CN112953864B - Honeycomb-free hybrid large-scale MIMO system channel estimation method for protecting privacy - Google Patents

Abstract

The invention discloses a privacy-protecting channel estimation method for a cell-free hybrid massive MIMO system, which is suitable for use in the communication field. By establishing an uplink signal transmission model and a hybrid structure sampling model, each AP obtains an incomplete baseband signal sampling matrix for channel estimation; a privacy-preserving matrix completion algorithm is designed to obtain the incomplete baseband signal obtained by each AP. The signal sampling matrix is the input. While protecting the privacy of the user's location, each AP outputs a complete matrix; each AP performs channel estimation according to the output complete matrix and the known pilot matrix, so as to effectively protect single-antenna users. location privacy while achieving the best channel estimation performance. It can well protect user location privacy and achieve good channel estimation performance.

Description

A Privacy-Preserving Channel Estimation Method for Cellless Hybrid Massive MIMO Systems

technical field

The present invention relates to the technical field of wireless communication, in particular to a channel estimation method for a non-cellular hybrid massive MIMO system that protects privacy.

Background technique

Cellless hybrid massive multiple input multiple output (Multiple Input Multiple Output, MIMO) systems usually have a large number of access points (Access points, AP) distributed in an area, and use the same time-frequency resources to cooperatively serve users. To reduce the high cost of equipping each antenna with a radio frequency (RF) link that includes a high-resolution analog-to-digital converter, systems typically employ a hybrid analog/digital architecture, where switch- or phase-shifter-based analog In combination, the antennas are usually randomly connected to a small number of RF chains.

In order to realize a cellular-free hybrid massive MIMO system, it is crucial to obtain channel information (Channel state information, CSI). In order to obtain better channel estimation results, each AP needs to send its observed received signals to a central processing unit (CPU) for unified processing, and the CPU performs channel estimation and data detection for all users. However, this will most likely result in the leakage of the user's location information to the CPU. Since the large-scale fading in CSI is highly dependent on the distance between the user and the AP, and the location of the AP is generally fixed, theoretically, the CPU has the ability to estimate the location of a user after obtaining the CSI between the user and three or more APs. , so that the leakage of user location information may occur. Therefore, how to provide accurate channel estimation under the premise of protecting user location privacy is a crucial issue, and there is no suitable solution in the prior art.

SUMMARY OF THE INVENTION

Purpose of the invention: The purpose of the present invention is to aim at the deficiencies of the prior art, to provide a privacy-protected non-cellular hybrid massive MIMO system channel estimation method that effectively protects user location privacy, aims to estimate the channel while protecting the user's location. privacy,

Technical solution: In order to achieve the above technical purpose, a privacy-protecting method for channel estimation of a hybrid massive MIMO system without cellularity of the present invention includes the following steps:

S1. Establish an uplink signal transmission model and a hybrid structure sampling model of a cellular-free hybrid massive MIMO system, and each AP obtains an incomplete baseband signal sampling matrix for channel estimation;

S2. Design a privacy-preserving matrix completion algorithm. The algorithm takes the incomplete baseband signal sampling matrix obtained by each AP as input. While protecting the privacy of the user's location, each AP outputs a complete matrix;

S3. Each AP performs channel estimation according to the output complete matrix and the known pilot frequency matrix, so as to achieve the best channel estimation performance while effectively protecting the privacy of the single-antenna user location.

The step S1 specifically includes:

表示AP集合，利用

表示单天线用户集合；相干间隔内时隙的集合表示为

其中前τ_p个时隙用来上行信道估计，表示为

剩下的τ_d＝τ_c-τ_p个时隙用来上行数据传输，表示为

使用s[t]表示K个单天线用户在时隙t的发射信号向量，其中，当

时s[t]代表用来估计信道的导频信号，当

时s[t]代表包含信息的数据符号；利用

表示第m个AP到第k个单天线用户的信道向量，其中

表示复数域；use

Indicates the AP set, using

represents the set of single-antenna users; the set of time slots within the coherence interval is expressed as

Among them, the first τ _p time slots are used for uplink channel estimation, which is expressed as

The remaining τ _d =τ _c -τ _p time slots are used for uplink data transmission, expressed as

