CN109951257B - Method for constructing different distributed signal sequences in STBC-OFDM system - Google Patents

Abstract

The invention discloses a method for constructing different distribution signal sequences in an STBC-OFDM system, which comprises the steps of firstly subdividing a received signal into two subsequences which are mutually overlapped, then calculating a correlation function of column vectors in the two subsequences, and finally obtaining two received signal sequences with different distributions. The method is based on the correlation characteristic of the space-time block code, fully utilizes the sequence length of the received signal, and can be used for identifying the algorithm of the STBC signal according to the distribution condition. The received signal is redefined into two different signal sequences, so that the sample utilization rate is doubled; and the effect of signal identification can be improved under the condition of low samples. Meanwhile, in the construction process, noise information, channel information and modulation information do not need to be considered, and the method has strong application value in the field of cognitive radio.

Description

Method for constructing different distributed signal sequences in STBC-OFDM system

The application is a divisional application of patent applications with the application date of 2016, 9 and 19, the application number of 201610831959.9 and the name of 'STBC-OFDM signal blind identification algorithm based on K-S detection'.

Technical Field

The invention belongs to a non-cooperative communication signal processing technology in the field of signal processing, and particularly relates to a STBC-OFDM (Space-Time Block Codes, STBC and Orthogonal Frequency Division Multiplexing, OFDM) signal blind identification method based on K-S (Kolmogrov-Smirnov, K-S) detection.

Background

In recent years, automatic identification of communication signals has been extended to the fields of military and civilian communications. Such as spectrum monitoring, electronic warfare, software radio, cognitive radio, and the like. The automatic identification of the communication Signal requires that the Signal parameters of the receiving end can be well identified under the condition of a low Signal to Noise Ratio (SNR) without any prior information and front-end processing of the transmitting end. Automatic identification of communication signals has been a hotspot and difficulty of non-cooperative communication research. Most of the automatic identification of communication signals mainly aims at modulation identification of a Single Input Single Output (SISO) communication system, Single carrier and multi-carrier transmission identification, different multi-carrier transmission identification and channel coding identification. However, at present, the automatic identification of communication signals has been extended to a Multiple Input Multiple Output (MIMO) communication system, mainly because it is adapted to wireless communication standards such as IEEE802.11 n, IEEE 802.16e, and 3GPP LTE.

Currently, in the non-cooperative processing field, the identification of STBC-OFDM signals is still in the phase of initiative. In the article "Blind STBC identification for multiple-antenna OFDM systems" in 62 nd 2014 of the journal IEEE transmission on Communication, Marey M blindly identifies STBC signals by calculating a second order correlation function of received signal elements, and obtains better results. But the algorithm is not ideal for recognition under low signal-to-noise ratio and low sample conditions. In 2015, eldermerdalsh Y a et al identified STBC signals by defining a cross-correlation function of received sequence blocks, and the identification performance was also ideal at low signal-to-noise ratio; but this method can only identify Al-OFDM signals and SM-OFDM signals and does not extend to STBC identification in a general sense. Karami E E et al, 2015, calculated the second order cyclostationarity of the received sequence, blindly identified the STBC signal by estimating the amplitude of the CCF (cyclic cross-function), comparing its amplitude to a threshold magnitude.

However, the conventional method is not applicable to a single receiving antenna, but is limited to a case of a multi-receiving signal antenna. A single receive antenna is an extreme case of multiple antennas, mainly because in certain situations, such as platform space, antenna size and cost constraints, only a single receive antenna can be used. Considering the special situation of a single receiving antenna, a single receiving antenna STBC-OFDM signal blind identification method needs to be researched.

Disclosure of Invention

The invention aims to solve the technical problem that aiming at the defects of the existing STBC blind identification technology, a frequency selection Rayleigh channel model is considered, and a STBC-OFDM signal blind identification method based on K-S detection is provided, so that the identification requirement of the STBC-OFDM signal can be met, the performance of an identification algorithm is greatly improved, and the calculation complexity is low. The invention can be directly applied to non-cooperative STBC communication systems and can also be applied to corresponding software radio systems and other systems.

