CN104935546A - MIMO-OFDM (Multiple Input Multiple Output-Orthogonal Frequency Division Multiplexing) signal blind separation method for increasing natural gradient algorithm convergence speed - Google Patents

Abstract

The invention discloses an MIMO-OFDM (Multiple Input Multiple Output-Orthogonal Frequency Division Multiplexing) signal blind separation method for increasing the natural gradient algorithm convergence speed. The method comprises the following steps: firstly, making improvements on a Flexible ICA algorithm under the constraint of ICA preprocessing in combination with an ICA principle to obtain an improved iterative algorithm; secondly, giving a method for adaptively feeding back and adjusting an iteration step size based on a separation error in combination with a BP neural network feedback thought with the separation error; and lastly, giving a comprehensive ending criterion of algorithm iteration from the aspects of the convergence of a separation matrix, iteration times and the separation error. Compared with the prior art, the method has the advantages that the requirements on the convergence speed and the separation accuracy are met on the basis of combining the MIMO-OFDM system features, and an effective separation effect is achieved.

Description

Improve the MIMO-OFDM blind signals separation method of Natural Gradient Algorithm convergence rate

Technical field

The invention belongs to signal blind source separating field, relate to multiple-input and multiple-output (MIMO) system, OFDM (OFDM) technology, Natural Gradient Algorithm (NGA) and independent component analysis (ICA) theory etc., be applicable to the blind separation of signals in wireless communications.

Background technology

MIMO-OFDM is the unique advantage relying on its band efficiency and anti-multipath fading aspect, is a kind of key technology being applied to Next generation cellular communication (3GPP-LTE, mobile WiMAX, IMT-Advanced), WLAN (wireless local area network) (IEEE802.11a, IEEE 802.11n), Wireless Personal Network (MB-OFDM) and broadcasting (DAB, DVB, DMB).

Blind source separating theory refers to that transmission source signal is unknown, when the hybrid mode of source signal is also unknown, by means of only some statistical properties of source signal, utilizes observation signal to recover the theory of source signal.Its keyword " blind " comprises two aspects, and one refers to that the source signal for sending receiving terminal can not directly be observed, is unknown; Two is the source signals sent is that what how to mix is also unknown in the channel, and namely channel parameter is also unknown.

Along with people's improving constantly the requirement of message transmission rate and band resource utilance, the theoretical separation MIMO-OFDM signal of blind source separating is used to have important researching value and realistic meaning.This theory is highly suitable for the communication scenes being difficult to founding mathematical models between source signal and observation signal, particularly in a broadband wireless communication system, the coupling that the modes such as traditional training sequence greatly can improve band efficiency and system is replaced with blind source separating.

Such as, although the blind source separating theory at present based on MIMO-OFDM system has numerous algorithms, Natural Gradient Algorithm, ICA algorithm etc., it all has some limitations:

(1) in MIMO-OFDM system, blind source separating theoretical research relatively early and many be blind source separating theory based on Natural Gradient Algorithm, Natural Gradient Algorithm can realize self adaptation rapidly in the environment of change, but there is the problem that convergence rate is slower, select suitable step-length also very crucial simultaneously, if step-length is selected improper, convergence may be destroyed.

(2) Fast ICA algorithm combines the advantage of fixed-point iteration, projection pursuit and Newton method, evaded falling step-length or other parameters to the restriction of convergence rate after, the there is secondary even convergence rate of three times, but due to the Newton optimization algorithm that it adopts, iteration initial value is more responsive, and performance is complicated, the problem that sometimes may occur dispersing and concussion etc. causes convergence to determine.

