CN109005133B - Double sparse multipath channel model and channel estimation method based on this model - Google Patents

Abstract

The invention discloses a double-sparse multi-path channel model, which is constructed by utilizing the characteristic of sparse time domain and angular domain, and designs a double-sparse multi-path channel estimation method based on compressed sensing according to the sparsity of the time domain and the angular domain.

Description

Double sparse multipath channel model and channel estimation method based on this model

technical field

The invention relates to the technical field of wireless communication, in particular to a time-domain angle-domain double-sparse multipath channel model, and also to a double-sparse multipath channel estimation method based on compressed sensing.

Background technique

With the development of 1G, 2G, 3G, and 4G, the transmission frequency is getting higher and higher. The higher the frequency, the wider the frequency band, and the faster the transmission rate. 5G is expected to support a frequency range from 400MHZ to 100GHZ, taking 30GHZ as an example, its wavelength is 10mm. That is, 5G mainly communicates in the millimeter wave band. The biggest feature of millimeter wave communication technology is that the wavelength is extremely short and the bandwidth is extremely large. At the same time, because millimeter waves have short wavelengths and mainly direct paths, the propagation stability is high. And the ultra-bandwidth of millimeter wave is thousands of times that of LTE, which provides a guarantee for the ultra-high speed and the number of ultra-connected 5G systems. If space division, time division, orthogonal polarization or other multiplexing technologies are added, the 5G Internet of Everything needs. The multiple access problem can also be easily solved. In addition, millimeter wave communication technology is also quite mature. The application of millimeter wave technology in the field of communication is mainly millimeter wave waveguide communication, millimeter wave wireless ground communication and millimeter wave satellite communication, and mainly wireless ground communication and satellite communication.

Obviously, millimeter-wave communication has high frequency and short wavelength. It is reflected or blocked when it encounters obstacles, and it propagates in a direct way. The beam is narrow and has good directivity. Compared with traditional wireless channels, mmWave transmission not only has stronger sparsity in the time domain, but also exhibits stronger sparsity in the angular domain. Time-domain sparse means that the signal propagates on multiple time-space distribution paths, which is a significant feature of traditional wireless channels; angular-domain sparse means that the signal propagates on multiple angular-domain spatial distribution paths, which is an important feature of the next-generation wireless channel. . Both involve a large number of propagation parameters, and a large number of studies have shown that millimeter wave technology can meet the transmission requirements of 5G. Therefore, it is particularly important to establish statistical channel models and design channel estimation methods.

On the other hand, according to the characteristics of the antenna, the length of the antenna is proportional to the wavelength, and the length of the antenna is about 1/10---1/4 of the wavelength. That is, the higher the frequency, the shorter the wavelength, and the shorter the antenna. That is to say, in millimeter wave communication, the antenna becomes millimeter-level. Therefore, MIMO (Multiple-Input Multiple-Output) in the LTE era has become an enhanced version of Massive MIMO (Massive Multiple Input Multiple Output) in the 5G era. Therefore, in the 5G era, it is generally an antenna array.

In the Massive MIMO system, if the traditional channel model that only considers the time domain sparse is used for channel estimation, the pilot frequency is huge and the complexity of the channel estimation will be greatly increased. As a result, the estimation performance of the channel will be degraded.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies in the prior art, provide a double sparse multipath channel model, and solve the technical problem of low estimation performance of the traditional sparse multipath channel.

In order to solve the above technical problems, the present invention provides a double sparse multipath channel model, which is characterized in that the double sparseness refers to time domain sparseness and angular domain sparseness, and the multipath channel model of time domain and angular domain double sparseness is:

H ^a = [H ^a (0), H ^a (1), H ^a (2), ..., H ^a (L-1)] (17)

Among them, L is the channel length, H ^a is the double sparse channel model in the time-domain angular domain with delay L, H ^a (τ) is the channel matrix in the τ time-angle domain, m is the time-domain sparsity, τ _j is the delay of the jth path,

of which

σ_i表示第i条路径的衰减，n_t表示发射天线数量，n_r表示接收天线数量，d_i表示第一副发射天线到第一副接收天线的第i条路径的长度，λ_c为载波波长，n代表信道路径数量，U_r,U_t为空间正交基，e_r(·)、e_t(·)为单位空间特征图，将式15代入式18得：in,

σ _i represents the attenuation of the ith path, n _t represents the number of transmit antennas, n _r represents the number of receive antennas, d _i represents the length of the ith path from the first transmit antenna to the first receive antenna, and λ _c is the carrier wavelength, n represents the number of channel paths, U _r , U _t are the spatial orthogonal basis, _{er ( ), e t (} ) are the unit space feature maps, and substitute Equation 15 into Equation 18 to get:

The present invention also provides a channel estimation method based on a double sparse multipath channel model, which is characterized by comprising the following steps:

Step S1, assume that the angular domain of the MIMO channel represents a matrix, and introduce time fluctuations;

得到时域信道表示，并用压缩感知理论高概率恢复时域信道

Step S2, estimation of temporal sparseness based on compressed sensing: by the formula

Get the time-domain channel representation, and use the compressed sensing theory to recover the time-domain channel with high probability

向量化，再利用压缩感知理论高概率恢复出角域表示的MIMO信道

Step S3, the sparse estimation of the angle domain based on compressed sensing: the

Vectorization, and then use the compressed sensing theory to restore the MIMO channel represented by the angle domain with high probability

Step S4, measuring the estimation accuracy of the double sparse multipath channel model.