In order to solve the technical problems, the invention is realized by the following technical scheme: redefining a received signal into two different signal sequences; then respectively obtaining the time delay correlation functions of the two signal sequences, and analyzing the distribution conditions of the two time delay correlation functions of different STBC; and finally, identifying different STBC by adopting a method based on K-S detection. The method does not need prior information such as noise information, modulation information, channel coefficients and the like, and is suitable for non-cooperative communication occasions.

The redefinition of the received signal into two different signal sequences is as follows: consider having N_TxA transmitting antenna and a receiving antenna N_RxUnlike the single carrier system, the STBC-OFDM communication system 1 performs space-time coding in units of blocks. It is assumed that the transmitted symbols are complex linear modulations (e.g., QPSK) and are independently identically distributed random variables. For complex modulation, its real and imaginary parts are also independently identically distributed. The length of an OFDM block is set to be N, the number of symbols transmitted by each coding matrix is set to be L, and the length of the coding matrix is set to be U. The data streams input into a single OFDM block are:

s_t＝[s_t(0),s_t(1),…,s_t(N-1)] (1)

thus, the data block [ s ] of the kth group_Lk,s_Lk+1,…,s_Lk+l]Wherein L is 0,1, …, L-1. The coding matrix after space-time coding is C(s)_Lk,s_Lk+1,…,s_Lk+l)。

According to the modulation principle of OFDM,

and U is 0,1, …, and the OFDM block of time domain can be obtained by inverse Fourier transform (IFFT) of U-1

In order to reduce inter-symbol interference (ISI) and inter-carrier interference (ICI), the method needs to be applied to the field of communication

Prefix with length v is added in advance to jointly form a new OFDM block

The transmission sequence of antenna i is xⁱ：

Wherein N is_BIs the number of OFDM blocks, x⁽ⁱ⁾Wherein the k-th element is x⁽ⁱ⁾(k)。

Thus, the received signal is:

wherein h is_i(p) represents the p-path channel coefficients corresponding to the ith transmitting antenna and receiving antenna, and w (k) represents the zero mean variance of

Complex white gaussian noise, path represents the number of paths.

Subdividing a received signal y (K) of length K into two mutually overlapping subsequences p₁And p₂：

p₁＝[y(0),y(1),…,y(K-t-1)] (6)

p₂＝[y(t),y(2),…,y(K-1)] (7)

Where t represents the time delay of the correlation function hereinafter.

The said time delay correlation function of two signal sequences is solved separately, and the distribution of two time delay correlation functions of different STBC is analyzed as follows:

at the receiving end, a single OFDM block g_Uk+uCan be expressed as:

g_Uk+u＝[y_Uk+u(N-v)…y_Uk+u(0)…y_Uk+u(N-1)]^T (8)

thus, the OFDM block R received by the receive antenna can be represented as:

wherein N is_BR is (N + v) x N, the number of OFDM blocks_BDimension matrix, g_iRepresenting a single OFDM block received. Defining two lengths as N_B-block matrix of t:

definition of R₀And R₁The correlation function between the middle column vectors is:

x_i(k)＝|[R_i(:,2tk)]^TR_i(:,2tk+t)| (12)

wherein i ═ 0,1, | · | represents absolute valueRepresents the block fetching matrix R_iAll of the rows of (a). Without loss of generality, let N_Bmod2t is 0 and if it is not zero, the receive block matrix R may be processed to remove the tail N_Bmod2t ═ 0 vector g_i。

Thus obtaining an autocorrelation vector X_iComprises the following steps:

X₀＝[x₀(0),x₀(1),…,x₀(M-1)] (13)

X₁＝[x₁(0),x₁(1),…,x₁(M-1)] (14)

wherein the content of the first and second substances,

taking Al-OFDM and SM-OFDM codes as examples, since the Al code length is 2 and the SM code length is 1, t is 1.

