitted by the users in one time slot, S represents the total of tau c A signal matrix sent by a user in each time slot comprises pilot frequency and data; wherein N on the mth AP a Root antenna at c The received signal matrix for a time slot is represented as:
each AP adopts a switch-based hybrid structure, and each time slot is from N a Randomly selecting N from root antenna r Root antenna and N r RF-coupled and then converted to baseband signals using high precision analog-to-digital converters, so that the m-th AP receives a signal vector r in time slot t m [t]Total N a Only N in a received signal r The reception signal becomes a baseband signal; let omega m For the set of m-th AP upsampling indexes (n, t), i.e. representing r m [t]N th element of (3) m (n, t) is sampled onto a certain RF and then becomes a baseband signal, let
And the baseband signal sampling matrix of the mth AP meets the following mapping relation:
the mapping table is shown as
It is obvious that Y m Each column having only N r A non-zero baseband signal, therefore Y m Is an incomplete matrix.
The matrix completion algorithm for protecting privacy in step S2 specifically includes:
with incomplete total baseband signal sampling matrix
As input, a complete low rank matrix is output
The low rank matrix completion problem of (a) can be expressed as a least squares problem as shown below
Wherein | · | purple nuc The number of the kernel norms is expressed,
represents the Frobenius norm,
represents a set of sampling indices across all APs; the problem (5) is a convex optimization problem, and the invention designs a matrix completion algorithm for protecting privacy to solve the problem; the matrix completion algorithm for protecting privacy is an iterative algorithm, and each AP m outputs a complete estimation matrix in the nth iteration
And estimating the output estimation matrix of the Tth iteration
As a low rank matrix
The method comprises the following concrete steps:
s31, inputting a specific numerical value of the privacy parameter (epsilon, delta); inputting an algorithm iteration number T; the baseband signal sampling matrix Y of each AP m is input m (ii) a Y is estimated from m Upper bound L of
Wherein beta is k,m Represents the large-scale fading coefficients, σ, of the m-th AP to k-th user channels 2 Representing the channel noise variance;
s32. Initialization
Giving weight values η for T iterations (1) ＝1，η (n) ＝1/T,n≠1，
S33, initializing iteration times, and enabling n =1;
s34, each AP m calculates a signal matrix according to the following formula
Then sending the signal matrix after noise interference to the CPU through an optical fiber return link
Wherein
For randomly generated tau c ×τ c The hermite of (a) perturbs the noise matrix,
subject to mean 0 and variance μ of the upper triangle element and diagonal element, respectively 2 The cyclic symmetric complex gaussian distribution and gaussian distribution of (a), wherein μ is calculated according to the following formula:
s35.CPU accumulates signal matrix sent by each AP m through optical fiber return link
To obtain
First of all, calculate
Maximum eigenvalue of
And corresponding feature vectors
Then correcting according to
S36. The CPU sends the corrected data to all APs through the optical fiber return link
And feature vectors
S37, each AP m is calculated according to the following formula
S38, if n is larger than T, going to S39, otherwise, making n = n +1 and returning to the step S34 for recalculation;
s39, each AP obtains a complete matrix:
as H m And (5) estimating S.
In step S34, the signal matrix including the location privacy information
Before sending to the CPU, in the signal matrix
And a disturbance noise matrix is added for protection, so that the position privacy of a user is protected from being disclosed to a CPU, the variance of disturbance noise is calibrated by using a calculation formula in a formula (9), and the proposed privacy protection matrix completion algorithm strictly realizes the combined differential privacy (belonging to the element and delta).
The step S3 specifically includes:
fetch a complete matrix for each AP m
Front τ of p Column, is marked as
As
Is estimated by the estimation of (a) a,
each AP m calculates its channel H according to m Estimation of (2):
wherein
Representing the pseudo-inverse of P.
Has the advantages that: the method can excavate the low-rank characteristic of the receiving signal matrix under the condition of no receiving noise of the large-scale MIMO, and estimate the channel with lower training overhead by utilizing the low-rank characteristic. In addition, the method applies the differential privacy technology to the channel estimation of the wireless communication system for the first time, and achieves better channel estimation performance while well protecting the position privacy of the user.