Preferably, in step 2, the specific process of the time-domain sparse estimation based on compressed sensing is: converting the assumed angular-domain representation into the time-domain representation of the channel, and quantizing the time-domain representation; using the compressed sensing theory for a single channel The time domain channel is recovered with high probability, and the same is true for other channels, which can be added to the loop.

Preferably, the specific steps for recovering the time-domain channel with high probability using compressed sensing theory:

1) Conversion from time domain to frequency domain

For the channel h _gk from the kth transmit antenna to the gth receive antenna, in the time domain, y _gk =h _gk (t)*x _k (τ-t)+w, 0≤t≤L, y _gk is the gth The signal received by the receiving antenna, * represents the convolution, x _k is the transmitted data of the kth transmitting antenna, w is the noise in the transmission process, and L is the channel length;

Convert it to frequency domain namely: Y _gk =X _k H _gk +W (21)

2) Put pilot frequency in MIMO-OFDM system

In an OFDM system with N subcarriers, it is assumed that the cyclic prefix length of the OFDM symbol is not less than the channel length L; the i-th transmitted data in OFDM is x(i), i=1,2,3,...N -1; In order to avoid interference, the pilot positions between the transmitting antennas are orthogonal. Among the N subcarriers of the OFDM symbol, p are used to place pilots, Ψ=(e _s1 , e _s2 , ...... .e _sp ) is a p×N pilot selection matrix, s _i , i=1, 2, 3,...p, represents the position of the i-th pilot, and e _si is a column vector of length N, which The _si -th element of is 1, and the other elements are all 0, then in formula (21),

Y _gk = [Y _gk (0), Y _gk (1) ...... Y _gk (N-1)], X _k = [x _k (0), x _k (1) ..... .x _k (N-1)]

H _gk =F _N×L h _gk is the channel frequency domain response sample value, wherein F _N×L is a partial DFT transformation matrix, which is formed by the first L columns of the N-dimensional DFT transformation matrix. W is an N-dimensional additive complex white Gaussian noise vector with variance σ ² , and the pilot selection matrix Ψ is applied to both ends of equation (21), we can get:

Y _{gk_p} =X _{g_p} F _p h _gk +W _p (22)

Wherein, Y _{gk_p} =ΨY _gk , W _p =ΨW are both p-dimensional column vectors, which are respectively the received pilot signal and its corresponding channel noise. X _{k_p} =ΨXΨ ^T is a p×p diagonal matrix, and the elements on the diagonal are p pilots at the transmitting end. F _p =ΨF _N×L is a p×L matrix.

Let T=X _{t_p} F _p , then equation (22) can be written as:

Y _{gk_p} =Th _gk +W _p (23)

Among them, T is a _p × _L matrix, and h _gk represents the channel time domain impulse response from the kth transmitting antenna to the _gth receiving antenna, which is sparse in wireless communication. and the receiver are known, so h _ik can be recovered with high probability from Y _{gk_p} using a reconstruction algorithm with known sparsity.

Preferably, the assumed angular domain representation is vectorized, and the angular domain channel is recovered with high probability using compressed sensing theory for a single channel, and the same is true for other channels, just adding a loop.

Preferably, the normalized mean square error is used to calculate the accuracy of the channel estimation.

Compared with the prior art, the beneficial effects achieved by the present invention are as follows: the present invention utilizes the sparse characteristics of both the time domain and the angular domain in millimeter wave communication to study the downlink channel propagation characteristics of the millimeter wave MIMO system fluctuating with time, and establishes a A double sparse multipath channel model is proposed. Furthermore, according to the sparsity in time domain and angle domain, an estimation method of double sparse multipath channel based on compressed sensing is designed. The results show that the estimation performance of double sparse multipath channel is better than that of traditional sparse multipath channel It is often better. Even in the case of unknown sparsity, the estimation performance of double-sparse multipath channel is better, and the original channel can be recovered with high probability.

Description of drawings

1 is a schematic diagram of a SIMO line-of-sight transmission channel of a pair of transmit antennas and n _r pairs of receive antennas;

FIG. 2 is a schematic diagram of the MISO line-of-sight transmission channel of n _t pair of transmit antennas and one pair of receive antennas;

Fig. 3 is a MIMO physical channel diagram including a direct path and a reflected path;

FIG. 4 is a schematic diagram of angular domain division of 4 receiving antennas (L _r =2) and 4 transmitting antennas (L _t =2);

FIG. 5 is a schematic diagram of a double sparse channel model;

Fig. 6 is a time-domain discrete sparse channel model diagram;

7 is a flowchart of an estimation method for a double sparse multipath channel model;

FIG. 8 is a shape diagram of an OFDM pilot;

FIG. 9 is a comparison diagram of the estimation performance between double sparse channels and the prior art where only time domain sparseness is considered.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings. The following examples are only used to illustrate the technical solutions of the present invention more clearly, and cannot be used to limit the protection scope of the present invention.

In the next generation wireless communication, the millimeter wave transmission has the characteristic of being sparse in both the time domain and the angle domain, so the present invention establishes a double sparse multipath channel model in the time domain and the angle domain. The specific process of its modeling is as follows.