Use s[t] to denote the transmitted signal vector of K single-antenna users in time slot t, where, when

Time s[t] represents the pilot signal used to estimate the channel, when

When s[t] represents a data symbol containing information; use

represents the channel vector from the mth AP to the kth single-antenna user, where

represents the field of complex numbers;

表示为：The received signal vector of _Na antennas on the mth AP in time slot t

Expressed as:

为第m个AP到所有用户的信道矩阵，n_m[t]是在时隙t时第m个AP接收到的噪声，服从均值为0方差为σ²的循环对称复高斯分布；in

is the channel matrix from the mth AP to all users, n _m [t] is the noise received by the mth AP at time slot t, which obeys a cyclic symmetric complex Gaussian distribution with mean 0 and variance σ ² ;

Define the following matrix

In the formula: R _m represents the received signal matrix of the _Na antenna on the mth AP in τ _c time slots, N _m represents the received noise matrix of the _Na antenna on the mth AP in τ _c time slots, P Represents the pilot matrix sent by users in the first τ _p time slots, D represents the data matrix sent by users in the next τ _d time slots, and S represents the signal matrix sent by users in a total of τ _c time slots, including pilot and data ; where the received signal matrix of _{Na antennas on the mth AP in τ c time} slots is expressed as:

为第m个AP的基带信号采样矩阵，满足下述映射关系：Each AP adopts _a switch-based hybrid structure, and each time slot randomly selects N _r antennas from Na antennas to connect to N _r RFs, and then uses high-precision analog-to-digital converters to convert into baseband signals. Therefore, the mth In the received signal vector rm [ _t ] of the APs in the time slot t, only N _r received signals become baseband signals in a total of N _a received signals; let Ω _m be the sampling index (n, t) of the mth AP Set, that is, the nth element R _m (n, t) representing r _m [t] is sampled to a certain RF and then becomes a baseband signal, let

is the baseband signal sampling matrix of the mth AP, which satisfies the following mapping relationship:

很显然Y_m每一列只有N_r个非零的基带信号，因此Y_m为不完整矩阵。Represent the map as

Obviously, each column of Y _m has only N _r non-zero baseband signals, so Y _m is an incomplete matrix.

The matrix completion algorithm for protecting privacy in the step S2 specifically includes:

作为输入，输出一个完整的低秩矩阵

的低秩矩阵补全问题可以表示为如下所示的最小二乘问题Sample matrix with incomplete total baseband signal

As input, output a full low-rank matrix

The low-rank matrix completion problem of can be expressed as a least squares problem as shown below

表示Frobenius范数，

表示所有AP上采样索引的集合；问题(5)是一个凸优化问题，本发明设计出一种保护隐私的矩阵补全算法求解该问题；保护隐私的矩阵补全算法是一个迭代算法，第n次迭代每个AP m输出一个完整的估计矩阵

并将第T次迭代的输出估计矩阵

作为低秩矩阵

where ||·|| _nuc denotes the nuclear norm,

represents the Frobenius norm,

Represents the set of all AP upsampling indices; problem (5) is a convex optimization problem, the present invention designs a privacy-preserving matrix completion algorithm to solve the problem; the privacy-preserving matrix completion algorithm is an iterative algorithm, the nth The next iteration outputs a complete estimation matrix for each AP m

and put the output of the T-th iteration to estimate the matrix

as a low-rank matrix

The specific implementation steps are as follows:

S31. Input the specific value of the privacy parameter (∈,δ); input the algorithm iteration number T; input the baseband signal sampling matrix Y _m of each AP m; estimate the upper bound L of Y _m according to the following formula

where β _k,m represents the large-scale fading coefficient from the mth AP to the kth user channel, and σ ² represents the channel noise variance;

给出T次迭代的权重值η⁽¹⁾＝1，η⁽ⁿ⁾＝1/T,n≠1，S32. Initialization

Given the weight value of T iterations η ⁽¹⁾ = 1, η ⁽ⁿ⁾ = 1/T, n≠1,

S33. Initialize the number of iterations, let n=1;

S34. Each AP m first calculates the signal matrix according to the following formula