Drawings
FIG. 1 is an algorithmic flow diagram of an embodiment of the present invention;
FIG. 2 is a schematic diagram of a hybrid massive MIMO system without cells, in accordance with an embodiment of the present invention;
fig. 3 is a comparison graph of normalized mean square error curves of channel estimates obtained by the method of the embodiment of the present invention and the method of estimating its channel by using only pilots for each AP alone, and the Frank-Wolfe iteration-based matrix completion method without privacy protection.
Detailed Description
The technical solutions of the present invention are further described below with reference to the accompanying drawings and the following embodiments, which should be understood as merely illustrative of the present invention and not limiting the scope of the present invention.
The invention considers a non-cellular hybrid large-scale MIMO system, which is configured with 1 CPU, M APs and K random antennasThe machine is distributed with single antenna users, each AP connected to the CPU through a fiber backhaul link, as shown in fig. 2. Each AP adopts a mixed structure and is provided with N a Root antenna and N r ＜N a An RF link. Are used separately
And
representing the AP and the set of users.
Represents the channel vectors of the m-th AP to the k-th user, where
Representing a complex field. Assuming that the channels between all users and all APs are block-faded, the channel coefficients have τ c The coherence interval of a time slot remains unchanged. The set of slots in the coherence interval is denoted as
Wherein front τ is p One time slot is used for uplink channel estimation and is expressed as
The rest of tau d ＝τ c -τ p One time slot is used for uplink data transmission and is represented as
s[t]A vector of transmitted signals representing K users in time slot t, wherein
Time s [ t ]]Represents a pilot signal used to estimate the channel when
Time s [ t ]]Representing data symbols containing information.
A method for estimating a channel of a non-cellular hybrid massive MIMO system for protecting privacy comprises the following steps:
s1, establishing an uplink signal transmission model and a mixed structure sampling model of a non-cellular mixed large-scale MIMO system, and obtaining an incomplete baseband signal sampling matrix for channel estimation by each AP;
s2, designing a privacy-protecting matrix completion algorithm, wherein the algorithm takes an incomplete baseband signal sampling matrix obtained by each AP as input, and each AP outputs a complete matrix while protecting the privacy of the user position;
and S3, each AP carries out channel estimation according to the output complete matrix and the known pilot frequency matrix, so that the privacy of the position of the single-antenna user is effectively protected and the optimal channel estimation performance is achieved.
N on mth AP a Signal vector received by root antenna in time slot t
Can be expressed as
Wherein
Channel matrix for mth AP to all users, n m [t]Is the noise received by the mth AP at time slot t subject to mean 0 and variance σ 2 Circularly symmetric complex gaussian distribution. The following matrix is defined:
in the formula: r m Represents N at the mth AP a Root antenna at c Received signal matrix of time slots, N m Represents N at the mth AP a Root antenna at c A received noise matrix of one slot, P denotes the front τ p Pilot matrix sent by user in one time slot, D represents rear tau d The matrix of data transmitted by the users in one time slot, S represents the total of tau c The signal matrix sent by the user in each time slot comprises pilot frequency and data. N on mth AP a Root antenna at c The received signal matrix for a time slot may be represented as:
each AP adopts a switch-based hybrid structure, and each time slot is from N a Randomly selecting N in root antenna r Root antenna and N r The RF signals are coupled and then converted to baseband signals by a high precision analog to digital converter. Therefore, the m-th AP receives the signal vector r in the time slot t m [t]Total N a Only N in a received signal r The received signal becomes a baseband signal. Let omega m For the set of m-th AP upsampling indexes (n, t), i.e. representing r m [t]N th element of (3) m (n, t) is sampled onto a certain RF and then becomes a baseband signal. Is provided with
And the baseband signal sampling matrix of the mth AP meets the following mapping relation:
the mapping table is shown as
It is obvious that Y m Each column having only N r A non-zero baseband signal, thus Y m Is an incomplete matrix.