1) Line-of-sight SIMO channel

First consider the SIMO (single input multiple output) line-of-sight transmission channel of a transmitting antenna and n _r receiving antennas. This SIMO transmission channel is shown in Figure 1. The n _r receiving antennas are arranged in the normalized length L _r respectively. In a uniform linear array, Δ _r =L _r /n _r is the normalized receiving antenna spacing.

Then the continuous time impulse response h _i (τ) of the channel between the transmitting antenna and the i-th receiving antenna is:

h _i (τ)=aδ(τ-d _i /c) i=1,2,...,n _r

where d _i is the distance between the transmitting antenna and the i-th receiving antenna, c is the speed of light, and a is the path attenuation, assuming that the path attenuation is the same for all antenna pairs. Let d _i /c<<1/W, where W is the transmission bandwidth, then the baseband gain of the line-of-sight transmission channel of the transmit antenna and n _r receive antennas is:

Among them, f _c is the carrier frequency, λ _c is the carrier wavelength, and since the distance between the transmitter and the receiver is much larger than the size of the receiving antenna array, the paths from the first transmitting antenna to each receiving antenna are parallel, Therefore:

d _i ≈d+(i-1)△ _r λ _c cosΦ _r i=1,2,...,n _r

Among them, d is the distance from the transmitting antenna to the first receiving antenna, △ _r is the normalized receiving antenna spacing, Φ _r is the angle between the line-of-sight path of the transmitting antenna and the receiving antenna array, that is, the angle of arrival, AOA).

Let Ω _r :=cosΦ _r , denote the direction cosine of the receiving antenna array, then the line-of-sight transmission channel gain vector of the transmitting antenna and n _r receiving antennas is:

For the convenience of notation, define

is the unit space feature map on the direction cosine Ω _r .

Substituting equation (2) into equation (1), the SIMO line-of-sight transmission channel gain vector is:

2) Line-of-sight MISO channel

Figure 2 shows the MISO (multiple input single output) line-of-sight transmission channel of n _t pairs of transmitting antennas and one pair of receiving antennas. The n _t pairs of receiving antennas are arranged in a uniform linear array with normalized length L _t respectively, △ _t = L _t / _nt is the normalized receive antenna spacing. Φ _t is the angle between the line-of-sight path of the transmitting antenna array and the receiving antenna, that is, the angle of departure (AOD). Let Ω _t :=cosΦ _t , denote the direction cosine of the transmitting antenna array. Similarly for the SIMO line-of-sight transmission channel, the MISO line-of-sight transmission channel gain vector is:

definition:

is the unit space feature map in the emission direction Ω _t .

Then formula (5) is substituted into formula (4) to get:

Among them, d is the distance from the first secondary transmitting antenna to the receiving antenna.

3) There is a MIMO channel with a line-of-sight path

Consider a multi-antenna MIMO (multiple input multiple output) channel with sparse time and angle domains corresponding to a transmitter with n _t antennas and a receiver with n _r antennas; assume that there are n _t transmit antennas and n _r receive antennas The antennas are arranged in uniform linear arrays with normalized lengths _Lt and _Lr , respectively. Δ _r =L _r /n _r is the normalized receiving antenna spacing, and Δ _t =L _t /n _t is the normalized transmitting antenna spacing. Then the channel gain between the t-th transmitting antenna and the r-th receiving antenna is:

h _rt =aexp(-j2πd _rt /λ _c ) (7)

In the formula, a is the attenuation of the path (assuming the attenuation of all antennas is the same), d _rt is the distance between the t-th transmitting antenna and the r-th receiving antenna. Generally, the size of the pseudo-antenna array is much smaller than that of the transmitting antenna and the receiving antenna array. The distance between is:

d _rt ≈d+(r-1)△ _r λ _c cosΦ _r -(t-1)△ _t λ _c cosΦ _t

d is the distance between the first sub-transmitting antenna and the first sub-receiving antenna. Φ _r is the angle between the line-of-sight path of the transmitting antenna and the receiving antenna array, that is, the angle of arrival (AOA). Ω _r :=cosΦ _r , indicating the direction cosine of the receiving antenna array. Φ _t is the angle between the line-of-sight path of the transmitting antenna array and the receiving antenna, that is, the angle of departure (AOD). Let Ω _t :=cosΦ _t , denote the direction cosine of the transmitting antenna array. Then substituting into (7) is equal to:

h _rt =aexp(-j2πd/λ _c )·exp(j2π(t-1)Δ _t Ω _t )·exp(-j2π(r-1)Δ _r Ω _r ) (8)

Therefore, at a certain moment, the MIMO channel matrix with a line-of-sight path is:

_{er (·) and e t (} ·) are respectively defined by formula (2) and formula (5), and (·) ^H represents a conjugate transposition.

4) MIMO channel including one direct path and one reflected path

As shown in Figure 3, there are two points A and B in the MIMO transmission channel, B is the reflection point encountered obstacles, and A is a point selected on the direct path according to the reflection point of the reflection path (virtual point, is our Hypothetical, does not actually exist). We can regard two points A and B as relays, then the MIMO channel including a direct path (denoted as path 1) and a reflection path (denoted as path 2) can be divided into two channels.

Channel 1: Line-of-sight transmission channel with n _t pairs of transmitting antennas and two receiving antennas A and B geographically spaced apart. Since the two receiving and transmitting antennas A and B are geographically spaced apart, the transmitting antenna array reaches The departure angles of A and B are different.