For the limitation that current algorithm exists, many documents have been had to make research.Some schemes are had to propose the concept of variable step, such as adopt large step-length at first at algorithm, convergence speedup speed, little step-length is adopted time algorithm terminates soon, improve convergence precision, take into account convergence rate and convergence precision balance to a certain extent, but remain a kind of mode of non-self-adapting.Also have some schemes to propose the FastICA method of improvement, but be all the signal for a certain type, do not break through the limitation of such algorithm in MIMO-OFDM system.Consider above-mentioned various factors, the present invention proposes a kind of MIMO-OFDM blind signals separation method based on natural gradient Flexible ICA algorithm, on the basis in conjunction with MIMO-OFDM system performance, take into account the requirement of convergence rate and separation accuracy, achieved effective separating effect.

Summary of the invention

The technical problem to be solved in the present invention is: for the blind signal separation problem of MIMO-OFDM, proposes a kind of blind signals separation method improving natural gradient Flexible ICA algorithm the convergence speed.

The technical solution adopted for the present invention to solve the technical problems is:

Improve a MIMO-OFDM blind signals separation method for Natural Gradient Algorithm convergence rate, comprise the steps:

First, under ICA preliminary treatment constraint, improvement has been made to Flexible ICA algorithm, has obtained new iterative formula wherein, W is separation matrix, and η (n) is Learning Step, and x is pretreated observation signal, for excitation function, n is for representing current iteration number of times;

Then, carry out separation iteration based on described new iterative formula, and utilize separation error to adjust iterative learning step-length adaptively;

Finally, from the convergence of separation matrix, iterations be separated error three aspect and judge whether to meet end condition, if meet, finishing iteration, draws separation signal.

Preferably, being separated error described in such scheme is

Wherein, I is unit vector, be two norms.

Preferably, the separation of utilization described in such scheme error adjusts iterative learning step-length adaptively and is, η (n+1)=α (n) η (n), wherein,

$\mathrm{\&alpha;}\left(n\right)=\left\{\begin{array}{cc}1+\mathrm{\&beta;}\&times;\mathrm{SE}\left(n\right),& \mathrm{SE}\left(n\right)<\mathrm{SE}(n-1)\\ \frac{1}{1+\mathrm{\&gamma;}\&times;\mathrm{SE}\left(n\right)},& \mathrm{SE}\left(n\right)>\mathrm{SE}(n-1)\\ 1,& \mathrm{SE}\left(n\right)=\mathrm{SE}(n-1)\end{array}\right.$

Wherein, β regulates the constant parameter of convergence rate and 0 < β < 1; γ regulates the constant parameter of separation accuracy and 0 < γ < 1.

Preferably, the constringent judgment formula of separation matrix described in such scheme is:

wherein, subscript k represents kth subchannels, ε ₁represent stable state convergence threshold.

Preferably, the judgment formula of iterations described in such scheme is: num > Num, num are the iterative algorithm iterationses at each subcarrier place, and Num is the iterations upper limit.

Preferably, the judgment formula being separated error described in such scheme is: wherein, be two norms, ε ₂it is separation accuracy threshold value constant.

Technical solution of the present invention has following beneficial effect: the MIMO-OFDM blind signals separation method that the present invention proposes, first based on the preliminary treatment mechanism of ICA theory, provide the iterative formula under preliminary treatment constraint, then based on BP neural network feedback thought, adopt and be separated Error Feedback front end, dynamic conditioning iterative increment, give the compound end condition of algorithm simultaneously, on the basis in conjunction with MIMO-OFDM system performance, take into account the requirement of convergence rate and separation accuracy, achieve effective separating effect.And the parameter beta in the weights of the separation Error Feedback in innovatory algorithm and γ have important impact to algorithm separating property curve, can algorithm the convergence speed be improved by increasing parameter beta, increasing parameter γ and can improve separation accuracy.This just makes algorithm can carry out dynamic conditioning according to the actual requirements, has very large flexibility.