Based on
The invention designs a privacy-protecting channel estimation algorithm, which can improve the accuracy of channel estimation while protecting the privacy of the user position. The algorithm flow is shown in fig. 1, and specifically includes the following steps:
s1, inputting a specific numerical value of a privacy parameter (epsilon, delta); inputting an algorithm iteration number T; inputting baseband signal sampling matrix Y of each AP m m (ii) a Y is estimated from m Upper bound L of
Wherein beta is k,m Represents the large-scale fading coefficients of the m-th AP to k-th user channels, sigma 2 Representing the channel noise variance;
s2. Initialization
Giving weight values η for T iterations (1) ＝1，η (n) ＝1/T,n≠1，
S3, initializing iteration times, and enabling n =1;
s4, each AP m calculates a signal matrix according to the following formula
Then sending the signal matrix after noise interference to the CPU through the optical fiber return link
Wherein
For randomly generated tau c ×τ c The hermite of (a) perturbs the noise matrix,
respectively obeys the mean value of 0 and the variance of mu 2 The cyclic symmetric complex gaussian distribution and gaussian distribution of (a), wherein μ is calculated according to the following formula:
s5.CPU accumulates the signal matrix sent by each AP m through the optical fiber return link
To obtain
First of all, calculate
Maximum eigenvalue of
And corresponding feature vectors
Then according toCorrection of formula
S6. The CPU sends the corrected data to all APs through the optical fiber return link
And feature vectors
S7, calculating each AP m according to the following formula
S8, if n is larger than T, S9 is reached, otherwise, n = n +1 is made and the step S4 is returned to for recalculation;
s9, each AP obtains a complete matrix
As X m ＝H m Estimating S;
s10, taking out each AP m
Front τ of p Column, is marked as
As
(ii) an estimate of (d);
s11. Each AP m calculates its channel H according to the following formula m Is estimated by
Wherein
Representing the pseudo-inverse of P.
Fig. 3 is a comparison graph of normalized mean square error curves of channel estimation obtained by using the channel estimation method (Algorithm 1) for privacy protection of a non-cellular hybrid large-scale multiple-input multiple-output system according to the present embodiment when the radius of a cell is 1km, each AP has 100 APs in the cell, each AP has 2 RF links with 4 antennas, and total 5 users, and the method (PO) for estimating its channel by using only pilots alone for each AP and the matrix completion method (NPFW) based on Frank-Wolfe iteration without privacy protection. The Frank-Wolfe iteration based matrix completion method, in which privacy is not protected, is a theoretical upper bound of this particular embodiment, but it does not have the ability to protect privacy. As can be seen from fig. 3, the channel estimation obtained by the method of the present embodiment is more accurate than the method using pilot estimation alone, and the accuracy of channel estimation can be significantly improved while maintaining a certain privacy level.
Claims (2)
1. A method for estimating a channel of a non-cellular hybrid massive MIMO system for protecting privacy is characterized in that: the cellular-free hybrid large-scale MIMO system comprises 1 baseband central processing unit CPU, M randomly distributed access points AP and K randomly distributed single-antenna users; each AP adopts a mixed structure and is provided with N a Root antenna and N r <N a All APs are connected to the CPU through optical fiber backhaul links; the channels between all single-antenna users and all APs are block-faded with channel coefficients at τ c Within a coherence interval of one time slotKeeping the original shape;
the method comprises the following steps:
s1, establishing an uplink signal transmission model and a mixed structure sampling model of a non-cellular mixed large-scale MIMO system, and obtaining an incomplete baseband signal sampling matrix for channel estimation by each AP;
s2, designing a privacy protection matrix completion algorithm, wherein the algorithm takes an incomplete baseband signal sampling matrix obtained by each AP as input, and each AP outputs a complete matrix while protecting the position privacy of a user;
s3, each AP carries out channel estimation according to the output complete matrix and the known pilot frequency matrix, so that the privacy of the position of the single-antenna user is effectively protected and the optimal channel estimation performance is achieved;
the step S1 specifically includes:
by using
Representing a set of APs, utilizing
Representing a set of single antenna users; the set of slots in the coherence interval is denoted as
Wherein front τ is p One time slot is used for uplink channel estimation and is expressed as
The rest of tau d ＝τ c -τ p One time slot is used for uplink data transmission and is represented as
Using s [ t ]]A vector of transmitted signals representing K single-antenna users in time slot t, wherein
Time s [ t ]]Represents a pilot signal used to estimate the channel when