For SM-OFDM coding, the g < th >_Uk+u-1And g_Uk+uThe OFDM blocks are independent, and Al-OFDM coding, g_Uk+u-1And g_Uk+uThe OFDM blocks may or may not be independent, depending on g_Uk+u-1And g_Uk+uWhether within the same coding matrix. As can be seen from equations (13) and (14), for SM-OFDM encoding, the column vector g of the OFDM block R is received_Uk+uAre independent identically distributed vectors, thus vector X₀And X₁Are all independently and identically distributed; whereas for Al-OFDM encoding, the column vector g for the OFDM block R is received_Uk+uAre not independently identically distributed vectors, so vector X₀And X₁And are not independently and identically distributed. Since the first OFDM block received in non-cooperative communication is not necessarily the first column of the corresponding Al-OFDM, there may be two cases:

event 1: the first OFDM block received is the g-th OFDM block if it is not the start of the corresponding Al-OFDM_Uk+u-1And g_Uk+uThe OFDM blocks being independent, X₁Are independently and identically distributed, and X₀Not independently distributed.

Event 2: if the first OFDM block received is the start of the corresponding Al-OFDM, X₀Are independently and identically distributed, and X₁Not independently the sameAnd (4) distribution.

Thus, can pass the decision vector X₀And X₁Whether to distinguish SM-OFDM and Al-OFDM encoding for independent equal distribution. Similarly, t can be differentiated from other patterns by taking an appropriate value.

Recording the Event occurrence of any Event of Event1 and Event2 as Event, and calculating the vector X as₀And X₁The case of independent and same distribution is iid. Note event Non as an undetermined event: it may be an Event or an Event iid. As shown in table 1, when t ∈ {1,2,4}, the distribution of events corresponding to STBC-OFDM is used as a characteristic parameter to distinguish the set Ω ═ SM-OFDM, Al-OFDM, ST3-OFDM, ST4-OFDM }, and can be represented by a decision tree. Each branch can be completed by binary hypothesis testing, defining event iid as H of hypothesis testing₀Defining non-iid as H for hypothesis testing₁：

H₀：X₀And X₁Are all independently distributed at the same time

H₁：X₀And X₁Are not all independently and identically distributed

Table 1 t is different, STBC-OFDM corresponds to the event

The whole process of the decision tree is as follows: rejecting H when t is 4₀The STBC-OFDM of (1) is ST 4-OFDM; rejecting H when t is 2₀The STBC-OFDM of (1) is ST 3-OFDM; rejecting H when t is 1₀The STBC-OFDM of (a) is Al-OFDM.

The method based on K-S detection is adopted to identify different STBC as

And

is a vector X₀And X₁Empirical distribution function of (2):

wherein M is a vector X_iI is 0, length of 1; ind (.) is an indicator function, when the input parameter is true, F_i(z) returning a value of 1; when the input parameter is false, F_i(z) returns a value of 0. The maximum distance between the two distribution functions can be expressed as:

as a goodness-of-fit statistic value when

Is established, refusing H₀Wherein

For the evaluation of the K-S test, β is the threshold value and α is the confidence interval, which can be expressed as:

wherein the content of the first and second substances,

compared with the prior art, the invention has the beneficial effects that:

(1) the STBC-OFDM signal type can be identified under the condition of a lower signal-to-noise ratio, the practical application can be met, and the calculation complexity is lower.

(2) The method does not need to estimate prior information such as noise information, modulation information, channel coefficients and the like in advance, is suitable for non-cooperative communication occasions, and has strong military significance. The algorithm has better robustness under different modulation modes, carrier frequency offset and non-Gaussian noise.

(3) The STBC-OFDM signal is blindly identified under the condition of frequency selective Rayleigh fading channel, and is consistent with the channel environment of high-speed transmission.