其中

为随机产生的τ_c×τ_c的厄米特扰动噪声矩阵，

的上三角元素和对角线元素分别服从均值为0，方差为μ²的循环对称复高斯分布和高斯分布，其中μ按照下式计算得到：Then the signal matrix after noise interference is sent to the CPU through the fiber backhaul link

in

is the randomly generated Hermitian perturbation noise matrix of τ _c ×τ _c ,

The upper triangular and diagonal elements of , respectively, obey a cyclic symmetric complex Gaussian distribution and a Gaussian distribution with a mean of 0 and a variance of μ ² , where μ is calculated according to the following formula:

得到

首先计算

的最大特征值

和相应的特征向量

然后根据下式校正

S35. The CPU accumulates the signal matrix sent by each AP m through the optical fiber backhaul link

get

Calculate first

The largest eigenvalue of

and the corresponding eigenvectors

Then correct it according to the following formula

以及特征向量

S36. The CPU sends the corrected

and eigenvectors

S37. Each AP m is calculated according to the following formula

S38. If n>T, go to S39, otherwise set n=n+1 and return to step S34 to recalculate;

作为H_mS的估计。S39. Each AP gets a complete matrix:

as an estimate of _HmS .

在发送给CPU之前，在信号矩阵

中添加扰动噪声矩阵进行保护，从而保护了用户位置隐私不被泄露给CPU，使用式(9)中的计算公式校准了扰动噪声的方差，使得所提出的保护隐私的矩阵补全算法严格实现(∈,δ)联合差分隐私。In the step S34, the signal matrix containing the location privacy information

Before sending to the CPU, in the signal matrix

The perturbation noise matrix is added to protect the user location privacy from being leaked to the CPU, and the variance of the perturbation noise is calibrated using the calculation formula in Eq. (9), so that the proposed privacy-preserving matrix completion algorithm is strictly implemented ( ∈,δ) joint differential privacy.

The step S3 specifically includes:

的前τ_p列，记为

作为

的估计，Take out the complete matrix for each AP m

The first τ _p column of , denoted as

as

's estimate,

Each AP m computes an estimate of its channel H _m according to:

表示P的伪逆。in

represents the pseudo-inverse of P.

Beneficial effects: the method can mine the low-rank characteristic of the received signal matrix under massive MIMO without receiving noise, and use the low-rank characteristic to estimate the channel with lower training overhead. In addition, this method applies differential privacy technology to channel estimation of wireless communication system for the first time, which can well protect user location privacy and achieve better channel estimation performance.

Description of drawings

Fig. 1 is the algorithm flow chart of the specific embodiment of the present invention;

FIG. 2 is a schematic diagram of a cellular-free hybrid massive MIMO system according to a specific embodiment of the present invention;

3 is the normalized mean square error of the channel estimation obtained by the method according to the specific embodiment of the present invention, the method that each AP only uses the pilot frequency to estimate its channel, and the method of matrix completion based on Frank-Wolfe iteration that does not protect privacy Comparison of curves.

Detailed ways

The technical solutions of the present invention will be further introduced below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and not to limit the scope of the present invention.

和

表示AP和用户集合。

表示第m个AP到第k个用户的信道向量，其中

表示复数域。假设所有用户和所有AP之间的信道是块衰落的，信道系数在有τ_c个时隙的相干间隔内保持不变。相干间隔内时隙的集合表示为

其中前τ_p个时隙用来上行信道估计，表示为

剩下的τ_d＝τ_c-τ_p个时隙用来上行数据传输，表示为

s[t]表示K个用户在时隙t的发射信号向量，其中，当

时s[t]代表用来估计信道的导频信号，当

时s[t]代表包含信息的数据符号。The present invention considers a hybrid massive MIMO system without cellular. The system is configured with 1 CPU, M APs and K randomly distributed single-antenna users. Each AP is connected to the CPU through an optical fiber backhaul link, as shown in FIG. 2 . Each AP adopts _a hybrid structure with Na antennas and N _r < _Na RF links. use separately

and

Indicates AP and user set.

represents the channel vector from the mth AP to the kth user, where

Represents the complex number field. Assuming that the channel between all users and all APs is block fading, the channel coefficients remain constant over a coherence interval of τ _c time slots. The set of time slots within the coherence interval is expressed as

Among them, the first τ _p time slots are used for uplink channel estimation, which is expressed as

The remaining τ _d =τ _c -τ _p time slots are used for uplink data transmission, expressed as

s[t] represents the transmitted signal vector of K users in time slot t, where, when

Time s[t] represents the pilot signal used to estimate the channel, when

Time s[t] represents a data symbol containing information.

