CN101572574A - Smart antenna self-adapting interference suppression method based on least square-lowest mean square - Google Patents

Abstract

A smart antenna adaptive interference suppression method based on least squares-least mean square, which is an interference suppression algorithm based on training sequences, and improves the convergence of the least mean square algorithm by combining the least square algorithm with the least mean square algorithm The speed has the following steps: change the radio frequency signal received by the array antenna into an intermediate frequency signal through a down converter; perform A/D conversion and digital down conversion of the intermediate frequency signal to obtain a zero intermediate frequency digital signal; use the zero intermediate frequency digital signal obtained in step 2 and The local training sequence is correlated with the calculation delay to obtain the local reference signal; the initial weight vector of the antenna array is calculated by using the least squares algorithm of small snapshots; the weight vector calculated in step 4 is used as the initial weight vector of the least mean square algorithm, and the minimum The mean square algorithm is used to update the antenna array weight vector; the user data is suppressed from interference by using the array weight vector calculated in step 5. The invention achieves the purposes of improving the system frequency spectrum utilization rate and reducing the system complexity.

Description

Smart Antenna Adaptive Interference Suppression Method Based on Least Squares-Least Mean Square

technical field

The invention relates to an intelligent antenna interference suppression algorithm. In particular, it relates to a training sequence-based least square-least mean square smart antenna adaptive interference suppression method.

Background technique

In the early 1990s, array signal processing technology was introduced into mobile communication, and soon formed a new research hotspot - smart antenna. Smart antennas are defined as antenna arrays with direction finding and beamforming capabilities, and are generally divided into two categories: multi-beam smart antennas and adaptive array smart antennas, referred to as multi-beam antennas and adaptive antennas. The direction of each beam of the multi-beam antenna is fixed. It determines the direction of arrival of the signal through detection technology, and then selects the corresponding beam by adjusting the weighting coefficient of each array element. The structure is simple. However, as the user moves, when the center of the beam is no longer fixed, the multi-beam antenna cannot obtain a good reception effect. The adaptive antenna uses array signal processing technology to identify the direction of arrival of the user, and then forms the main beam in this direction, and the main beam is constantly changed and adjusted according to the change of the signal direction of arrival, so as to maintain alignment with the desired signal direction, and at the same time Nulls are formed in the interference direction, and thus are widely used in mobile communication systems.

At present, adaptive interference suppression technologies for smart antennas can be roughly divided into three categories: (1) Beamforming technologies based on known useful signal direction vectors, typically Standard Capon Beamformer (SCB). (2) Based on the known beamforming technique of the reference signal, the method finds a suitable weight vector by minimizing the difference between the array output and the reference signal. In general, reference signals are difficult to obtain. In a communication system, in order to obtain this reference signal, a training sequence known to both the transmitter and the receiver must be periodically sent. Transmitting training sequences will occupy precious frequency resources of the communication system. (3) Blind adaptive beamforming technology, which does not need to transmit training signals, and does not need to know prior knowledge such as the array direction vector and the spatial autocorrelation matrix of interference and noise, but uses the statistical properties of the signal or the signal itself Deterministic nature for beamforming.

The Least Mean Squares (LMS) adaptive interference method based on the training sequence is widely used in communication systems, but because the LMS algorithm is sensitive to the initial value, the convergence speed is slow, and the convergence performance is related to the interference environment, so A long training sequence is required to achieve an ideal interference suppression effect, which seriously wastes precious frequency resources. Although the least squares (LS) optimal beamforming has high interference suppression performance and the interference suppression performance is independent of the interference environment, the computational complexity of the algorithm is large, which is not conducive to the actual system implementation.

Contents of the invention

The technical problem to be solved by the present invention is to provide a smart antenna adaptive interference suppression method based on least squares-least mean squares (LeastSquares-Least Mean Squares, referred to as LS-LMS). Calculate the weighted vector of the array, and use this weighted vector as the initial weighted vector of the LMS algorithm, which effectively improves the convergence speed of the LMS algorithm and reduces the length of the training sequence, thereby achieving the goal of improving system spectrum utilization and reducing system complexity Purpose.

