CN117394895A - Hybrid near-far field beam training method for ultra-large scale communication system - Google Patents

Abstract

The invention belongs to the technical field of wireless communication, and particularly relates to a rapid mixed beam training method for a super-large-scale communication system, wherein a traditional scheme adopts an exhaustive search method to design a beam training method, and the training cost of the method is high, so the invention aims at providing an efficient near-field/far-field mixed beam training scheme. The beam training scheme provided by the invention is based on a multidirectional beam training sequence of a near-field unitary matrix, and the optimal beam alignment is effectively identified from a received signal in a probability intersection mode. Experiments show that the method provided by the invention can identify the optimal alignment with high probability, and the training cost is far lower than that of the existing studied exhaustive search beam training scheme.

Description

Hybrid near-far field beam training method for ultra-large scale communication system

Technical Field

The invention belongs to the technical field of wireless communication, and particularly relates to a hybrid near-far field beam training method for a super-large-scale communication system.

Background

Ultra-large-scale antenna arrays are considered as one of the key technologies of the next-generation mobile communication system, which generally operates in Millimeter Wave (mmWave) or Terahertz (Thz) frequency bands. The spectral efficiency of the communication system is significantly improved because the ultra-large-scale antenna array can provide high beamforming gain to compensate for the severe path loss in the high frequency band. As the number of base station antennas increases to hundreds of thousands, the rayleigh range of the base station will reach several tens of meters, which means that the user can be located in both the near field and far field regions. In this case, beam training in the hybrid near field/far field is a challenging problem. Conventional exhaustive search schemes can in principle be used to handle the beam training task of near field/far field mixed channels. However, the training overhead of an exhaustive search scheme is significant, and this approach typically takes a long time to find the strongest propagation path.

Disclosure of Invention

The invention aims to provide a downlink beam training scheme suitable for a super-large-scale millimeter wave/terahertz system, designs a multidirectional beam training sequence based on a near-field unitary matrix, and effectively identifies the optimal beam alignment from a received signal in a probability intersection mode. Compared with the existing exhaustive search beam training method, the designed method can identify the optimal alignment with high probability, and the training cost is far lower than that of the existing studied exhaustive search beam training scheme.

The technical scheme of the invention is as follows:

in view of downlink training and beam alignment problems of a millimeter wave/terahertz system in very large scale, a Multiple-Input Single-Output (MISO) communication system is considered, and a Base Station (BS) configures a very large scale uniform linear array (Uniform Linear Array, ULA) to serve a plurality of Single-antenna users. The base station adopts a mixed analog and digital wave beam forming structure, has N antenna number and R radio frequency link number, satisfies R < N, and the mobile user terminal (user) configures an omnidirectional antenna.

The technical scheme comprises the following steps:

s1, constructing a channel. When the user is in the far field region, the wavefront is a plane wave, and when the user is in the near field region, a spherical wave model should be used to characterize the channel. In particular, a hybrid near-field/far-field channel can be modeled as

Wherein L is the number of paths, g ₀ G is the complex gain of the channel line-of-sight path _l L epsilon {1, …, L-1} is the complex gain of the first non-line-of-sight path of the channel, r _l For the distance between the first antenna (as reference antenna) at the base station and the scattering/user of the first path, θ _l For the departure Angle (AOD) of the first path, a (θ, r) represents a steering vector related to angle and distance, and has the following expression:

where λ is the wavelength of the carrier frequency, r ⁽ⁿ⁾ Is the distance between the nth antenna and the scatterer/user. r is (r) ⁽ⁿ⁾ The relation with r is:

where d=λ/2 denotes the antenna spacing, Δ is defined as:

it should be noted that (N-1) d is the length of the array, which is typically much smaller than r. Therefore, the delta value is small. Approximation toObtaining r ⁽ⁿ⁾ The expression of (2) is as follows:

it should be noted that r ⁽¹⁾ ≡r, since the first antenna is taken as the reference antenna, in this case Δ= 0.r is (r) ⁽ⁿ⁾ Comprising two parts, namely a part related to the angle and a part not related to the angle. Thus, a (θ, r) can be re-expressed as

Wherein,representing the Hadamard product, a (θ) is the far field steering vector, defined as:

b (r) is a given distance-related term:

when r is _l Greater than the Rayleigh distance, (N-1) ² d ² /2r _l And 0. At this time, b (r _l ) It can be approximated as:

it will result in:

wherein,the channel response vector h thus obtained _l Is a conventional far-field channel model because it is characterized only in the angular domain. When r is _l When the distance is smaller than Rayleigh distance, b (r _l ) And generally cannot be further simplified. Thus, h _l Expressed as:

s2, modeling a beam training problem. The transmitted signal at time t can be expressed as

Wherein,is a hybrid beamforming vector, ">And->Respectively an RF precoding matrix and a baseband coding matrix, b (t) =1 is a transmission symbol. Only the beam training method for a particular user is of interest. The signal received by the user at time t can be expressed as:

x(t)＝h ^H s(t)+n(t)

＝h ^H f(t)+n(t)

wherein,representing additive complex gaussian noise.