A privacy-preserving channel estimation method for a cell-free hybrid massive MIMO system, the steps of which are:

S1. Establish an uplink signal transmission model and a hybrid structure sampling model of a cellular-free hybrid massive MIMO system, and each AP obtains an incomplete baseband signal sampling matrix for channel estimation;

S2. Design a privacy-preserving matrix completion algorithm. The algorithm takes the incomplete baseband signal sampling matrix obtained by each AP as input. While protecting the privacy of the user's location, each AP outputs a complete matrix;

S3. Each AP performs channel estimation according to the output complete matrix and the known pilot frequency matrix, so as to achieve the best channel estimation performance while effectively protecting the privacy of the single-antenna user location.

可以表示为Signal vector received by _Na antennas on the mth AP in time slot t

It can be expressed as

为第m个AP到所有用户的信道矩阵，n_m[t]是在时隙t时第m个AP接收到的噪声，服从均值为0方差为σ²的循环对称复高斯分布。定义下述矩阵：in

is the channel matrix from the mth AP to all users, n _m [t] is the noise received by the mth AP at time slot t, which obeys a cyclic symmetric complex Gaussian distribution with mean 0 and variance σ ² . Define the following matrix:

In the formula: R _m represents the received signal matrix of the _Na antenna on the mth AP in τ _c time slots, N _m represents the received noise matrix of the _Na antenna on the mth AP in τ _c time slots, P Represents the pilot matrix sent by users in the first τ _p time slots, D represents the data matrix sent by users in the next τ _d time slots, and S represents the signal matrix sent by users in a total of τ _c time slots, including pilot and data . The received signal matrix of _{Na antennas on the mth AP in τ c time} slots can be expressed as:

为第m个AP的基带信号采样矩阵，满足下述映射关系：Each AP adopts _a switch-based hybrid structure, and each time slot randomly selects N _r antennas from Na antennas to connect to N _r RFs, and then converts them into baseband signals through a high-precision analog-to-digital converter. Therefore, only N _r received signals of the total N _a received signals of the received signal vector rm [t] of the _mth AP in the time slot t become baseband signals. Let Ω _m be the set of sampling indices (n, t) on the m-th AP, that is, the n-th element R _m (n, t) representing r _m [t] is sampled to a certain RF and then becomes a baseband signal . Assume

is the baseband signal sampling matrix of the mth AP, which satisfies the following mapping relationship:

很显然Y_m每一列只有N_r个非零的基带信号，因此Y_m是个不完整矩阵。Represent the map as

Obviously, each column of Y _m has only N _r non-zero baseband signals, so Y _m is an incomplete matrix.

本发明设计保护隐私的信道估计算法在保护用户位置隐私的同时提升信道估计的精度。算法流程如图1所示，具体包括以下步骤：based on

The present invention designs a privacy-protecting channel estimation algorithm to improve the channel estimation accuracy while protecting the user's location privacy. The algorithm flow is shown in Figure 1, which includes the following steps:

S1. Input the specific value of the privacy parameter (∈,δ); input the number of algorithm iterations T; input the baseband signal sampling matrix Y _m of each AP m; estimate the upper bound L of Y _m according to the following formula

where β _k,m represents the large-scale fading coefficient from the mth AP to the kth user channel, and σ ² represents the channel noise variance;

给出T次迭代的权重值η⁽¹⁾＝1，η⁽ⁿ⁾＝1/T,n≠1，S2. Initialization

Given the weight value of T iterations η ⁽¹⁾ = 1, η ⁽ⁿ⁾ = 1/T, n≠1,

S3. Initialize the number of iterations, let n=1;

S4. Each AP m first calculates the signal matrix according to the following formula

