Channel estimation algorithm based on fourth-order nested PARAFAC model

Abstract

The invention relates to a channel estimation algorithm based on a fourth-order nested PARAFAC model, and provides a KRD-LiSe-TALS receiver algorithm, which comprises the following steps of: in a first stage, obtaining estimations U (1) and Grd of U (1) and Grd by using a LiSe-TALS algorithm according to a first-layer tensor y; in the second stage, according to a second-layer tensor y and a known coding matrix C2, a KRD algorithm is used to obtain an estimator of the sum V (1) and the sum V (1); in the third stage, according to the tensor v of the third layer, using the LiSe-TALS algorithm to obtain estimators Z (1) and Gsr of Z (1) and Gsr; and in the fourth stage, the KRD algorithm is used according to the innermost tensor and the known coding matrix C1 to obtain the estimator of the sum S, and on the premise of reducing the number of iterations and reducing the operation time of the algorithm, the improved algorithm can obtain the estimation performance equivalent to that of C-ALS. Compared with LS and TST receiver algorithms, the semi-blind estimation algorithm provided by the invention obtains better estimation performance and lower BER compared with a comparison algorithm on the premise of reducing pilot frequency overhead.

Description

Technical Field

[0001] This invention belongs to the field of information acquisition, specifically involving a channel estimation algorithm for millimeter waves. Background Technology

[0002] With the continuous development of 5G technology, millimeter wave technology is widely used due to its advantages such as wide spectrum, good stability, and strong beam directionality. Therefore, research on channel estimation algorithms for millimeter waves is of significant research value. This invention conducts a preliminary study on channel estimation and symbol detection algorithms for time-varying channels in dual-hop MIMO millimeter waves, and proposes two semi-blind receiver algorithms based on tensor decomposition. The first algorithm is based on the traditional least squares channel estimation algorithm, which has high computational complexity. The algorithm is then improved, achieving estimation performance comparable to the first algorithm while significantly reducing complexity. Compared with the traditional two-stage training (TST) algorithm and least squares receiver algorithm, the proposed algorithm has the advantages of more accurate channel estimation and lower bit error rate. Summary of the Invention

[0003] The purpose of this invention is to provide a channel estimation algorithm based on a fourth-order nested PARAFAC model to solve the problems of difficulty in obtaining channel state information in the above-mentioned background art.

[0004] A receiver algorithm based on a fourth-order nested PARAFAC model is provided, including the following steps:

[0005] First, let's explain the data model of this algorithm. The number of radio frequency chains and antennas of the source node are respectively... and M s The number of transmit radio links and the number of antennas of the relay node are respectively and The number of receiving radio links and the number of antennas of the relay node are respectively and The number of receive radio links and the number of antennas at the destination node are respectively and M d The source node and relay node transmit the signal through the P and Q time slots, respectively.

[0006] Step 1: The source transmits the symbol matrix in P time slots. Therefore, in the p-th time slot, the transmitted signal can be represented as:

[0007]

[0008] in, and and These represent the radio frequency precoding matrix and the baseband precoding matrix of the source node, respectively. The encoding matrix representing the source node, This represents the symbol matrix transmitted by the source node. R and T are the number of symbols and the length of a code, respectively.

[0009] Step 2: The radio frequency signal reaches the relay node through the first hop channel. After processing by the radio frequency combiner and the baseband combiner, the signal received by the relay node can be represented as:

[0010]

[0011] in, and and These represent the radio frequency combiner matrix and the baseband combiner matrix of the relay node, respectively, and K represents the number of symbols in a codeword of the baseband signal of the relay node. This represents the millimeter-wave channel between the source node and the relay node during the n1-th time block.

[0012] Step 3, in a uniform linear array, the millimeter-wave channel can be represented as:

[0013]

[0014] in, This represents the complex gain of the l1-th subpath. and These are the angle of departure (AOA) and angle of arrival (AOD) of the millimeter wave at the relay node and source node, respectively. L1 is the channel H. sr The number of scattering paths included. This represents the Doppler frequency offset of the l1-th path in the first hop. s N1 represents the channel sampling period, and N1 represents the number of time blocks in the first hop, where n1 = 1, 2, ..., N1. and These are the receive and transmit array steering vectors, as shown below:

[0015]

[0016]

[0017] Where d represents the spacing of the uniform antenna array, and λ is the carrier wavelength.

[0018] Step 4, further, through identity deformation, H sr It can be rewritten as follows:

[0019]

[0020] Among them, As (θ s A represents the steering matrix of the source node's emission angle. r (θ r G represents the guidance matrix of relay node AOA. sr The complex gain and Doppler joint matrix of the first-hop channel is expressed as follows:

[0021]

[0022]

[0023] G sr =G d,sr diag(a sr (9)

[0024] In equation (9), G d,sr and a sr Let Doppler matrix and path gain vector of the first hop channel be represented respectively, and their specific expressions are as follows:

[0025]

[0026]

[0027] in, The Doppler vector of the l1-th path in the first-hop channel is expressed as follows:

[0028]

[0029] Step 5, similar to the source node, the relay node transmits the following radio frequency signal:

[0030]

[0031] in, and These represent the radio frequency and baseband precoding matrices of the relay node, respectively. The magnification matrix representing the relay node; This represents the encoding matrix of the relay node.