S3, considering carrier frequency offset (Carrier Frequency Offset, abbreviated as CFO), only the amplitude of the received signal is reliable for beam training. I.e.

Assuming a total of T' received signals, the goal is to base on the received signalsAn optimal beam alignment scheme between the user and the base station is determined. The problem of interest for the present invention is to design the beam training sequence +.>And developing an estimation algorithm that uses a small number of training samples to identify the optimal beam alignment.

Since the near-field steering vector can be approximated as a Hadamard product of the far-field steering vector and the distance-dependent unit mode vector. Since b (r) is a unit modulus vector, it can be easily verified

Using a dictionaryThe near-field steering vector a (θ, r) may be sparsely represented as

a(θ,r)＝A _r z

Where z is an n-dimensional sparse vector. Obviously, channel h is in the dictionaryThere is a sparse representation with the largest element corresponding to the LOS path of the channel. Thus (2)

Thus, if z can be found ₀ The largest component of (a) then the best beam alignment between the base station and the terminal can be determined. However, the problem is that there is no reference to r ₀ Is a priori knowledge of (c). To address this difficulty, the distance domain is discretized into a number of grid points, e.gFor each distance d _i Structure->Order the

If d _i Just close to r ₀ ThenThe largest component of (a) may be considered the dominant path of the channel. If the distance d _j Deviation fromr ₀ D is then _j And r ₀ Mismatch between these will lead to an angular dispersion effect, resulting in a block sparse vector +.>In addition, due to mismatch, the drug is->Maximum element ratio ∈>The largest element in (a) is small. Based on this fact, the distance r ₀ By selection ofIs the most sparse vector or choice->The vector containing the largest component. The present invention proposes an efficient beam training scheme that simultaneously identifies distance and angular parameters associated with the LOS path.

Consider first the case of no noise. The basic idea is to form multiple directional beams simultaneously, causing them to scan different directions. Specifically, at each time instant, the precoding vector f (t) is selected as

Wherein c (t) ∈ {0,1} ^N Is a randomly generated sparse vector of R non-zero terms. The R directional beams can be formed simultaneously by the above precoding vector f (t). Neglecting noise to obtain

In the middle ofIs->Q' th element, S _c And (t) is a support set of sparse vectors c (t).

Recording deviceIs->Support set of (1), define->Is->And S is equal to _c Intersection of (t). Obviously, the collection +.>Base of>Three different situations are indicated, namely:

1.in this case, the selection vector c (t) does not detect sparse vectors +.>Is a non-zero element of the group. This condition is referred to as the Empty Detection (ED) condition.

2.In this case, c (t) detects only sparse vectors +.>Is a non-zero element of (c). This case is referred to as a Single Detection (SD) case.

3.In this case c (t) selects +.>Is not zero. This situation is referred to as the Multiplex Detection (MD) situation.

For each distance d _i A round of full coverage scanning, i.e. command, may be performedWherein the method comprises the steps ofOrthogonal to each other. Is provided with->Representing the relevant observations. Based on->With correlations of different distances, a pre-screening operation may be performed, preserving the distances that the correlated observations contain a large number of ED observations.

To determineSeveral full coverage scans, such as a total of L rounds, need to be performed. For the first round, the scan vector is noted +.>The scan vectors for each scan are randomly generated and satisfy the following two conditions:

1. for each of l and t, c _l (t) is a sparse vector of R non-zero elements, and these non-zero elements are all equal to 1.

2. For each of the l's,are mutually orthogonal, i.e. they have disjoint sets of supports.

Order theRepresenting the signal received by the user at the t-th moment of the first full-coverage scan, i.e

Is provided withRepresentation->Maximum element of->Representation->Index of the largest term in (c). Since all observations are ED or SD observations, & gt can be derived>Must belong to the collection->I.e.

Thus (2)Index of the largest term in (i.e.)>Can be identified as set +.>Common elements in (i.e.)