Channel 2: Contrary to channel 1, it is the line-of-sight transmission channel of two transmitting antennas A, B and n _r receiving antennas that are geographically spaced apart. The angles of arrival of the receive antenna arrays are different.

The channel gain vector of channel 1 is the superposition of the line-of-sight MISO channel gain vector (6), which is

In the formula, a _t1 and a _t2 are the attenuation of the transmitting antenna to point A and point B respectively (assuming that the attenuation of all antennas is the same). d _t1 and d _t2 are the distances from the first secondary transmitting antenna to point A and point B, respectively. Φ _t1 and Φ _t2 are the departure angles of path 1 and path 2 in FIG. 3 , respectively. Let Ω _t1 :=cosΦ _t1 , Ω _t2 :=cosΦ _t2 represent the direction cosine of the transmitting antenna array. e _t (·) is defined by equation (5).

The channel gain vector of channel 2 is the superposition of the line-of-sight SIMO channel gain vector (3), which is

In the formula, a _r1 and a _r2 are the attenuations from point A and point B to the receiving antenna array respectively (assuming that the attenuations of all antennas are the same). d _r1 and d _r2 are the distances from point A and point B to the first receiving antenna, respectively. Φ _r1 and Φ _r2 are the arrival angles of path 1 and path 2 in Fig. 3, respectively. Let Ω _r1 :=cosΦ _r1 , Ω _r2 :=cosΦ _r2 represent the direction cosine of the receiving antenna array. _er (·) is defined by equation (2).

The MIMO channel gain including a direct path and a reflected path is the combination of channel 1 and channel 2, which is:

Let σ _i = _{ari a ti denote the attenuation of the i-th path (assuming all antennas have the same attenuation), and d i =d ri + d ti denote} the i-th path from the first transmit antenna to the first receive antenna length. Put it into equation (12) to get:

且将MIMO信道扩展到n条路径，则窄带MIMO多径信道为：For the convenience of writing, let

And extending the MIMO channel to n paths, the narrowband MIMO multipath channel is:

5) Narrowband MIMO multipath channel angle domain modeling

In a narrowband MIMO channel, the transmit antenna array length L _t and receive antenna array length L _r control the degree of resolution in the angular domain: the difference between the cosines of the transmit direction is less than 1/L _t and the difference of the cosines of the receive direction is less than 1/L _r . Paths are paths that cannot be resolved by the antenna array. This means that in the angular domain, the transmitter should "sample" with a fixed angular interval of 1/L _t , while the receiver should "sample" with a fixed angular interval of 1/L _r .

Therefore, the space orthogonal basis (unitary matrix) of the received signal and the transmitted signal can be defined as:

It provides the angle domain representation of the received signal and the transmitted signal, respectively.

时，角域窗口与角域基矢量为一一对应关系，这种情况是最简单的。在后续讨论中，假设天线是临界间隔的，即

如图4所示，其中4副发射天线与4副接收天线分别排列在归一化长度为L_t＝2与L_r＝2的均匀线性阵列中。△_r＝L_r/n_r＝1/2,△_t＝L_t/n_t＝1/2为临界间隔，故角域被划分为4个接收区域(图4右侧)和4个发射区域(图4左侧)。When the normalized receiving antenna spacing △ _r and the normalized transmitting antenna spacing △ _t are both

When , there is a one-to-one correspondence between the angular domain window and the angular domain basis vector, which is the simplest case. In the subsequent discussion, the antennas are assumed to be critically spaced, i.e.

As shown in FIG. 4 , four transmitting antennas and four receiving antennas are arranged in a uniform linear array with normalized lengths L _t =2 and L _r =2, respectively. △ _r =L _r /n _r =1/2, △ _t =L _t /n _t =1/2 is the critical interval, so the angular domain is divided into 4 receiving areas (right side of Figure 4) and 4 transmitting areas (left side of Figure 4).

Therefore, in the angular domain, the channel gain from the kth transmit area to the gth receive area is roughly equal to the cosine of the transmit direction in an angular window of width 1/ _Lt around _k /Lt, and the cosine of the receive direction at g/Lt The sum of all path gains within an angular window of width 1/L _r around L _r .

Therefore, the narrowband MIMO multipath channel, that is, formula (14), is expressed in the angular domain as:

which is:

The elements in the 1st row and the 1st column in h ^a represent the angular domain gain from the first transmitting area to the first receiving area, and the elements in the 1st row and the 1st column in h represent the first sub-transmitting antenna to the first Channel gain of the secondary receive antenna. Due to the high frequency and short wavelength of millimeter-wave communication, it will be reflected or blocked when it encounters obstacles, and it mainly propagates in a direct way. Therefore, narrow-band MIMO channels have strong sparseness in the angular domain, that is, in many angular domain regions, The channel gain is 0.

6) Model of double sparse multipath channel in time domain and angle domain

The model of the double sparse multipath channel shown in Figure 5. The horizontal axis represents the time axis. There are path sets at three time taps in the figure, and the instant domain is sparse, and at each non-zero tap point (the moment when the path set exists), its angular domain is sparse, that is, in the figure, At each non-zero tap point in the time domain, there are path sets in the three angular domain directions. And the angular domain gain usually changes more slowly than the delay gain. Therefore, it is reasonable to assume that the orientation of the set of non-zero paths in the angular domain does not change at different instants within the time scale under study.