The technical scheme adopted in the present invention is: a smart antenna adaptive interference suppression method based on least squares-least mean square, which is an interference suppression algorithm based on training sequences, by combining the least square algorithm with the least mean square algorithm , to improve the convergence speed of the least mean square algorithm, including the following steps:

(1) Convert the radio frequency signal received by the array antenna into an intermediate frequency signal through a down converter;

(2) A/D conversion and digital down-conversion are performed on the intermediate frequency signal to obtain a zero intermediate frequency digital signal;

(3) Utilize step (2) gained zero intermediate frequency digital signal and local training sequence to carry out correlation processing calculation delay and obtain local reference signal;

(4) Utilize the small snapshot number least squares algorithm to calculate the initial weight vector of the antenna array;

(5) the weighted vector calculated by step (4) is used as the initial weighted vector of the least mean square algorithm, and the update of the antenna array weighted vector is carried out by the least mean square algorithm;

(6) Using the array weight vector calculated in step (5) to perform interference suppression on the user data.

In step (3), the intermediate frequency digital signal and the local training sequence are carried out to correlate and calculate the delay to obtain the local reference signal, which is to gradually delay the local training sequence, and each delayed training sequence and the output data of the array respectively in a training Correlation calculations are performed in the sequence period, and then the output of each correlator is compared, and the maximum output is selected, and the training sequence on the branch corresponding to the maximum output is the local reference signal.

The calculation of the initial weight vector of the array using the least squares algorithm in step (4) is to calculate the weight vector using the number of small snapshots by taking the minimum sum of squared errors as the cost function.

The updating of the weighted vector of the antenna array using the least mean square algorithm described in step (5) is to use the least mean square algorithm as a cost function with the mean square error and the stochastic gradient algorithm as an optimization method to update the weights, and the least mean square algorithm The initial weight vector of is provided by the weight vector calculated in step (4).

The smart antenna self-adaptive interference suppression method based on least squares and least mean squares of the present invention is a method proposed for a communication system with a long training sequence using the LS algorithm to estimate the array weight vector with a large amount of computation and the slow convergence speed of the LMS algorithm. Interference suppression method. The present invention uses the array weighted vector calculated by the LS algorithm as the initial weighted vector of the LMS algorithm, and when the LS algorithm calculates the weighted vector, it uses the number of snapshots for calculation, which can reduce the calculation amount of the LS algorithm. Using the weighted vector calculated by the small snapshot LS algorithm as the initial weighted vector of the LMS algorithm greatly speeds up the convergence speed of the LMS algorithm, reduces the sensitivity of the LMS algorithm to the interference environment, and can reduce the length of the training sequence, thereby achieving The purpose of improving system spectrum utilization and reducing system complexity.

Description of drawings

Fig. 1 is a flow chart of the smart antenna adaptive interference suppression method based on least squares-least mean square;

Fig. 2 is a weighted vector update array structure diagram based on the training sequence;

Fig. 3 a is the array direction diagram of the LMS algorithm when the snapshot number=180;

Fig. 3b is the array direction diagram of the LS-LMS algorithm when the snapshot number=180;

Fig. 3c is the array direction diagram of the LMS algorithm when the snapshot number=100;

Fig. 3d is the array direction diagram of the LS-LMS algorithm when the snapshot number=100;

Fig. 3e is the array direction diagram of the LMS algorithm when the snapshot number=30;

Fig. 3f is the array direction diagram of the LS-LMS algorithm when the snapshot number=30;

Figure 4a shows the convergence of LMS algorithm and LS-LMS algorithm output SINR when the initial weight vector of LMS algorithm is [0, 0, 0, 0] ^T and Jamming-to-noise Ratio (JNR for short) = 10dB Graph;

Fig. 4b is the LMS algorithm, LS-LMS algorithm output SINR convergence curve when the initial weighting vector of the LMS algorithm is [0,0,0,0] ^T , JNR=15dB;

Fig. 4c is the LMS algorithm, LS-LMS algorithm output SINR convergence curve when the initial weight vector of the LMS algorithm is [0, 0, 0, 0] ^T , JNR=20dB;

Figure 5a is the convergence curve of LMS algorithm and LS-LMS algorithm output SINR when the initial weight vector of LMS algorithm is [0.5+0.5i, 0.5+0.5i, 0.5+0.5i, 0.5+0.5i] ^T , JNR=10dB picture;