The maximum element estimate of (2) is the average of the maximum measurements of the L scans:

at each distance d _i A kind of electronic deviceThe distance r of the LOS path can then be estimated ₀ As->The distance corresponding to the maximum value of (2). After determining the distance (e.g. d _p ) Thereafter, it can be according to->The index of the largest entry in (c) correspondingly determines the angular parameter associated with the LOS path. Specifically, the angle parameter is estimated as AND +.>Is->The angle associated with the column, i.e., the angle.

In the presence of noise, the received signal is

Binary hypotheses are used to determine whether an observation is ED. Such binary detection tasks can be handled by employing a simple energy detector, i.e

Where e is a parameter that can be selected to meet a pre-specified false alarm probability.

For noisy scenes, turn onA more robust solution is developed, in particular, for the first round,the probability of the nth element of (2) being the largest is calculated as

In c _l,n (t) represents c _l The nth item of (t).

After the probabilities for all the L rounds are obtained, the index of the maximum position can be determined by the following maximum likelihood estimates:

the rapid beam training method provided by the invention has the beneficial effects that reliable beam estimation can be provided, the training overhead is slightly large, but multiple rounds of feedback are not needed, and effective channel state information is provided for a very large-scale antenna communication system.

Drawings

Fig. 1 is an exhaustive search method (exhaustive search) and the proposed method (proposed method) with η versus training overhead, with experimental conditions snr=0 dB;

FIG. 2 is a graph showing the relation between the RMSE and training overhead for the position of the exhaustive search method (exhaustive search) and the proposed method (proposed method), with the experimental condition being SNR=0 dB

FIG. 3 is a plot of RMSE position versus training overhead for θ for the exhaustive search method (exhaustive search) and the proposed method (proposed method), with experimental conditions of SNR=0 dB

Fig. 4 is an exhaustive search method (exhaustive search) and the proposed method (proposed method) η and position and RMSE of θ versus signal to noise ratio for experimental conditions r=32, l=5;

fig. 5 is a graph of RMSE versus signal-to-noise ratio for the proposed method (proposed method), TPM and TSH methods η and location θ.

Detailed Description

The present invention will be described in detail below with reference to the accompanying drawings and simulation examples to demonstrate the applicability of the present invention.

The invention is oriented to the downlink training and beam alignment problems of a super-large-scale millimeter wave/terahertz system, considers a Multiple-Input Single-Output (MISO) communication system, and a Base Station (BS) configures a super-large-scale uniform linear array (Uniform Linear Array, ULA) to provide services for a plurality of Single-antenna users. The base station adopts a mixed analog and digital wave beam forming structure, has N antenna number and R radio frequency link number, satisfies R < N, and the mobile user terminal (user) configures an omnidirectional antenna. The transmitted signal at time t can be expressed as

Wherein,is a hybrid beamforming vector, ">And->Respectively an RF precoding matrix and a baseband coding matrix, b (t) =1 is a transmission symbol. Note that for the downlink training scenario, each user receives the transmission signal separately and identifies the primary path associated with its own channel. Therefore, only the beam training method for a specific user is focused.

Order theRepresenting the channel from the base station to the user, the signal received by the user at time t can be expressed as:

x(t)＝h ^H s(t)+n(t)

＝h ^H f(t)+n(t)

wherein,representing additive complex gaussian noise.

With the increase of the number of antennas, an electromagnetic radiation area of the ultra-large-scale antenna communication system is divided into a near field area and a far field area according to the Rayleigh distance, and the near field area can reach tens of meters to hundreds of meters and cannot be ignored. When the user is in the far field region, the wavefront is a plane wave, and when the user is in the near field region, a spherical wave model should be used to characterize the channel. In particular, a hybrid near-field/far-field channel can be modeled as

Wherein L is the number of paths, g ₀ G is the complex gain of the Line of Sight (LOS) path of the channel _l L epsilon {1, …, L-1} is the complex gain of the first non-line-of-sight path (None Line of Sight, NLOS for short) of the channel, r _l For the distance between the first antenna (as reference antenna) at the base station and the scattering/user of the first path, θ _l For the departure Angle (AOD) of the first path, a (θ, r) represents the guiding vector in relation to angle and distance. In particular, a (θ, r) has the following expression:

where λ is the wavelength of the carrier frequency, r ⁽ⁿ⁾ Is the distance between the nth antenna and the scatterer/user. r is (r) ⁽ⁿ⁾ The relation with r is:

where d=λ/2 denotes the antenna spacing, Δ is defined as:

it should be noted that (N-1) d is the length of the array, which is typically much smaller than r. Thus, delta valueSmaller. Approximation toObtaining r ⁽ⁿ⁾ The expression of (2) is as follows:

it should be noted that r ⁽¹⁾ ≡r, since the first antenna is taken as the reference antenna, in this case Δ= 0.r is (r) ⁽ⁿ⁾ Comprising two parts, namely a part related to the angle and a part not related to the angle. Thus, a (θ, r) can be re-expressed as