Accompanying drawing explanation

Fig. 1 is SISO-OFDM system block diagram;

Fig. 2 is MIMO-OFDM system block diagram;

Fig. 3 (a) is the symbol constellations figure signal constellation (in digital modulation) figure that source signal is modulated at the 4-QAM that transmitting terminal adopts;

Fig. 3 (b) is that modulation signal is through the mixed signal constellation (in digital modulation) figure of channel;

Fig. 3 (c) is the oscillogram of the mixed signal observed of receiving terminal;

Fig. 3 (d) is the output estimation signal constellation (in digital modulation) figure after adopting improvement natural gradient Flexible ICA algorithm to process observation signal;

Fig. 4 improves natural gradient Flexible ICA algorithm performance of BER figure;

Fig. 5 is detach Spline performance map.

Embodiment

The present invention is introduced in detail below in conjunction with drawings and the specific embodiments.Be separated on the theoretical basis of independent component analysis (ICA), first the present invention is MIMO-OFDM signal modeling in conjunction with ICA theory, the blind source separating problem of this system is converted into N number of independent component analysis problem, then unified with nature gradient theory, illustrate and improve natural gradient FlexibleICA algorithm, emulate by experiment, indicate the validity of algorithm.Should understand these embodiments to be only not used in for illustration of the present invention and to limit the scope of the invention, after having read the present invention, the amendment of those skilled in the art to the various equivalent form of value of the present invention has all fallen within the application's claims limited range.

One, signal modeling

First the present invention carries out modeling in conjunction with independent component analysis (ICA) theory to MIMO-OFDM system signal.As shown in Figure 1, the signal input/output relation of single-input single-output (SISO) ofdm system can be expressed as the ofdm signal transmitting and receiving FB(flow block) of being modulated by FFT:

X ^k＝H ^kS ^k+η ^k(1)

In formula, S ^kand X ^krepresent the data symbol that transmitting terminal and a receiving terminal kth subcarrier carry respectively, η ^krepresent kth sub-channels interchannel noise, H ^krepresent the frequency domain response of kth sub-channels.

In multiple-input and multiple-output (MIMO) ofdm system, from single subchannel k, as shown in Figure 2, it is an expansion of single-input single-output ofdm system to its system block diagram, when its mathematical expression is:

In formula, m _tdata symbol on the kth subcarrier that individual transmitting antenna sends separately, the data symbol on a kth subcarrier that receiver receives, channel noise on a kth subcarrier, it is a complex scalar.The vector representation form of formula (2) is:

X ^k＝H ^kS ^k+η ^k(3)

Above-mentioned equation is known, MIMO-OFDM system constructs a linear space mixed model at each subcarrier place, sending signal is in time domain, and hybrid matrix is the complex scalar value of transfer function matrix at each sub-carrier frequencies place, and namely hybrid matrix is at frequency domain.So far, the blind source separating problem of MIMO-OFDM signal is converted into N (sub-band number) and organizes independent component analysis problem.

Two, natural gradient Flexible ICA basic theory

Natural gradient Flexible ICA algorithm is the ICA learning algorithm of a kind of self-adaptation nonlinear proposed by Choi etc., this algorithm proposes a kind of parameterized Generalized Gaussian density model to suppose the distribution of signal source in the structure of Riemannian natural gradient, can be separated the blind separation problem of the instantaneous mixed signal of super-Gaussian and sub-Gaussian, its basic iteration expression formula solving separation matrix W is:

In formula, be column vector, its i-th component is:

In formula, nonlinear activation function, q _i(x _i) be source signal S _ithe approximate model of probability density.

The core of algorithm carries out dynamic estimation to source signal probability density distribution, and select suitable excitation function.For super-Gaussian distribution signal, nonlinear activation function can be wherein for sub-Gaussian signals, nonlinear function can be for the mixing of subalpine forests and super-Gaussian, according to parameterized Generalized Gaussian Distribution Model, nonlinear function is defined as follows:

In formula, sgn (x _i) be x _isign function.

In order to a suitable Gaussian index α can be selected flexibly _i, natural gradient Flexible ICA algorithm is by estimated output signal y _ikurtosis and select corresponding α _i, Choi etc. give kurtosis k in document Flexible independentcomponent analysis (Journal of VLSI signal processing systems for signal, image andvideo technology, 2000) _σalong with Gaussian index α _ivariation relation.