Figure 5b is the LMS algorithm and LS-LMS algorithm output SINR convergence curve when the initial weight vector of the LMS algorithm is [0.5+0.5i, 0.5+0.5i, 0.5+0.5i, 0.5+0.5i] ^T , JNR=15dB picture;

Figure 5c is the LMS algorithm and LS-LMS algorithm output SINR convergence curve when the initial weight vector of the LMS algorithm is [0.5+0.5i, 0.5+0.5i, 0.5+0.5i, 0.5+0.5i] ^T , JNR=20dB picture;

Figure 6a is a comparison diagram of the calculation amount of the LS algorithm, the LMS algorithm, and the LS-LMS algorithm;

Figure 6b is a comparison curve of the number of times of multiplication and addition of the LS algorithm, the LMS algorithm, and the LS-LMS algorithm with the number of snapshots;

Fig. 6c is a graph comparing the number of complex multiplication and addition of the LS algorithm, the LMS algorithm, and the LS-LMS algorithm with the change of the number of array elements.

Detailed ways

The method for adaptive interference suppression of smart antennas based on least squares and least mean squares of the present invention will be described in detail below in conjunction with the accompanying drawings of the embodiments.

The smart antenna adaptive interference suppression method based on least squares-least mean squares (Least Squares-Least Mean Squares, referred to as LS-LMS) of the present invention is an adaptive interference suppression method based on training sequences. , referred to as LS) algorithm combined with LMS (Least Mean Squares, referred to as LMS) algorithm to improve the convergence speed of the LMS algorithm, that is, the transmitter periodically transmits a sequence signal known to the receiver, and the receiver itself generates the The sequence signal is used as the reference signal of the adaptive algorithm, and the weight vector is obtained by minimizing the cost function. As shown in Figure 1, it includes the following steps:

The first step: convert the radio frequency signal received through the array antenna into an intermediate frequency signal through a down converter;

Step 2: Perform A/D conversion and digital down-conversion of the intermediate frequency signal to obtain a zero intermediate frequency digital signal;

When there is interference, the signal received by the array antenna can be expressed as:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; K</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, x(l) represents the lth sampling snapshot (l=0, 1, ..., L-1), L represents the number of samples, s _d (l) represents the useful signal, s _k (l) (k=1 ,..., K) represents the kth interference signal, K represents the number of interference sources, $a\left({\mathrm{\&theta;}}_d\right)={[1,e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20091006909000122.png,A20091006909000123.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;d}}{\mathrm{\&lambda;}}\sin {\mathrm{\&theta;}}_d},...,e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20091006909000122.png,A20091006909000123.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;d}}{\mathrm{\&lambda;}}(m-1)\sin {\mathrm{\&theta;}}_d}]}^T$ represents the steering vector of the desired signal, $a\left({\mathrm{\&theta;}}_k\right)={[1,e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20091006909000122.png,A20091006909000123.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;d}}{\mathrm{\&lambda;}}\sin {\mathrm{\&theta;}}_k},...,e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20091006909000122.png,A20091006909000123.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;d}}{\mathrm{\&lambda;}}(m-1)\sin {\mathrm{\&theta;}}_k}]}^T$ Represents the steering vector of the kth interference, λ represents the signal wavelength, e(l) represents the array receiving noise vector, θ is the direction of arrival of the signal, M is the number of array elements, and d is the distance between array elements. In this embodiment, uniform Linear array, the number of array elements is 4, the spacing is 1/2 wavelength, the received signal is a useful signal and an interference signal, and the directions of arrival are 30° and 0° respectively.

The third step: use the zero-IF digital signal obtained in the second step to perform correlation processing with the local training sequence to calculate the delay to obtain the local reference signal. In the adaptive algorithm based on the training sequence, an important step is to realize the synchronization of the training sequence. In this embodiment, the local training sequence is gradually delayed, and each delayed training sequence is correlated with the array output data in one training sequence cycle, and then the output of each correlator is compared to select the largest output, and the training sequence on the branch corresponding to the maximum output is the local reference signal.