[0032] Step 6, the baseband signal received by the destination node is:

[0033]

[0034] in, and These represent the radio frequency and baseband precoding matrices of the destination node, respectively. This represents the millimeter-wave channel matrix between the relay and the destination node in time block n2.

[0035]

[0036] in, It is the complex gain of the l2th subpath. and These are the AOA and AOD of millimeter waves at the relay node and source node, respectively. and These are the guide vectors for the receive and transmit arrays, respectively. Let N2 represent the Doppler shift of the l2-th path in the first hop. N2 represents the number of time blocks in the first hop, and n2 = 1, 2, ..., N2.

[0037] Step 7, with processing H sr The method is the same, H rd It can be rewritten as:

[0038]

[0039] Among them, B r (φ r B represents the steering matrix for the relay node's transmission angle. d (φ d G represents the guidance matrix of the destination node AOA. rd The complex gain and Doppler joint matrix of the first-hop channel is expressed as follows:

[0040]

[0041]

[0042] G rd =G d,rd diag(a rd (19)

[0043] Step 8, correspondingly, the path gain vector and Doppler matrix of the second-hop channel are:

[0044]

[0045]

[0046] in, The Doppler vector representing the l2-th path of the second-hop channel is expressed as follows:

[0047]

[0048] Step 9, substitute (1), (2), and (13) into (14), and consider the influence of the complex Gaussian channel on the signal during transmission. Then, the noisy received signal can be written as

[0049]

[0050] in, This represents the noise component in the received signal.

[0051] Step 10: To facilitate signal processing and formula transformation, rewrite equation (23) to obtain equation (24).

[0052]

[0053] in,

[0054] Step 11, rearranging the P time slots in equation (24) yields:

[0055]

[0056] in, This represents the noise component.

[0057] Step 12, similarly, by rearranging the above equation sequentially for time block n1, time slot q, and time block n2, we can obtain the following equation:

[0058]

[0059] The PARAFAC model conforms to tensors, and is a fourth-order nested PARAFAC tensor model, represented from the innermost to the outermost layer as follows: The revised expression is shown below.

[0060]

[0061]

[0062]

[0063] Attached Figure Description

[0064] Figure 1 For system model;

[0065] Figure 2 The performance of the KRD-LiSe-TALS algorithm in estimating AOA / AOD in a communication system under different search accuracies is presented.

[0066] Figure 3 For this algorithm to achieve a search accuracy of f d =OFD max / 500, f d =OFD max / 200 and fd =OFD max Estimation performance of Doppler frequency offset at / 100.

[0067] Figure 4 The corresponding channel gain estimation performance of the algorithm is given under three search accuracies. Detailed Implementation

[0068] The present invention will now be described in detail with reference to the embodiments shown in the accompanying drawings. However, it should be noted that these embodiments are not intended to limit the present invention. Equivalent transformations or substitutions in function, method, or structure made by those skilled in the art based on these embodiments are all within the protection scope of the present invention.

[0069] This invention provides a KRD-LiSe-TALS receiver algorithm, comprising the following steps:

[0070] The joint estimation algorithm based on KRD and LiSe-TALS (KRD-LiSe-TALS) is mainly divided into four stages, corresponding to the four-layer PARAFAC model. The first stage is based on the first-layer tensor. Using the LiSe-TALS algorithm, we obtain U (1) and G rd estimator U (1) and G rd In the second stage, based on the second-layer tensor... Using the KRD algorithm with the known encoding matrix C2, we obtain and V (1) estimator and V (1) The third stage, based on the third-level tensor Using the LiSe-TALS algorithm, we obtain Z (1) and G sr estimator Z (1) and G sr The fourth stage is based on the innermost tensor. Using the KRD algorithm with the known encoding matrix C1, we obtain and the estimator of S and The detailed algorithm steps are shown in Algorithm 3. Algorithm 1 shows the detailed steps of the KRD algorithm, and the specific algorithm steps of LiSe-TALS are shown in Algorithm 2.

[0071]

[0072]

[0073]

[0074] Figure 2 The performance of the KRD-LiSe-TALS algorithm for estimating AOA / AOD in a communication system is shown at different search accuracies. It is clear from the figures that higher search accuracy leads to more accurate angle estimation. Furthermore, the improvement in search accuracy significantly increases the accuracy of θ estimation. s and φ d The improvement is most obvious, φ r Secondly, θ r The improvement effect is the least obvious.

[0075] Figure 3 This demonstrates that the algorithm achieves a search accuracy of f. d =OFD max / 500, f d =OFD max / 200 and f d =OFD max The estimation performance of Doppler frequency offset at / 100 is shown in the figure. As can be seen from the figure, the search accuracy can improve the estimation accuracy of DFO, and the improvement effect on the estimation performance of the second hop channel is significantly better than that of the first hop channel.