Specifically, the double-sparse multipath channel model in the time domain and angle domain is:

H ^a = [H ^a (0), H ^a (1), H ^a (2), ..., H ^a (L-1)] (17)

Among them, L is the channel length, H ^a is the double sparse channel model in the time-domain angular domain with delay L, H ^a (τ) is the channel matrix in the angular-domain time τ, m is the non-zero tap point of the channel in the time domain The number of (the moment when the path set exists), the sparsity in the instant domain, ^ha is the angular domain representation of the narrowband MIMO multipath channel (see Equation (15)), and τ _j is the delay of the jth path.

First of all, the channel is sparse in the time domain, that is, there are path sets at some moments and no path sets at some moments. Figure 6 shows the time-domain discrete sparse channel model generated by superimposing the Rayleigh channel model (at this time, the channel length L=60, the number of non-zero tap points m=5 in the time domain, that is, there are only 5 time-domain path sets).

Secondly, when there is a set of paths (for example, a total of 10 paths are gathered at a certain moment), due to some characteristics of millimeter waves (the communication frequency of millimeter wave is high and the wavelength is short, it will be reflected or blocked when it encounters a block, so that the direct radiation The 10 paths may come from one or less angular domain regions, so they are also sparse in the angular domain.

Specifically, substitute formula (15) into (18) to get:

The channel estimation method for designing the model is as important as building the model. Currently, one of the most popular and widespread methods for learning multipath wireless channels is to probe the channel with a signaling waveform known to the receiver (called a training waveform) and process the corresponding channel output to estimate channel parameters. The performance of this training-based channel estimation method is generally judged by the assumed original channel and the mean squared error (MSE) of the channel estimated from the received signal and the transmitted signal. Therefore, the training-based channel estimation scheme has two salient features: perception and reconstruction. Perception refers to the design of the training waveform for the probing channel, while reconstruction is the problem of obtaining the corresponding channel output at the receiver to recover the channel response.

However, traditional channel estimation methods lead to over-utilization of critical communication resources of energy and bandwidth in sparse multipath channels. Therefore, there are traditionally many training-based methods to estimate single-antenna and multi-antenna sparse multipath channels, and these similar studies lack quantitative theoretical analysis of the performance of the proposed method. In contrast, channel estimation methods based on training and the key ideas of Compressed Sensing (CS) theory are more effective.

In addition, by using the double sparsity of the time domain and the angle domain, pilots can be placed only in certain angle domain directions (these angle domains have path sets). Therefore, by using the model of double sparse multipath channel in time domain and angle domain, the overhead of pilot frequency can be greatly reduced, and the complexity of channel estimation can be greatly reduced. In addition, since the pilot frequency is only placed in the angular domain direction of the path set, less noise is mixed, and the channel estimation performance is also greatly improved. Using the double sparse multipath channel model for estimation not only removes the noise in the time domain, but also filters out the noise in the angle domain.

A channel estimation method based on a double sparse multipath channel model in the present invention, as shown in Figure 7, includes the following steps:

Step S1, initialize the angular domain representation matrix of the MIMO channel, and introduce time fluctuation.

Specifically, it is first assumed that there are 16 transmit antennas and 8 receive antennas, the channel length is 60, the time domain sparsity is 5 (that is, there are only 5 moment sets of paths), and the angular domain sparsity is 3. Use matlab to generate a 16x8x60 all-zero matrix H ^a (the meaning is the same as H ^a in formula 17), and then use matlab to generate 3x5 normally distributed random numbers. The first and second dimensions of matrix H ^a represent the angular domain, and the third dimension Each dimension represents the time domain, 5 times are randomly selected, 3 data are placed at each time, and the storage locations of the 3 data at each time are the same. Because angles typically change on time scales much slower than time-domain gains, it is reasonable to assume that paths do not change from one angular-domain region to another within the time-scale under study.

且U_r,U_t都为酉矩阵，而酉矩阵的共轭转置和它的逆矩阵相等，所以

得到时域信道表示，并用压缩感知理论高概率恢复时域信道

Step S2, estimation of temporal sparseness based on compressed sensing: formula (16)

And U _r , U _t are unitary matrices, and the conjugate transpose of the unitary matrix is equal to its inverse matrix, so

Get the time-domain channel representation, and use the compressed sensing theory to recover the time-domain channel with high probability

其它信道同理，加入循环即可。ha refers to the angular domain representation at ^{a certain moment, namely H a (} τ _j ), see formula (18), therefore, the assumed angular domain representation can be converted into the time domain representation of the channel, and h is vectorized; It should be pointed out that h here is only for a certain moment, and the same is true for other moments, just add a loop. Finally, a 128x60 matrix is obtained (16x8=128, which means 128 channels, and 60 means the channel length), and the time-domain channel is restored with high probability using compressed sensing theory for a certain channel.

The same is true for other channels, just add a loop.

The following are the specific steps for recovering the time-domain channel with high probability using compressed sensing theory (this is known in the prior art):

OFDM technology is used when using compressed sensing theory to restore time-domain channels with high probability. The OFDM technology divides the wireless transmission channel into several mutually orthogonal sub-channels, so that the spectrum of each sub-channel is approximately flat, so that frequency selective fading can be effectively overcome. In addition, the OFDM technology uses a cyclic prefix (Cyclic prefix, CP) as a guard interval (Guard Interval), so that the guard interval is greater than the maximum delay spread of the channel, which can avoid inter-symbol interference caused by multipath effects.