Wherein,representing the Hadamard product, a (θ) is the far field steering vector, defined as:

b (r) is a given distance-related term:

the channel model may capture characteristics of both the near field region and the far field region. In particular, for a particular propagation path, e.g. the channel response of the first pathWhen r is _l Greater than the Rayleigh distance, (N-1) ² d ² /2r _l And 0. At this time, b (r _l ) It can be approximated as:

it will result in:

wherein,the channel response vector h thus obtained _l Is a conventional far-field channel model because it is characterized only in the angular domain. When r is _l When the distance is smaller than Rayleigh distance, b (r _l ) And generally cannot be further simplified. Thus, h _l Expressed as:

only the amplitude of the received signal is reliable for beam training, taking into account the carrier frequency offset (Carrier Frequency Offset, CFO for short). I.e.

Assuming a total of T' received signals, the goal is to base on the received signalsAn optimal beam alignment scheme between the user and the base station is determined. The problem of interest for the present invention is to design the beam training sequence +.>And developing an estimation algorithm that uses a small number of training samples to identify the optimal beam alignment.

An exhaustive search is a natural way to find the LOS path and achieve beam alignment. The idea of an exhaustive search is to discretize the angular range into grid points, in particular, angles and distances into two sets of grid points.

θ∈{θ _p |θ _p ＝θ _min +(p-1)△θ,p＝1,…,P}

d∈{d _i |d _i ＝d _min +(i-1)△d,i＝1,…,I}

Wherein Δθ and Δd are the resolution of the angular and distance domains, respectively;and(assuming that P and I are integers) are the angle grid number and the distance grid number, respectively; { θ _max ,θ _min ,d _max ,d _min The parameter to be determined.

With these discrete angle and distance points, the beamforming vector f (t) may be set to a (θ) _p ,d _i ) To sequentially scan the entire angular range space, whereinThus, the signal received by the user is composed of

y(t)＝|h ^H f(t)+n(t)|

＝|h ^H a(θ _p ,d _i )+n(t)|

CollectingThereafter, the optimal beam alignment can be estimated as

{p,i}＝argmax _t {y _t }

Obviously, for such an exhaustive search scheme, it requires a total PI measurement number, which is typically high, since p=n needs to be set to obtain the highest angular resolution. In the present invention, an objective is to propose a fast hybrid far/near field beam training method for a very large scale antenna array system.

Since the near-field steering vector can be approximated as a Hadamard product of the far-field steering vector and the distance-dependent unit mode vector. Since b (r) is a unit modulus vector, it can be easily verified

From the above equation, near-field steering vectors having the same distance but different angle parameters are approximately orthogonal to each other. Based on this approximate orthogonality, a near-field unitary matrix of a particular distance r is constructed such that near-field steering vectors a (θ, r) of the same distance can be represented succinctly. Definition of the definition

Wherein, is a Discrete Fourier Transform (DFT) matrix. Can easily verify A _r Is a unitary matrix, i.e. +.>In addition, see A _r Is equal to +.>This is the near field steering vector a (θ _n R).

Using dictionary a _r The near-field steering vector a (θ, r) may be sparsely represented as

a(θ,r)＝A _r z

Where z is an n-dimensional sparse vector. For ease of description, assume approximationsIn a strict sense, rather than in an approximate sense, the approximation error may be absorbed into the noise term as noise treatment. In this case, z contains only one dominant element if θ is located on the discrete grid specified by the DFT matrix. This can be easily verified as follows. Due to A _r Each element of z, such as the nth element, is an identity matrix, which can be obtained by

z(n)＝a ^H (θ _n ,r)a(θ,r)

＝a ^H (θ _n )a(θ)

Obviously, a (θ) comes from the DFT matrix if θ _n θ, z (n) =1; if theta is _n ≠θ，z(n)＝1。

Note that channel h consists of one line-of-sight (LOS) path and some non-line-of-sight (NLOS) paths. In addition, many channel measurements show that the power of the LOS component is much higher than the sum of the power of the NLOS components (about 13dB higher in the millimeter wave band and about 20dB higher in the terahertz band). If the distance r is related to the LOS path ₀ Is known, r can be used ₀ Is constructed by knowledge of (a)It is obvious that channel h is in dictionary +.>There is a sparse representation with the largest element corresponding to the LOS path of the channel. Thus (2)