Time s [ t ]]Representing data symbols containing information; by using
Represents the channel vectors of the m-th AP to the k-th single-antenna user, where
Representing a complex field;
n on mth AP a Received signal vector of root antenna in time slot t
Expressed as:
wherein
Channel matrix for mth AP to all users, n m [t]Is the noise received by the mth AP at time slot t, subject to mean 0 and variance σ 2 Circularly symmetric complex gaussian distribution of (a);
defining the following matrix
In the formula: r m Represents N at the mth AP a Root antenna at c Received signal matrix of one time slot, N m Represents N at the mth AP a Root antenna at c A received noise matrix of one slot, P denotes the front τ p Pilot matrix sent by user in time slot, D represents rear tau d The matrix of data transmitted by the users in one time slot, S represents the total of tau c A signal matrix sent by a user in each time slot comprises pilot frequency and data; wherein N on the mth AP a Root antenna at c The received signal matrix for a time slot is represented as:
each AP adopts a switch-based hybrid structure, and each time slot is from N a Randomly selecting N in root antenna r Root antenna and N r RF-coupled and then converted to baseband signals using high precision analog-to-digital converters, so that the m-th AP receives a signal vector r in time slot t m [t]Total of N a Only N in a received signal r The received signal becomes a baseband signal; let omega m For the set of m-th AP upsampling indexes (n, t), i.e. representing r m [t]N th element of (3) m (n, t) is sampled onto a certain RF and then becomes a baseband signal, let
And the baseband signal sampling matrix of the mth AP meets the following mapping relation:
the mapping table is shown as
Y m Each column having only N r A non-zero baseband signal, thus Y m Is an incomplete matrix;
the matrix completion algorithm for protecting privacy in step S2 specifically includes:
with incomplete total baseband signal sampling matrix
As input, a complete low rank matrix is output
The low rank matrix completion problem of (a) can be expressed as a least squares problem as shown below
Wherein | · | purple nuc The number of the nuclear norms is represented,
represents the Frobenius norm,
represents a set of sampling indices across all APs; problem (5) is a convex optimization problem; the matrix completion algorithm for protecting privacy is an iterative algorithm, and the mth AP of the nth iteration outputs a complete estimation matrix
And estimating the output estimation matrix of the Tth iteration
As a low rank matrix
The method comprises the following concrete steps:
s31, inputting a specific numerical value of the privacy parameter (epsilon, delta); inputting an algorithm iteration number T; inputting the baseband signal sampling matrix Y of the mth AP m (ii) a Y is estimated from m Upper bound L of
Wherein beta is k,m Represents the large-scale fading coefficients, σ, of the m-th AP to k-th user channels 2 Representing the channel noise variance;
s32. Initialization
Giving weight values η for T iterations (1) ＝1，η (n) ＝1/T,n≠1，
S33, initializing iteration times, and enabling n =1;
s34. The mth AP firstly calculates a signal matrix according to the following formula
Then sending the signal matrix after noise interference to the CPU through an optical fiber return link
Wherein
For randomly generated tau c ×τ c The hermite of (a) perturbs the noise matrix,
respectively obeys the mean value of 0 and the variance of mu 2 The cyclic symmetric complex gaussian distribution and gaussian distribution of (a), wherein μ is calculated according to the following formula:
s35.CPU accumulates the signal matrix sent by mth AP through the optical fiber return link
To obtain
First of all, calculate
Maximum eigenvalue of
And corresponding feature vectors
Then correcting according to
S36. The CPU sends the corrected data to all APs through the optical fiber return link
And feature vectors
S37, the mth AP is calculated according to the following formula
S38, if n is larger than T, going to S39, otherwise, making n = n +1 and returning to the step S34 for recalculation;
s39, each AP obtains a complete matrix:
as H m Estimating S;
in the step S34, the signal matrix including the location privacy information
Before sending to the CPU, in the signal matrix
And a disturbance noise matrix is added for protection, so that the position privacy of a user is protected from being disclosed to a CPU, the variance of disturbance noise is calibrated by using a calculation formula in a formula (9), and the proposed privacy protection matrix completion algorithm strictly realizes the combined differential privacy (belonging to the element and delta).
2. The method for channel estimation in a hybrid massive MIMO system without cellular according to claim 1, wherein the step S3 specifically comprises:
taking out the complete matrix from the mth AP
Front τ of p Column, is marked as
As
Is estimated by the estimation of (a) a,
the mth AP calculates its channel H according to the following equation m Estimation of (2):
wherein
Representing the pseudo-inverse of P.
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