Three, the algorithm steps after the present invention's optimization

To sum up, disclosed in the embodiment of the present invention, a kind of method improving the MIMO-OFDM system signal blind separation of natural gradient Flexible ICA algorithm the convergence speed, comprises the steps:

The first step, observation signal preliminary treatment.Zero-mean whitening processing is carried out to observation data matrix, obtains pretreated observation signal matrix: $X=\left[\begin{array}{cccc}{x}_1& x_2& ...& x_{M_r}\end{array}\right].$

Under above-mentioned preliminary treatment prerequisite, made improvement to FlexibleICA algorithm under pretreated orthogonality constraint, the iterative formula that must make new advances is:

In formula, W is separation matrix, and η (n) is Learning Step, and x is pretreated observation signal, for excitation function.

Second step, in conjunction with BP neural network feedback thought, utilizes and is separated Error Feedback dynamic conditioning step-length adaptively.Separation error is defined as:

Wherein, I is unit vector, be two norms.Be separated the degree that error characterizes Signal separator, if Signal separator is complete, its value is less; Otherwise, be separated angle value larger.

Definition weight α (n) is:

$\mathrm{\&alpha;}\left(n\right)=\left\{\begin{array}{cc}1+\mathrm{\&beta;}\&times;\mathrm{SE}\left(n\right),& \mathrm{SE}\left(n\right)<\mathrm{SE}(n-1)\\ \frac{1}{1+\mathrm{\&gamma;}\&times;\mathrm{SE}\left(n\right)},& \mathrm{SE}\left(n\right)>\mathrm{SE}(n-1)\\ 1,& \mathrm{SE}\left(n\right)=\mathrm{SE}(n-1)\end{array}\right.---\left(9\right)$

In formula, β regulates the constant parameter of convergence rate and 0 < β < 1; γ regulates the constant parameter of separation accuracy and 0 < γ < 1.

The expression formula being separated Error Feedback self-adjusting iteration step length is:

η(n+1)＝α(n)η(n) (10)

Determine that initial parameter and the threshold parameter of algorithm are: k=1, n=0, stochastic generation initialization weight vector ω ^k(0) initial step length η, is determined ₀, provide beta, gamma, ε ₁, ε ₂initial value.

3rd step, according to parameterized generalized gaussian model, chooses nonlinear function from physical model

4th step, carries out interative computation.Make iterations n=n+1,

Calculate according to formula (8) and be separated error SE;

Adaptive weight factor-alpha (n) is calculated according to formula (9);

Next iteration step-length η (n+1) is calculated according to formula (10);

5th step, calculates iterative formula:

Normalized: ${\mathrm{\&omega;}}^k(n+1)=\frac{{\mathrm{\&omega;}}^k(n+1)}{\left|\right|{\mathrm{\&omega;}}^k(n+1)\left|\right|}.$

6th step, the comprehensive termination criterion of definition algorithm.From the convergence of separation matrix, iterations and the termination criterion being separated error three aspects and providing algorithm iteration, that is:

In formula, subscript k represents kth subchannels, and n represents iterations, ε ₁represent stable state convergence threshold. be two norms, ε ₂be a separation accuracy threshold value constant, num is each subcarrier place, actual iterations when iterative algorithm is not restrained, and Num is the iteration upper limit.

Due to the diversity of source signal, the complexity of the characteristic of channel, particularly multi-path environment, algorithm can not adapt to all situations, namely algorithm possibly cannot be restrained, so algorithm can not infinitely iteration go down, and must force finishing iteration, and provide information by setting an iterations upper limit Num.Simultaneously after the separation accuracy of algorithm reaches requirement, criterion can be fed back to immediately, thus end loop.If separation matrix has been restrained in the process of iteration, so algorithm has not also just continued necessity of iteration, must stop iteration.