其中

为随机产生的τ_c×τ_c的厄米特扰动噪声矩阵，

的上三角元素和对角线元素分别服从均值为0，方差为μ²的循环对称复高斯分布和高斯分布，其中μ按照下式计算得到：Then the signal matrix after noise interference is sent to the CPU through the fiber backhaul link

in

is the randomly generated Hermitian perturbation noise matrix of τ _c ×τ _c ,

The upper triangular and diagonal elements of , respectively, obey a cyclic symmetric complex Gaussian distribution and a Gaussian distribution with a mean of 0 and a variance of μ ² , where μ is calculated according to the following formula:

得到

首先计算

的最大特征值

和相应的特征向量

然后根据下式校正

S5. The CPU accumulates the signal matrix sent by each AP m through the optical fiber backhaul link

get

Calculate first

The largest eigenvalue of

and the corresponding eigenvectors

Then correct it according to the following formula

以及特征向量

S6. The CPU sends the corrected

and eigenvectors

S7. Each AP m is calculated according to the following formula

S8. If n>T then go to S9, otherwise let n=n+1 and return to step S4 to recalculate;

作为X_m＝H_mS的估计；S9. Each AP gets a complete matrix

as an estimate of X _m =H _m S;

的前τ_p列，记为

作为

的估计；S10. Take out each AP m

The first τ _p column of , denoted as

as

estimate;

S11. Each AP m calculates an estimate of its channel H _m according to the following equation

表示P的伪逆。in

represents the pseudo-inverse of P.

Figure 3 shows that the cell radius is 1km, there are 100 APs in the cell, each AP has 4 antennas, 2 RF links, and a total of 5 users, this specific embodiment is used for the hybrid large-scale multiple-input multiple-output system without cellular The privacy-preserving channel estimation method (Algorithm1) and the channel estimation method obtained by each AP using only pilots to estimate its channel (PO) and the non-privacy-preserving Frank-Wolfe iteration-based matrix completion method (NPFW) Comparison plot of normalized mean squared error curves. The Frank-Wolfe iteration-based matrix completion method that does not protect privacy is the theoretical limit of this specific embodiment, but it does not have the ability to protect privacy. It can be seen from FIG. 3 that the channel estimation obtained by the method of this specific embodiment is more accurate than the method of using the pilot estimation alone, and the accuracy of the channel estimation can be significantly improved while maintaining a certain level of privacy.

Claims (2)

1. a kind of channel estimation method of the non-cellular hybrid massive MIMO system of protecting privacy, it is characterized in that: described non-cellular hybrid massive MIMO system comprises 1 baseband central processing unit CPU, M randomly distributed access points AP, K randomly distributed single-antenna users; each AP adopts a hybrid structure with N _a antennas and N _r < N _a radio frequency RF links, all APs are connected to the CPU through fiber backhaul links; all single-antenna users and all The channel between APs is block fading, and the channel coefficients remain unchanged within the coherence interval of τ _c time slots; The steps are: S1. Establish an uplink signal transmission model and a hybrid structure sampling model of a cellular-free hybrid massive MIMO system, and each AP obtains an incomplete baseband signal sampling matrix for channel estimation; S2. Design a privacy-preserving matrix completion algorithm. The algorithm takes the incomplete baseband signal sampling matrix obtained by each AP as input. While protecting the privacy of the user's location, each AP outputs a complete matrix; S3. Each AP performs channel estimation according to the output complete matrix and the known pilot frequency matrix, so as to achieve the best channel estimation performance while effectively protecting the privacy of the single-antenna user location; The step S1 specifically includes: use

Indicates the AP set, using

represents the set of single-antenna users; the set of time slots within the coherence interval is expressed as

Among them, the first τ _p time slots are used for uplink channel estimation, which is expressed as

The remaining τ _d =τ _c -τ _p time slots are used for uplink data transmission, expressed as

Use s[t] to denote the transmitted signal vector of K single-antenna users in time slot t, where, when

Time s[t] represents the pilot signal used to estimate the channel, when

When s[t] represents a data symbol containing information; use

represents the channel vector from the mth AP to the kth single-antenna user, where

represents the field of complex numbers; The received signal vector of _Na antennas on the mth AP in time slot t