[0076] Figure 4 The channel gain estimation performance is shown for three search accuracies. The effect is similar to that of Doppler estimation accuracy; higher search accuracy results in higher path gain estimation accuracy.

[0077] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within the present invention.

Claims

1. A channel estimation algorithm based on a four-layer nested PARAFAC model, characterized by including: The following steps are required: S1. A millimeter-wave communication system model was established, and the expression of the signal at each node was derived in detail. S2. Construct the signal into a four-layer nested PARAFAC model at the destination node. S3. Using the proposed algorithm based on tensor low-rank decomposition and its uniqueness, the channel state information and symbol matrix are jointly estimated.

2. The channel estimation algorithm based on a four-layer nested PARAFAC model according to claim 1, characterized in that, In step S1, the derivation of the system model and the signal expressions of each node is as follows: S1.1 The system model is a single-relay, double-hop millimeter-wave MIMO-OFDM uplink communication link model using Khatri-Rao Space-Time (KRST) coding, consisting of a source node, relay node, and destination node. The number of radio frequency chains and antennas of the source node are respectively... and M s The number of transmit radio links and the number of antennas of the relay node are respectively and The number of receiving radio links and the number of antennas of the relay node are respectively and The number of receive radio links and the number of antennas at the destination node are respectively and M d The source node and relay node transmit the signal through the P and Q time slots, respectively. S1.2 If the source transmits the symbol matrix in P time slots, then the transmitted signal in the p-th time slot can be expressed as: in, and and These represent the radio frequency precoding matrix and the baseband precoding matrix of the source node, respectively. The encoding matrix representing the source node, This represents the symbol matrix transmitted by the source node. R and T are the number of symbols and the length of a code, respectively. S1.3 The radio frequency signal reaches the relay node after passing through the first hop channel. The signal received by the relay node can be represented as: in, This represents the millimeter-wave channel between the source node and the relay node during the n1-th time block. S1.4 In a linear antenna array, the millimeter-wave channel can be represented as: Furthermore, through identity deformation, H sr It can be rewritten as follows: Among them, A s (θ s A represents the steering matrix of the source node's transmission angle. r (θ r G represents the guidance matrix of relay node AOA. sr This represents the complex gain and Doppler joint matrix of the first-hop channel. S1.5 The radio frequency signal transmitted by the relay node is: in, and These represent the radio frequency and baseband precoding matrices of the relay node, respectively. The magnification matrix representing the relay node; This represents the encoding matrix of the relay node. S1.6 The baseband signal received by the destination node is: in, and These represent the radio frequency and baseband precoding matrices of the destination node, respectively. The millimeter-wave channel matrix representing the relay and destination nodes in time block n²: S1.7, and processing H sr The method is the same, H rd It can be rewritten as: Among them, B r (φ r B represents the steering matrix for the relay node's transmission angle. d (φ d G represents the guidance matrix of the destination node AOA. rd This represents the complex gain and Doppler joint matrix of the first-hop channel. S1.8 Considering the influence of complex Gaussian noise during signal transmission, the received signal can be written as:

3. The channel estimation algorithm based on a four-layer nested PARAFAC model according to claim 2, characterized in that, In step S2, the derivation of the four-layer nested PARAFAC model of the received signal is as follows: S2.1 Rewriting the above received signal expression and rearranging time slot P, time block n1, time slot q, and time block n2, we get the following formula: S2.2, It is a four-layer nested PARAFAC tensor model, represented from the innermost to the outermost layer as follows: Its expansion is shown below.

4. The channel estimation algorithm based on the four-layer nested PARAFAC model according to claim 2, characterized in that, In step S3, the algorithm steps based on tensor low-rank decomposition and its uniqueness are as follows: S3.1, Based on the first layer tensor Using the LiSe-TALS algorithm, we obtain U (1) and G rd estimator U (1) and G rd . S3.2, Based on the second-level tensor Using the KRD algorithm with the known encoding matrix C2, we obtain and V (1) estimator and V (1) . S3.3, Based on the third-level tensor Using the LiSe-TALS algorithm, we obtain Z (1) and G sr estimator Z (1) and G sr . S3.4, Based on the innermost tensor Using the KRD algorithm with the known encoding matrix C1, we obtain and the estimator of S and 5. A wireless communication receiver simulation program product, comprising a computer program that, when executed, implements the system model of claim 2.

6. A wireless communication information acquisition algorithm program product, comprising a computer program that, when executed, implements the information acquisition algorithm of claim 4.

7. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that... When the processor executes the program, it implements the channel estimation algorithm based on the four-layer nested PARAFAC model as described in any one of claims 1 to 4.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that... When the computer program is executed by the processor, it implements the channel estimation algorithm based on the four-layer nested PARAFAC model as described in any one of claims 1 to 4.

Images