If algorithm does not meet stopping criterion for iteration formula, then forward the 4th step to.Otherwise iteration terminates, obtain an independent element, wherein ω is the separation matrix that iteration goes out, and X is observation signal.Y is separation signal, he is an estimation of source signal, i, j is a certain road signal in signal array respectively, the road signal recovered is the estimation of a certain road signal in source signal, but due to blind source separating self uncertainty (uncertainty of signal amplitude and signal arrangement) theoretical.Such as: the signal array [s1, s2, s3] of transmission, recovering to be sequentially [s2, s1, s3].

7th step, subcarrier k=k+1, and make ω (0)=ω (n-1), if k < is N (N represents subcarrier number), forward the 3rd step to, otherwise end loop, export and recover data.

Four, simulation result

Theoretical according to the improvement natural gradient Flexible ICA that the embodiment of the present invention provides, by matlab, algorithm is emulated, and simulation result is analyzed.MIMO-OFDM system parameters is in table 1, assuming that be ideal synchronisation, without chnnel coding, channel model adopts flat fading channel.In simulations, each transmitting antenna sends different user data, and each antenna uses 200 OFDM frames, and repeats to obtain separation matrix by 100 times, then uses the separation matrix of acquisition to be separated observation signal, and analyzes separating resulting.

Table 1 MIMO-OFDM system emulation parameter

In order to contrast algorithm improvement effect, adopt formula $\mathrm{\&eta;}\left(n\right)=\left\{\begin{array}{cc}{\mathrm{\&eta;}}_0,& n{\&le;n}_0\\ {\mathrm{\&eta;}}_0{e}^{-a(n-n_0)},& n>n_0\end{array}\right.$

Classical Variable Step Size Natural Gradient Algorithm and the improvement natural gradient Flexible ICA algorithm of the present invention of representative contrast.Initial parameter sets is as follows:

Classical Variable Step Algorithm, namely based in exponential damping Variable Step Size Natural Gradient Algorithm, initial step length η ₀=0.005, n ₀=1500, a=0.001.

Innovatory algorithm, namely based in separation error adaptive step natural gradient Flexible ICA algorithm, initial step length η ₀=0.05, γ=5.8 × 10 ^-5, β=6.5 × 10 ^-5, ε ₁=ε ₂=1 × 10 ^-5.

What algorithm simulating result Fig. 3 provided is in MIMO-OFDM system, signal based on Variable Step Size Natural Gradient Algorithm sends, mix and planisphere when being separated, wherein Fig. 3-(a) is the symbol constellations figure that source signal is modulated at the 4-QAM that transmitting terminal adopts, what Fig. 3-(b) represented is that modulation signal is through the mixed signal constellation (in digital modulation) figure of channel, the oscillogram of the mixed signal observed of receiving terminal that what Fig. 3-(c) represented is, Fig. 3-(d) is the output estimation signal constellation (in digital modulation) figure after adopting improvement natural gradient Flexible ICA algorithm to process observation signal, the blind separation of signal is successfully achieved from algorithm directly perceived.

Simulation result Fig. 4 gives and adopts Variable Step Size Natural Gradient Algorithm at receiving terminal and improve the bit error rate situation that natural gradient Flexible ICA algorithm recovers source signal.Therefrom can find out, Natural Gradient Algorithm is than more sensitive to noise, and the performance of algorithm obviously reduces along with the increase of noise effect.The improvement natural gradient Flexible ICA algorithm provided herein, according to Signal separator error self-adaptative adjustment iteration step length, obtain good bit error rate performance, particularly after signal to noise ratio reaches 10dB, the more traditional Variable Step Algorithm of innovatory algorithm is greatly improved at separation signal overall bit-error rate aspect of performance, has good stability.