1) Conversion from time domain to frequency domain

For any channel h _gk (representing the kth transmit antenna to the gth receive antenna), the time domain has y _gk =h _gk (t)*x _k (τ-t)+w, 0≤t≤L

y _gk is the signal received by the gth receiving antenna (sent by antenna k), * represents convolution, and x _k is the transmitted data of the kth transmitting antenna. w is the noise in the transmission process, generally Gaussian white noise. L is the channel length.

Convert it to frequency domain namely: Y _gk =X _k H _gk +W(21)

2) Put pilot frequency in MIMO-OFDM system

In an OFDM system with N subcarriers, it is assumed that the cyclic prefix (CP) length of the OFDM symbol is not less than the channel length (L). The i-th transmitted data in OFDM is x(i), (i=1, 2, 3, . . . N-1). In order to avoid interference, the pilot positions between the transmitting antennas are orthogonal, as shown in FIG. 8 (shown in FIG. 8 is the information about the orthogonal pilot positions). Among the N subcarriers of the OFDM symbol, p are used to place pilots, Ψ=(e _s1 , e _s2 , ...... e _sp ) is a p×N pilot selection matrix, s _i (i =1,2,3,...p) represents the position of the ith pilot, e _si is a column vector of length N, its _si th element is 1, and the other elements are all 0. In the formula (21),

Y _gk = [Y _gk (0), Y _gk (1) ...... Y _gk (N-1)], X _k = [x _k (0), x _k (1) ..... .x _k (N-1)]

H _gk =F _N×L h _gk is the channel frequency domain response sample value, wherein F _N×L is a partial DFT transformation matrix, which is formed by the first L columns of the N-dimensional DFT transformation matrix. W is an N-dimensional additive complex white Gaussian noise vector with variance ^σ2 . Applying the pilot selection matrix Ψ to both ends of equation (20), we can get:

Y _{gk_p} =X _{g_p} F _p h _gk +W _p (22)

Wherein, Y _{gk_p} =ΨY _gk , W _p =ΨW are both p-dimensional column vectors, which are respectively the received pilot signal and its corresponding channel noise. X _{k_p} =ΨXΨ ^T is a p×p diagonal matrix, and the elements on the diagonal are p pilots at the transmitting end. F _p =ΨF _N×L is a p×L matrix.

Let T=X _{t_p} F _p , then equation (22) can be written as:

Y _{gk_p} =Th _gk +W _p (23)

Among them, T is a p×L matrix, and h _gk represents the channel time-domain impulse response from the kth transmitting antenna to the gth receiving antenna, showing sparsity in wireless communication. Since Y _{ik_p} , X _{i_p} , and F _p are known at the sender and receiver, h _gk can be recovered with high probability from Y _{gk_p} using a reconstruction algorithm with known sparsity. The reconstruction algorithm with known sparsity belongs to the prior art, and the specific calculation process is as follows:

According to formula (23), input: Y _{gk_p} : received pilot signal; T: recovery matrix; m: sparsity of channel time domain;

Initialization: residual r ₀ =Y _{gk_p} , index set Λ ₀ =O, number of iterations i=1, Γ ₀ =O, where O represents an empty set;

The i-th iteration process is as follows:

τ_j为矩阵T的第j列；(1) The residual r _i-1 is matched with each column in the recovery matrix T, and the column with the highest degree of correlation is found. Since the larger the inner product of the two vectors, the higher the degree of correlation, so the inner product is used to obtain the residual and The index of the column with the highest correlation in the recovery matrix is:

τ _j is the jth column of matrix T;

(2) Update Λ _i ={Λ _i-1 ∪λ _i },Γ _i =Γ _i-1 ∪τ _λi ;

其中

表示Γ_i的伪逆；(3) Use the LS algorithm to obtain a new channel estimate:

in

represents the pseudo-inverse of Γ _i ;

(4) Calculate the new residual value:

(5) i=i+1, let the λ _i column of the matrix T be a 0 vector, and λ _i is obtained from step (1).

(6) Start the cycle from step (1).

Terminate loop condition: when i>=m, terminate the iteration.

并将其转换成n_r×n_t的矩阵形式，即估计得到的时域信道

Output: Channel estimate

and convert it into a matrix form of n _r × _nt , that is, the estimated time-domain channel

In this embodiment, only one channel is used as an example, and the same is true for other channels, and a loop can be added to the simulation.

In the MIMO-OFDM system, the pilot can be placed in the frequency domain or directly in the angular domain. For the convenience of description, the present invention places the pilot in the frequency domain. Placing pilots in the angular domain can reduce overhead for practical massive MIMO systems. For example, if it is detected that certain angular regions contain path sets, it is only necessary to place pilots in these angular regions containing path sets. According to the characteristics of mmWave transmission, only a few angular regions contain path sets. Therefore, the number of pilots is relatively small, and the estimation process is similar to the above-mentioned process, both of which are double denoised in the time domain and angular domain to improve the performance of channel estimation.

向量化，再利用压缩感知理论高概率恢复出角域表示的MIMO信道

Step S3, sparse estimation of the angle domain based on compressed sensing: according to formula (20)

Vectorization, and then use the compressed sensing theory to restore the MIMO channel represented by the angle domain with high probability

表示估计值。in

represents an estimated value.