Expressed as:

in

is the channel matrix from the mth AP to all users, n _m [t] is the noise received by the mth AP at time slot t, which obeys a cyclic symmetric complex Gaussian distribution with mean 0 and variance σ ² ; Define the following matrix

In the formula: R _m represents the received signal matrix of the _Na antenna on the mth AP in τ _c time slots, N _m represents the received noise matrix of the _Na antenna on the mth AP in τ _c time slots, P Represents the pilot matrix sent by users in the first τ _p time slots, D represents the data matrix sent by users in the next τ _d time slots, and S represents the signal matrix sent by users in a total of τ _c time slots, including pilot and data ; where the received signal matrix of _{Na antennas on the mth AP in τ c time} slots is expressed as:

Each AP adopts _a switch-based hybrid structure, and each time slot randomly selects N _r antennas from Na antennas to connect to N _r RFs, and then uses high-precision analog-to-digital converters to convert into baseband signals. Therefore, the mth In the received signal vector rm [ _t ] of the APs in the time slot t, only N _r received signals become baseband signals in a total of N _a received signals; let Ω _m be the sampling index (n, t) of the mth AP Set, that is, the nth element R _m (n, t) representing r _m [t] is sampled to a certain RF and then becomes a baseband signal, let

is the baseband signal sampling matrix of the mth AP, which satisfies the following mapping relationship:

Represent the map as

Each column of Y _m has only N _r non-zero baseband signals, so Y _m is an incomplete matrix; The matrix completion algorithm for protecting privacy in the step S2 specifically includes: Sample matrix with incomplete total baseband signal

As input, output a full low-rank matrix

The low-rank matrix completion problem of can be expressed as a least squares problem as shown below

where ||·|| _nuc denotes the nuclear norm,

represents the Frobenius norm,

represents the set of upsampling indices of all APs; problem (5) is a convex optimization problem; the privacy-preserving matrix completion algorithm is an iterative algorithm, and the mth AP of the nth iteration outputs a complete estimation matrix

and put the output of the T-th iteration to estimate the matrix

as a low-rank matrix

The specific implementation steps are as follows: S31. Input the specific value of the privacy parameter (∈,δ); input the number of algorithm iterations T; input the baseband signal sampling matrix Y _m of the mth AP; estimate the upper bound L of Y _m according to the following formula

where β _k,m represents the large-scale fading coefficient from the mth AP to the kth user channel, and σ ² represents the channel noise variance; S32. Initialization

Given the weight value of T iterations η ⁽¹⁾ = 1, η ⁽ⁿ⁾ = 1/T, n≠1, S33. Initialize the number of iterations, let n=1; S34. The mth AP first calculates the signal matrix according to the following formula

Then the signal matrix after noise interference is sent to the CPU through the fiber backhaul link

in

is the randomly generated Hermitian perturbation noise matrix of τ _c ×τ _c ,

The upper triangular and diagonal elements of , respectively, obey a cyclic symmetric complex Gaussian distribution and a Gaussian distribution with a mean of 0 and a variance of μ ² , where μ is calculated according to the following formula:

S35. The CPU accumulates the signal matrix sent by the mth AP through the optical fiber backhaul link

get

Calculate first

The largest eigenvalue of

and the corresponding eigenvectors

Then correct it according to the following formula

S36. The CPU sends the corrected

and eigenvectors

S37. The mth AP is calculated according to the following formula

S38. If n>T then go to S39, otherwise set n=n+1 and return to step S34 to recalculate; S39. Each AP gets a complete matrix:

as an estimate of H _m S; In the step S34, the signal matrix containing the location privacy information

Before sending to the CPU, in the signal matrix

The perturbation noise matrix is added to protect the user location privacy from being leaked to the CPU, and the variance of the perturbation noise is calibrated using the calculation formula in Eq. (9), so that the proposed privacy-preserving matrix completion algorithm is strictly implemented ( ∈,δ) joint differential privacy. 2. The method for channel estimation in a non-cellular hybrid massive MIMO system that protects privacy according to claim 1, wherein the step S3 specifically comprises: The mth AP takes out the complete matrix

The first τ _p column of , denoted as

as

's estimate, The _mth AP computes its estimate of its channel Hm according to:

in

represents the pseudo-inverse of P.

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