Table 2 algorithm is at the correlation matrix contrast table of subcarrier k=25

Table 2 gives the sub-carrier space separation signal correlation matrix of two kinds of algorithms at k=25, can find out in the similar matrix of the output signal that the innovatory algorithm that application provides recovers herein, be similar to the element of 1 closer to 1, the element being similar to 0 is closer to 0, and the effect of separation has higher accuracy than traditional Variable Step Size Natural Gradient Algorithm.

Simulation result Fig. 5 gives the performance curve of algorithm performance index with iterations, and as can be seen from the figure, innovatory algorithm is all better than traditional Variable Step Size Natural Gradient Algorithm in convergence rate and separation accuracy.The initial step length η of traditional Variable Step Size Natural Gradient Algorithm ₀coefficient k is started with exponential damping variable step ₀all will behind the basis of test of many times, just can provide a suitable value.If η ₀bigger than normal, although convergence rate is very fast, algorithm can be made not restrain, separating effect worsens, if η ₀less than normal, convergence rate is very slow, and algorithmic statement may be made in Local Minimum, and algorithm is lacked of proper care.Can find by repeatedly adjusting simulation parameter, parameter beta in the weights of the separation Error Feedback in innovatory algorithm and γ have important impact to algorithm separating property curve, can algorithm the convergence speed be improved by increasing parameter beta, increasing parameter γ and can improve separation accuracy.This just makes algorithm can carry out dynamic conditioning according to the actual requirements.

Claims (6)

1. improve a MIMO-OFDM blind signals separation method for Natural Gradient Algorithm convergence rate, it is characterized in that, comprise the steps:

First, under ICA preliminary treatment constraint, improvement has been made to Flexible ICA algorithm, has obtained new iterative formula wherein, W is separation matrix, and η (n) is Learning Step, and x is pretreated observation signal, for excitation function, n is for representing current iteration number of times;

Then, carry out separation iteration based on described new iterative formula, and utilize separation error to adjust iterative learning step-length adaptively;

Finally, from the convergence of separation matrix, iterations be separated error three aspect and judge whether to meet end condition, if meet, finishing iteration, draws separation signal.

2. a kind of MIMO-OFDM blind signals separation method improving Natural Gradient Algorithm convergence rate according to claim 1, is characterized in that: described separation error is

Wherein, I is unit vector, be two norms.

3. a kind of MIMO-OFDM blind signals separation method improving Natural Gradient Algorithm convergence rate according to claim 1, it is characterized in that: described utilization separation error adjusts iterative learning step-length adaptively and is, η (n+1)=α (n) η (n), wherein

$\mathrm{\&alpha;}\left(n\right)=\left\{\begin{array}{c}1+\mathrm{\&beta;}\&times;\mathrm{SE}\left(n\right),\mathrm{SE}\left(n\right)<\mathrm{SE}(n-1)\\ \frac{1}{1+\mathrm{\&gamma;}\&times;\mathrm{SE}\left(n\right)},\mathrm{SE}\left(n\right)>\mathrm{SE}(n-1)\\ 1,\mathrm{SE}\left(n\right)=\mathrm{SE}(n-1)\end{array}\right.$

Wherein, β regulates the constant parameter of convergence rate and 0 < β < 1; γ regulates the constant parameter of separation accuracy and 0 < γ < 1.

4. a kind of MIMO-OFDM blind signals separation method improving Natural Gradient Algorithm convergence rate according to claim 1, is characterized in that: the constringent judgment formula of described separation matrix is:

wherein, subscript k represents kth subchannels, ε ₁represent stable state convergence threshold.

5. a kind of MIMO-OFDM blind signals separation method improving Natural Gradient Algorithm convergence rate according to claim 1, it is characterized in that: the judgment formula of described iterations is: num > Num, num is the iterative algorithm iterations at each subcarrier place, and Num is the iterations upper limit.

6. a kind of MIMO-OFDM blind signals separation method improving Natural Gradient Algorithm convergence rate according to claim 1, is characterized in that: the judgment formula of described separation error is: wherein, be two norms, ε ₂it is separation accuracy threshold value constant.