向量化，以符合使用重构算法的条件。1) will

Vectorized to qualify for use of the reconstruction algorithm.

其中

为两者的克罗克内积，将

向量化：according to

in

is the Crocker's inner product of the two, the

Vectorize:

其中(·)^*表示复共轭

where ( ) ^* denotes complex conjugate

remember:

角域窗口与角域基矢量为一一对应关系，也就是说，角域量化的网格数等于接收天线数n_t乘以发射天线数n_r。Since the antennas discussed in this patent are critically spaced, i.e.

There is a one-to-one correspondence between the angular domain window and the angular domain base vector, that is to say, the number of grids for angular domain quantization is equal to the number of receiving antennas n _t multiplied by the number of transmitting antennas n _r .

2) Using the compressive sensing reconstruction algorithm to restore the angular domain sparse channel with high probability

Due to the sparseness of the angular domain, the channel estimation problem in the angular domain can also be formulated as a reconstruction problem of sparse signals. That is: g=Af, since g and A are known and f is sparse, the reconstruction algorithm of compressed sensing can be used to restore f with high probability. Finally, the vector f is converted into a matrix form of n _r × _nt , that is, the MIMO channel represented by the estimated angular domain is obtained.

The compressive sensing reconstruction algorithm used above is the same as the above reconstruction algorithm with known sparsity. The angular domain estimation at other time domain non-zero tap points is the same.

Step S4, using NMSE to measure the estimation performance of the double sparse multipath channel model.

其中H表示假设的信道，

表示估计得出的信道)，并将其换成以dB为单位，10*log10(NMSE)。MIMO信道为假设有16副发射天线和16副接收天线，天线为临界间隔，信道长度为60。假设时域稀疏度为5，角度域稀疏度为3。带有*的折线表示的是本发明双稀疏多径信道的估计性能，即同时考虑了时域稀疏和角域的稀疏性。带有

的折线表示传统时域稀疏多径信道的估计性能，即此种情况仅考虑了时域的稀疏性。由于毫米波在时域和角度域的双稀疏性，即在时域，仅有某几个时刻是有信息的，但在传输的过程中，其他时刻也会收到‘信息’，而这些信息即所谓的噪声。用本发明介绍的基于压缩感知的信道估计算法，利用其稀疏性，很好的抑制了噪声。同理在某一时刻，仅有几个角度区域是有信息的，同样，其他的角度区域在接收端也会收到‘信息’，而这些信息也是传输过程中的噪声。利用基于压缩感知的信道估计算法，利用其稀疏性，也能很好的抑制来自其他方向的噪声。也就是说，在进行信道估计时，考虑信道传输时时域和角度域的双稀疏性，进行两次去噪，必然比传统的仅考虑时域稀疏的信道估计方法抑制噪声的能力强。即使在稀疏度未知的情况下，双稀疏多径信道的估计性能也表现较好，能够高概率的恢复出原始信号，具有更强的抑制噪声的能力。FIG. 9 shows a comparison chart of the estimation performance of the dual sparse channel of the present invention and the channel estimation performance only considering time domain sparseness in the prior art. In the figure, the abscissa is the signal-to-noise ratio (SNR, whose unit of measurement is dB). It is generally fixed; the ordinate represents the normalized mean-square error (NMSE) between the initially assumed channel and the final estimated channel. The calculation method is

where H represents the hypothetical channel,

represents the estimated channel), and replace it in dB, 10*log10(NMSE). The MIMO channel is assumed to have 16 transmit antennas and 16 receive antennas, the antennas are critically spaced, and the channel length is 60. Suppose the time domain sparsity is 5 and the angle domain sparsity is 3. The broken line with * represents the estimation performance of the double sparse multipath channel of the present invention, that is, the sparseness in the time domain and the sparseness in the angular domain are considered at the same time. with

The broken line represents the estimation performance of the traditional time-domain sparse multipath channel, that is, only the time-domain sparsity is considered in this case. Due to the double sparsity of millimeter waves in the time domain and the angular domain, that is, in the time domain, only a few moments have information, but in the process of transmission, other moments will also receive 'information', and these information This is the so-called noise. With the channel estimation algorithm based on compressed sensing introduced in the present invention, the sparseness of the channel estimation algorithm is used to suppress the noise very well. Similarly, at a certain moment, only a few angular areas have information, and similarly, other angular areas will also receive 'information' at the receiving end, and these information are also noise in the transmission process. Using the channel estimation algorithm based on compressed sensing and its sparsity, the noise from other directions can also be well suppressed. That is to say, when performing channel estimation, considering the double sparsity of the time domain and the angle domain during channel transmission, performing denoising twice must be more capable of suppressing noise than the traditional channel estimation method that only considers the time domain sparsity. Even when the sparsity is unknown, the estimation performance of the double-sparse multipath channel is good, the original signal can be recovered with a high probability, and it has a stronger ability to suppress noise.

The above are only the preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, without departing from the technical principle of the present invention, several improvements and modifications can be made. These improvements and modifications It should also be regarded as the protection scope of the present invention.