Thus, if z can be found ₀ The largest component of (a) then the best beam alignment between the base station and the terminal can be determined. However, the problem is that there is no reference to r ₀ Is a priori knowledge of (c). To address this difficulty, the distance domain is discretized into a number of grid points, e.gFor each distance d _i Structure->Order the

If d _i Just close to r ₀ ThenMaximum of (3)The component may be considered the dominant path of the channel. On the other hand, if the distance d _j Deviation r ₀ D is then _j And r ₀ Mismatch between these will lead to an angular dispersion effect, resulting in a block sparse vector +.>In addition, due to mismatch, the drug is->Maximum element ratio ∈>The largest element in (a) is small. Based on this fact, the distance r ₀ By selecting +.>Is the most sparse vector or choice->The vector containing the largest component. In the following, the present invention proposes an efficient beam training scheme that can simultaneously identify distance and angular parameters associated with the LOS path.

To more clearly illustrate the idea of the proposed beam training scheme, consider first the case of no noise. The extension to the noisy case will be discussed later. The basic idea of the method is to form multiple directional beams simultaneously, causing them to scan different directions. Specifically, at each time instant, the precoding vector f (t) is selected as

Wherein c (t) ∈ {0,1} ^N Is a randomly generated sparse vector of R non-zero terms. Note that the number of the components to be processed,is a near-field steering vector directing its beam in a direction and distance d _i A specified point. Thus from the aboveThe encoding vector f (t) may form R directional beams simultaneously. Neglecting noise to obtain

In the middle ofIs->Q' th element, S _c And (t) is a support set of sparse vectors c (t).

Recording deviceIs->Support set of (1), define->Is->And S is equal to _c Intersection of (t). Obviously, the collection +.>Base of>Three different situations are indicated, namely:

4.in this case, the selection vector c (t) does not detect sparse vectors +.>Is a non-zero element of the group. This condition is referred to as the Empty Detection (ED) condition.

5.In this case, c (t) detects only sparse vectors +.>Is a non-zero element of (c). This case is referred to as a Single Detection (SD) case.

6.In this case c (t) selects +.>Is not zero. This situation is referred to as the Multiplex Detection (MD) situation.

In the ED case, the received signal isFor SD and MD, the received signal contains single or multiple signal components. Thus, depending on the size of the received signal, it can be easily determined whether an observation is ED.

For different moments, e.g. t ₁ ≠t ₂ ,c(t ₁ ) And c (t) ₂ ) Designed to be orthogonal to each other, meaning that they have disjoint sets of supports. Then, atTime slots (assuming N/R is an integer) can be covered +.>Such a scan is called a "one-round full coverage scan", and the corresponding scan vector is +.>For each distance d _i A round of full coverage scanning, i.e. let +.>Wherein->Orthogonal to each other. Is provided with->Representing the relevant observations.

As previously described, if d _i Deviation r ₀ The optical system, due to the effect of the angular dispersion,will become less sparse. On the other hand, if d _i di is close to 0, < ->Only a few non-zero components are included. Obviously, given +.>If->More sparse, the number of ED observations is greater and vice versa. Thus, based on->With correlations of different distances, a pre-screening operation may be performed, preserving the distances that the correlated observations contain a large number of ED observations.

In order not to lose generality, setRepresenting the set of distances remaining after the pre-screening operation. Discussed as the collection->Each d of (3) _i Determine->Index of the largest term in (c). Obviously, it is not possible to determine +.>Is the largest component of (a) the composition.

To determineSeveral full coverage scans, such as a total of L rounds, need to be performed. For the first round, the scan vector is noted +.>The scan vectors for each scan are randomly generated and satisfy the following two conditions:

3. for each of l and t, c _l (t) is a sparse vector of R non-zero elements, and these non-zero elements are all equal to 1.

4. For each of the l's,are mutually orthogonal, i.e. they have disjoint sets of supports.

Due toIs a sparse vector consisting of only a few non-zero terms, and for proper selection of R, each full coverage scan contains only high probability ED and SD observations. Such a round of scanning is referred to as a non-MD round. Here, for simplicity, it is assumed that all L-wheels are non-MD wheels. If some of the wheels are MD wheels, they are identified and removed according to a simple criteria, as discussed in the following section.