Step 4: Use the small snapshot number LS algorithm to calculate the initial weighted vector of the antenna array, by using the small snapshot number N (N<<L) to calculate the weighted vector by taking the minimum sum of squared errors as the cost function;

The adaptive array structure based on the training sequence is shown in Figure 2.

Assuming the data vector x(n) of N snapshots, n=0, 1, ..., N-1, then the cost function of the LS algorithm is:

$\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; w</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Among them, d(n) is the expected signal at time n,

Its gradient is:

$<span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; d</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Let it be zero to get the optimal weight vector for the least squares method:

w＝(XX ^H ) ^-1 Xd ^H (4)

Where: X = [x(0), x(1), ..., x(N-1)], d = [d(0), d(1), ..., d(N-1)],

In this embodiment, the number of sampling snapshots is N=8.

Step 5: Use the weight vector calculated in step 4 as the initial weight vector of the LMS algorithm, and use the LMS algorithm to update the weight vector of the antenna array. The LMS algorithm uses the mean square error as the cost function and the stochastic gradient algorithm as the optimization method. Weight update, the initial weight vector of the LMS algorithm is provided by the weight vector calculated in the fourth step;

The principle of the LMS algorithm is to minimize the mean square value of the estimation error, that is, the cost function is:

J(w)＝E{|e(l)| ² } (5)

In the formula, E{} represents the statistical average, e(l) is the error, e(l)=w ^H x(l)-d(l).

but:

J(w)＝E{e(l)e ^* (l)}＝E{|d(l)| ² }-2Re[w ^H r _xd ]+w ^H R _xx w (6)

Among them, Re means to take the real part, R _xx =E{x(l)x ^H (l)} is the autocorrelation matrix of the input vector, r _xd =E{xl))d ^* (l)} is the input vector x( l) and the cross-correlation matrix of the desired signal d(l).

Deriving equation (6) and setting it to zero yields:

${\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; opt</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; xx</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; xd</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Considering the stochastic gradient algorithm, the general formula for weight vector update is:

$\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&mu;</span>}<span\; class="notranslate">\; \&dtri;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

in, $\&dtri;=\frac{\&PartialD;}{\&PartialD;w\left(l\right)}J\left(w\left(l\right)\right),$ μ is the step factor, which can be obtained from formula (6):

$<span\; class="notranslate">\; \&dtri;</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; xd</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; d</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

In the LMS algorithm, the mathematical expectation is replaced by the instantaneous value, and the weight update formula is obtained:

$\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&mu;</span>}\stackrel{<span\; class="notranslate">\; ^</span>}{<span\; class="notranslate">\; \&dtri;</span>}$

$<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&mu;</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; d</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&mu;x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span>$

Step 6: Using the array weight vector calculated in Step 5 to perform interference suppression on user data.

Figure 3 shows the LMS and LS-LMS algorithms obtained from 100 Monte Carlo experiments under the conditions of Signal-to-noise Ratio (SNR)=10dB and SIR=-20dB. In the simulation experiment, the initial value of the LMS algorithm is [0.5+0.5i, 0.5+0.5i, 0.5+0.5i, 0.5+0.5i] ^T , and LS-LMS uses 8 snapshots to calculate the initial weight The step size of vector, LMS and LS-LMS algorithms are both 0.00005. Figure 3a and Figure 3b are the array pattern diagrams of LMS and LM-LMS algorithms respectively when the number of snapshots is 180, and Figure 3c and Figure 3d are respectively The array pattern of the two algorithms LMS and LM-LMS when the number of snapshots = 100, Fig. 3e and Fig. 3f are the array pattern of the two algorithms of LMS and LM-LMS when the number of snapshots = 30, respectively. It can be seen from Figure 3 that as the number of snapshots decreases, the LMS algorithm can no longer form a null point in the interference direction, but the new method still aligns the main beam with the useful signal and the null trap with the interference signal.