Claims (6)

1. A method for constructing a double-sparse multi-path channel model is characterized in that the double sparsity refers to time domain sparsity and angular domain sparsity, and the time domain and angular domain double-sparse multi-path channel model is as follows:

H^a＝[H^a(0),H^a(1),H^a(2),...,H^a(L-1)] (17)

where L is the channel length, H^aIs a double sparse channel model of the time domain angular domain with a channel length L, H^a(tau) is a channel matrix of an angular domain at the time of tau, m is sparsity of a time domain, delta (t) is an impulse function, and tau_jFor the channel length of the jth path,

and wherein

Wherein,

σ_irepresenting the attenuation of the ith path, n_tRepresenting the number of transmitting antennas, n_rIndicating the number of receiving antennas, d_iDenotes the length of the ith path from the first transmit antenna to the first receive antenna, λ_cFor carrier wavelength, n represents the number of channel paths, U_r、U_tIs a space orthogonal basis (·)^HRepresents a conjugate transpose; omega_ri:＝cosΦ_ri,Ω_ti:＝cosΦ_tiThe symbol ": means" defined as "wherein Φ_tIs the angle between the line-of-sight path of the transmitting antenna array and the transmitting antenna, i.e. the departure angle, phi_tiDenotes the ith angle of departure; phi_rIs the included angle between the sight distance path of the transmitting antenna and the receiving antenna array, namely the arrival angle，Φ_riRepresents the ith angle of arrival; e.g. of the type_r(·)、e_t(. h) is a unit space characteristic diagram, and formula 15 is substituted into formula 18 to obtain:

2. a channel estimation method based on the dual sparse multipath channel model of claim 1, comprising the steps of:

step S1, an angular domain representation matrix of the MIMO channel is assumed, and time fluctuation is introduced;

step S2, estimation of time domain sparsity based on compressed sensing

Obtaining the time domain representation h of the channel, and recovering the time domain channel with high probability by using the compressed sensing theory

Is an estimated value of a time domain channel h;

step S3, estimation of angular sparsity based on compressed sensing

Vectorization of where h^aMIMO channel represented for angular domain; MIMO channel with estimated angular domain representation obtained by compressed sensing theory

Step S4, the accuracy of the dual sparse multipath channel model estimation is measured.

3. The channel estimation method according to claim 2, wherein in step S2, the specific process of estimating the time-domain sparsity based on compressed sensing is as follows: converting the hypothesized angular domain representation into a time domain representation and vectorizing the time domain representation; and (3) recovering the time domain channel by using the compressed sensing theory with high probability aiming at a single channel, and adding circulation to other channels in the same way.

4. The channel estimation method according to claim 3, wherein the step of recovering the time domain channel with high probability using compressed sensing theory comprises:

1) time-to-frequency domain conversion

Time domain channel h for k-th sub-transmitting antenna to g-th sub-receiving antenna_gkTime domain has y_gk＝h_gk(t)*x_k(τ-t)+w，0≤t≤L，y_gkFor the signal received by the g-th receiving antenna, x represents the convolution_kTransmitting data of a kth transmitting antenna, wherein w is noise in the transmission process, and L is channel length;

converting it to the frequency domain i.e.: y is_gk＝X_kH_gk+W (21)

2) Pilot frequency amplification in MIMO-OFDM system

In an OFDM system with N subcarriers, assuming that the cyclic prefix length of an OFDM symbol is not less than the channel length L; in OFDM, the ith transmission data is x (i), i is 1,2, 3.. N-1; to avoid interference, pilot positions between transmitting antennas are orthogonal, and of N subcarriers of an OFDM symbol, p are used for placing pilots, and psi ═ (e)_s1,e_s2,......e_sp) For a pilot selection matrix of p × N, s_iIndicates the position of the ith pilot, i-1, 2,3, … p, e_siIs a column vector of length N, of which the s-th_iWhen one element is 1 and the other elements are all 0, in the formula (21),

Y_gk＝[Y_gk(0),Y_gk(1)......Y_gk(N-1)]，X_k＝[x_k(0),x_k(1)......x_k(N-1)]

H_gk＝F_N×Lh_gksampling values for the channel frequency domain response, where F_N×LFor partial DFT transform matrix, from NThe first L columns of the dimensional DFT transform matrix are formed, W is a variance of σ²The N-dimensional additive complex gaussian white noise vector of (2) is obtained by applying the pilot selection matrix Ψ to both ends of equation (21):

Y_{gk_p}＝X_{g_p}F_ph_gk+W_p (22)

wherein, Y_{gk_p}＝ΨY_gk,W_pPsi W are p-dimensional column vectors, X being the received pilot signal and its corresponding channel noise, respectively_{g_p}＝ΨXΨ^TThe pilot frequency array is a p multiplied by p diagonal array, and elements on the diagonal are p pilot frequencies of a transmitting end; f_p＝ΨF_N×LA matrix of p × L;

let T ═ X_{g_p}F_pEquation (22) can be written as:

Y_{gk_p}＝Th_gk+W_p (23)

where T is a p × L matrix, h_gkRepresenting the time-domain channel from the kth sub-transmitting antenna to the gth sub-receiving antenna, exhibits sparsity in wireless communication due to Y_{gk_p},X_{g_p},F_pIs known at the transmitting end and the receiving end, and therefore can be reconstructed according to Y by using a reconstruction algorithm with known sparsity_{gk_p}High probability recovery h_gk。

5. The channel estimation method of claim 2, wherein the assumed angular domain representation is vectorized, the angular domain channel is recovered with high probability by using a compressed sensing theory for a single channel, and other channels are added into a loop similarly.

6. The channel estimation method of claim 2, wherein the accuracy of the channel estimate is calculated using a normalized mean square error.

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