Order theRepresenting the signal received by the user at the t-th moment of the first round of full coverage scanning, i.e +.>

Is provided withRepresentation->Maximum element of->Representation->Index of the largest term in (c). Since all observations are ED or SD observations, & gt can be derived>Must belong to the collection->I.e.

Thus (2)Index of the largest term in (i.e.)>Can be identified as set +.>Common elements in (i.e.)

The basic principle of this intersection scheme is: since the scan vectors for each scan are random, except for the largest term, inIt is unlikely that another term lies in the intersection of these sets, especially when L is large. Therefore, it is desirable to be able to identify +.>Is the largest component of (a). />Can be estimated as the maximum measurement value of the L-round scanAverage value of (2):

note that the averaging operation is used to improve the estimation accuracy in the presence of noise.

At each distance d _i A kind of electronic deviceThe distance r of the LOS path can then be estimated ₀ As->The distance corresponding to the maximum value of (2). After determining the distance (e.g. d _p ) Thereafter, it can be according to->The index of the largest entry in (c) correspondingly determines the angular parameter associated with the LOS path. Specifically, the angle parameter is estimated as AND +.>Is->The angle associated with the column, i.e., the angle.

To date, distance and angle parameters associated with LOS paths have been determined by multiple full coverage scans. The expansion of the proposed beam training scheme to noise situations will now be discussed. In the presence of noise, determining whether an observation is ED is not as simple as in the case of no noise. In practice, for noisy situations, the received signal is

Thus, the received ED observations areObeying the rayleigh distribution. For the SD and MD cases, the received signal is the sum of the signal and noise. Binary hypotheses are used to determine whether an observation is ED. Binary hypothesis testing problem is expressed as

H ₀ : the scan at time t is ED

H ₁ : the scan at time t is not ED

Such binary detection tasks can be handled by employing a simple energy detector, i.e

Where e is a parameter that can be selected to meet a pre-specified false alarm probability.

Another problem is determining in the presence of noiseIs the largest entry of (a). For noisy scenes, the crossover scheme may perform poorly due to the effects of noise. In order to develop a robust solution, is +.>Instead of 0/1 hard votes, each element of (a) is assigned a probability and the intersection operation is converted into a product of probabilities. Specifically, for the first round, < > the>The probability of the nth element of (a) being the largest entry is calculated as

In c _l,n (t) represents c _l The nth item of (t). Recall, c _l,n (t) either 1 or 0. When c _l,n When (t) =1,is activated. Thus (S)>In practice the measure is from +.>Which implicitly reflects the probability that the element is the largest element.

After deriving the probabilities for all L rounds of scanning, the index of the largest entry can be determined by the following maximum likelihood estimates:

in the simulation, the present invention configures ULA of n=256 antennas for BS, carrier frequency is set to 100GHz, wavelength is set to λ=0.003 m, and distance between adjacent antennas is set to d=λ/2. In the set-up, the rayleigh distance is about 97.5m. The distance between the user and the base station is in the range of (5 m,120 m), covering the near field and far field areas.

The number of channel paths is set to 3, including one LOS path and 2 NLOS paths. The complex gain of the LOS path is based on a complex Gaussian distributionThe complex gain of the NLOS path is generated to also follow a complex gaussian distribution, the variance of which is determined by the rice factor, set to 13.2dB in the simulation. The Signal-to-Noise Ratio (SNR) is defined asWherein sigma ² Is the noise power.

The normalized mean square error of angle and distance is used to evaluate the beam training performance of the respective algorithm, i.e

Where θ and r are the best alignment geometry of the resulting beam training scheme, respectively. Furthermore, beam training performance is evaluated by a relative reachability ratio, which is defined as

Where AR (f) is the achievable rate at the mixed beamforming vector f:

AR(f)＝log ₂ (1+γ|h ^H f| ² )

for beamforming based on perfect channel state information, f is set to h, and for these considered beam training schemes, f is set toWherein->Representing an estimate of each scheme. Clearly, η ε [0,1 ]]Since the reachability based on perfect channel state information is an upper bound on the reachability derived from estimating channel state information, higher values of η represent more accurate beam training. />

As can be seen from fig. 1, 2 and 3, the method provided by the present invention can obtain better beamforming performance than the exhaustive search method under the condition of smaller training overhead. This is quite different from the results of far-field beam training, where the exhaustive search method has an upper bound on other beam training schemes. Note that for hybrid far/near field beam training, it involves estimating the distance and angle of the LOS path. Empirical results indicate that the method proposed by the present invention can provide a more accurate distance estimation. This is probably because the proposed method uses the measured values of the L-round full coverage scan, has a noise averaging effect, and thus contributes to an improvement in the estimation accuracy of the distance. It should be noted that, although the accuracy of estimating the angle parameter by the method provided by the present invention is lower when the training overhead is limited, when the training overhead is greater than 1536 (i.e., l=4), the RMSE of θ obtained by the method provided by the present invention is always smaller than 0.08, which means that the estimated angle is very close to the real angle, and the influence of the estimated error on the beamforming performance is negligible.