Figure 4 shows the convergence curves of the output Signal to Interference and Noise Ratio (SINR) of the LMS algorithm and the LS-LMS algorithm when SNR=10dB, where the JNRs in Figure 4a, Figure 4b, and Figure 4c are 10dB respectively , 15dB, 20dB. The initial value of the LMS algorithm is taken as [0, 0, 0, 0] ^T , 8 snapshots are used in LS-LMS to calculate the initial weight vector, the step size of the two algorithms is 0.00005, and 100 times of Mont Carlo simulation experiments are obtained The transformation curve of the average signal-to-interference-noise ratio output by the beamformer with the number of sampling snapshots is shown in Fig. 4 . It can be seen that as the number of snapshots increases, both algorithms converge to the theoretical value (the corresponding SCB method when the number of snapshots is infinite), but the LMS algorithm is significantly slower than LS-LMS, and the convergence of the LMS algorithm increases with the increase of JNR. The speed is reduced, but it has little effect on the LS-LMS algorithm. The content and conditions of the simulation experiment in Figure 5 are the same as those in Figure 4, except that the initial value of the LMS algorithm is [0.5+0.5i, 0.5+0.5i, 0.5+0.5i, 0.5+0.5i] ^T . Comparing Figure 4 and Figure 5, it can be found that the LMS algorithm is sensitive to the initial weight vector. Different initial weight vectors have a greater impact on the convergence speed of the LMS algorithm, but have little effect on the convergence speed of the LS-LMS algorithm.

Figure 6a shows the comparison diagram of LS algorithm, LMS algorithm, and LS-LMS algorithm, where M is the number of array elements, L is the number of snapshots, and N is the number of snapshots for calculating the initial weighted vector in the LS-LMS algorithm. In the figure, the complexity of the matrix inversion operation is approximated as the calculation amount of the matrix inversion. Fig. 6b shows a comparative graph of the number of complex multiplications and additions of the LS algorithm, the LMS algorithm, and the LS-LMS algorithm when M=4 and N=8. Fig. 6c shows a comparative graph of the number of complex multiplication and addition of the LS algorithm, the LMS algorithm, and the LS-LMS algorithm when L=120 and N=8. From the comparison in Figure 6, it can be found that with the increase of the number of snapshots and the number of array elements, the calculation amount of the LS algorithm increases sharply, but the increase of the calculation amount of the LS-LMS algorithm is relatively small.

Claims (4)

1. A smart antenna adaptive interference suppression method based on least squares-least mean square, is characterized in that, is based on the interference suppression algorithm of training sequence, by combining least square algorithm and least mean square algorithm, improves The convergence speed of the least mean square algorithm includes the following steps: (1) Convert the radio frequency signal received by the array antenna into an intermediate frequency signal through a down converter; (2) A/D conversion and digital down-conversion are performed on the intermediate frequency signal to obtain a zero intermediate frequency digital signal; (3) Utilize step (2) gained zero intermediate frequency digital signal and local training sequence to carry out correlation processing calculation delay and obtain local reference signal; (4) Utilize the small snapshot number least squares algorithm to calculate the initial weight vector of the antenna array; (5) the weighted vector calculated by step (4) is used as the initial weighted vector of the least mean square algorithm, and the update of the antenna array weighted vector is carried out by the least mean square algorithm; (6) Using the array weight vector calculated in step (5) to perform interference suppression on the user data. 2. the smart antenna adaptive interference suppression method based on least squares-least mean square according to claim 1, is characterized in that, step (3) described intermediate frequency digital signal and local training sequence are carried out correlation processing calculation delay To obtain the local reference signal, the local training sequence is gradually delayed, and each delayed training sequence is correlated with the array output data in one training sequence cycle, and then the output of each correlator is compared to select the largest The output of , the training sequence on the branch corresponding to the maximum output is the local reference signal. 3. the smart antenna adaptive interference suppression method based on least squares-least mean square according to claim 1, is characterized in that, utilizes the initial weighting vector of least squares algorithm to calculate array described in step (4), is By using the minimum sum of squared errors as the cost function, the weighted vector is calculated using the number of small snapshots. 4. the smart antenna adaptive interference suppression method based on least squares-least mean square according to claim 1, is characterized in that, utilizes least mean square algorithm described in step (5) to carry out the update of antenna array weighting vector, The least mean square algorithm uses the mean square error as the cost function and the stochastic gradient algorithm as the optimization method to update the weights, and the initial weight vector of the least mean square algorithm is provided by the weight vector calculated in step (4).

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