Figure 4 depicts the performance of the proposed method and the exhaustive search method of the present invention as a function of signal to noise ratio. For the method proposed by the present invention, r=16, l=5 is set. The training overhead is therefore T' =1920, which is much smaller than the training overhead required for the exhaustive search. From fig. 4, it is observed that in the low signal-to-noise region, the proposed method has significant advantages over the exhaustive search scheme. Again, this improvement can be attributed to the improvement in the robustness of the proposed algorithm to noise. It can be seen that the proposed method can provide a more accurate distance estimation than the exhaustive method.

Then, the method proposed by the present invention is compared with two most advanced near field beam training methods, namely the TPM method and the TSH method. R=16 and l=5 are set. For the TPM method, 3 candidate angles are considered in the first angle estimation stage. For TSH, the number of layers in the first stage is set to log ₂ (N) -2=6, and the number of layers in the second stage is set to 2. Figure 5 plots the performance of the respective methods as a function of signal to noise ratio. It can be seen from fig. 5 that the TSH method performs the worst with respect to all these metrics among all considered methods. Furthermore, in both the TPM method and the TSH method, increasing the number of training sequences can improve their performance in low signal-to-noise ratio areas, while in high signal-to-noise ratio areas the performance improvement is limited. The proposed MBT method maximizes the η value among the algorithms. When the signal-to-noise ratio is less than 0dB, the eta value of the TPM-PR method is close to that of the TPM-PR method, but the performance gap of the TPM-PR method and the TPM-PR method gradually increases with the increase of the signal-to-noise ratio. When the signal-to-noise ratio is below 0dB, it performs poorly compared to the MBT method, while when the signal-to-noise ratio is further increased. For the estimation precision of theta, the method is inferior to a TPM method in a low signal-to-noise ratio area, and the performance of the MBT method gradually exceeds the TPM method along with the increase of the signal-to-noise ratio.

Overall, although the method requires more training than the two feedback-assisted methodsTraining sequences (still much smaller than the training sequences required for the EXH method), but the MBT method is competitive with these prior methods. However, it should be noted that the feedback process is a custom process for each particular user. Therefore, in the multi-user scenario, the TPM method and the TSH method should complete beam training one by one, while the MBT method can broadcast predefined training sequences, and each user can estimate its own best alignment beam individually according to these sequences, so that the method of the present invention is more suitable for the multi-user scenario. Among these algorithms, the proposed MBT method can provide the most accurate r ₀ And (5) estimating. It should be noted that the TPM-PR method has similar performance.

In summary, the present invention addresses the beam training problem of ultra-large scale millimeter wave/terahertz communication systems with near field/far field hybrid channels. The distances are discretized into a finite set and a multi-directional beam training sequence is designed for each specific distance. An efficient probability intersection-based phase-free measurement beam optimal alignment scheme. Furthermore, the performance of the method, as well as the training overhead of reliable beam estimation, is analyzed theoretically. Simulation results show that compared with the existing method, the method can provide reliable beam estimation, has slightly larger training overhead, and does not need multiple rounds of feedback.

Claims (1)

1. A mixed near-far field wave beam training method for a super-large scale communication system defines a base station BS in the system to configure a large scale uniform linear array to provide service for a plurality of single antenna users, the base station adopts a mixed analog and digital wave beam forming structure, has N antenna number and R radio frequency link number, satisfies R < N, and configures an omnidirectional antenna at a mobile user end; characterized in that the method comprises:

s1, establishing a mixed near field/far field channel model as follows:

wherein L is the number of paths, g ₀ Complex gain for channel line-of-sight path，g _l L epsilon {1, …, L-1} is the complex gain of the first non-line-of-sight path of the channel, r _l For the distance between the first antenna at the base station and the scatterer/user of the first path, θ _l For the departure angle of the first path, a (θ, r) represents a steering vector related to angle and distance:

where λ is the wavelength of the carrier frequency, r ⁽ⁿ⁾ R is the distance between the nth antenna and the scatterer/user ⁽ⁿ⁾ The relation with r is:

where d=λ/2 denotes the antenna spacing, Δ is defined as:

where (N-1) d is the length of the array, much smaller than r, and therefore the delta value is small, by approximationObtaining r ⁽ⁿ⁾ Is represented by the expression:

thereby re-expressing a (θ, r) as:

wherein,representing the Hadamard product, a (θ) is the far field steering vector, defined as:

b (r) is a given distance-related term:

will finally be h _l Expressed as:

s2, defining a transmission signal at the t time as follows:

wherein,is a hybrid beamforming vector, ">And->Respectively an RF precoding matrix and a baseband coding matrix, b (t) =1 being the transmission symbol;

according to the channel model in S1, the signal received by the user at the t moment is obtained as follows:

x(t)＝h ^H s(t)+n(t)

＝h ^H f(t)+n(t)

wherein,representing additive complex gaussian noise;

s3, defining total T' received signals, wherein each received signal is:

based on the received signalThe optimal beam alignment scheme between the user and the base station is decided, specifically:

definition dictionaryWherein-> Is a discrete Fourier transform matrix, using dictionary A _r The near-field steering vector a (θ, r) is sparsely represented as:

a(θ,r)＝A _r z

wherein z is an n-dimensional sparse vector; defining a distance r associated with the LOS path ₀ Is known, using r ₀ Knowledge construction of (a)So that channel h is in dictionary->There is a sparse representation with the largest element corresponding to the LOS path of the channel:

by finding z ₀ To determine the best beam alignment between the base station and the terminal, in particular: discretizing the distance domain into I grid points for each distance d _i Structure ofOrder the

Distance r ₀ By selectingIs the most sparse vector or choice->The vector containing the largest component is identified, specifically:

firstly, considering the noiseless situation, forming a plurality of directional beams simultaneously, enabling the directional beams to scan different directions, and selecting a precoding vector f (t) as follows at each moment:

wherein c (t) ∈ {0,1} ^N The method is a randomly generated sparse vector with R non-zero terms, R directional beams are formed by a precoding vector f (t) at the same time, and noise is ignored to obtain the following steps:

in the middle ofIs->Q' th element, S _c (t) is a support set of sparse vectors c (t);

recording deviceIs->Support set of (1), define->Is->And S is equal to _c Intersection of (t), set->For the base of (2)Three different cases are shown, namely:

1)selecting vector c (t) does not detect sparse vector +.>Any non-zero element of (a);

2)c (t) only detects sparse vectors +.>Is a non-zero element of (a);

3)c (t) select->Is not zero;

for each distance d _i Executing a round of full coverage scanning, namely, commandWherein->Mutually orthogonal; definitions->Representing relevant observations based on +.>Carrying out pre-screening operation on the correlation with different distances, and reserving the distance between the correlation observations and ED observations;

to determinePerforming an L-round full coverage scan, for the first round, marking the scan vector as +.>The scan vectors for each scan are randomly generated and satisfy the following two conditions:

1) For each of l and t, c _l (t) is a sparse vector of R non-zero elements, and the non-zero elements are all equal to 1;

2) For each of the l's,are mutually orthogonal, i.e. they have disjoint sets of supports;

order theRepresenting the signal received by the user at the t-th moment of the first full-coverage scan, i.e

Is provided withRepresentation->Maximum element of->Representation->The index of the largest term in (1) is derived as all observations are ED or SD observations>Must belong to the collection->I.e.

Thus (2)Index of the largest term in (i.e.)>Identified as set +.>Common elements in (i.e.)

The maximum element estimate of (2) is the average of the maximum measurements of the L scans:

at each distance d _i A kind of electronic deviceThen, the distance r of the LOS path is estimated ₀ As->A distance corresponding to the maximum value of (2); determine the distance d _p Thereafter, according to->The index of the largest entry in (a) correspondingly determines the angle parameter associated with the LOS path, the angle parameter being estimated as being associated with +.>Is->Angles associated with columns, i.e.

In the presence of noise, the received signal is

Using binary hypotheses to determine whether an observation is ED is handled by employing an energy detector, i.e

Wherein E is a parameter that is selected to satisfy a pre-specified false alarm probability;

for noisy scenes, for the first round,the probability of the nth element of (2) being the largest is calculated as

In c _l,n (t) represents c _l The nth item of (t);

after the probabilities for all the L rounds are obtained, the index of the maximum position can be determined by the following maximum likelihood estimates:

the rest of the calculation process is the same as the noiseless case, and finally the optimal beam alignment between the base station and the terminal is determined.