Drawings

FIG. 1 is a general flow diagram of the process of the present invention;

fig. 2 is a schematic diagram illustrating two different signal sequences defined by t ═ 1;

FIG. 3 is a STBC-OFDM signal transmission structure;

FIG. 4 is a diagram of calculating an autocorrelation vector X₁And X₂A schematic diagram;

FIG. 5 is a tree identification scheme;

FIG. 6 is a comparison of performance of different STBC-OFDM signal identifications in an example;

FIG. 7 is a comparison of the performance of STBC-OFDM identification at different numbers of subcarriers in an example;

FIG. 8 is a comparison of performance of STBC-OFDM identification at different block numbers in an example;

FIG. 9 is a comparison of performance of STBC-OFDM identification at different prefix lengths in an example;

Detailed Description

The invention is described in further detail below with reference to the figures and examples.

Fig. 1 is a general flow chart of the present invention, and the implementation process of the method described in this embodiment is as follows:

(1) intercepting an STBC-OFDM signal y (k) of a single receiving antenna;

(2) grouping the intercepted signals y (k) by taking OFDM blocks as units, defining a new OFDM block matrix R, and defining two new length N_BBlock matrix R of-t₀And R₁，

(3) And calculateAutocorrelation vector X of column vector_i；

(4) Calculating a threshold value beta;

(5) obtaining an empirical cumulative distribution function F_i(z) and calculating F_i(z) maximum distance between

(6) If it is not

Judgment H₀If true, otherwise, H is determined₁This is true.

In the examples: the OFDM signal is based on IEEE802.11e standard, the number of OFDM symbol sub-carriers N is 256, the length of cyclic prefix v is N/4, and the number of receiving antennas is N _Rx1, the number of received OFDM blocks N _B2000, confidence interval 99%, the channel is a frequency selective rayleigh fading channel and comprises 4 statistically independent paths, the above 4 paths having exponential power delay and σ²(p) ═ exp (-p/5), p ═ 0,1,. and path-1. The noise is zero mean additive white Gaussian noise and the signal-to-noise ratio

The signal adopts QPSK modulation mode, and adopts correct identification probability P (lambda), lambda belongs to { SM-OFDM, Al-OFDM, ST3-OFDM, ST4-OFDM } and average identification probability P_cThe performance of the algorithm is measured.

Fig. 6 shows the probability of correct identification of different STBC-OFDM signals. As can be seen from FIG. 6, the SM-OFDM identification effect is the best, and the SM-OFDM correct identification probability is close to the confidence interval of 0.99; the recognition effect of ST3-OFDM is the worst, because the ST3-OFDM code matrix contains symbol 0, which will affect X_iSuch that an empirical distribution function

And

the distance therebetween becomes smaller, thereby resulting inST3-OFDM is not ideal for identification at low signal-to-noise ratio. The recognition performance of Al-OFDM, ST3-OFDM and ST4-OFDM improves with the improvement of SNR. The main reason is that the strong noise makes the empirical distribution function in low signal-to-noise ratio environment

And

the distance between the two is reduced, so that the identification performance of the STBC-OFDM is not ideal at low SNR.

FIG. 7 shows the average correct identification probability P for 64, 128, 256, 512 subcarriers N_cCurve as a function of subcarrier. As can be seen from fig. 7, the performance of the identification improves as the number of subcarriers increases at low signal-to-noise ratios. Mainly when the number of subcarriers N increases, OFDMg in the formula (9)_Uk+uIncrease of elements of the block, R₀And R₁Correlation function x between middle column vectors_i(k) More accurate, thereby enabling the empirical distribution function

And

more precisely, and therefore its probability of correct identification increases with the number of subcarriers.

FIG. 8 shows the average correct identification probability P for OFDM blocks of 1000, 2000, 3000, 4000_cThe curve varies with OFDM block. As can be seen from FIG. 8, the average correct recognition probability P is obtained under low SNR environment_cThe identification effect is more ideal when the number of the OFDM blocks is 4000, the identification effect is least ideal when the number of the OFDM blocks is 1000 under the condition of high signal to noise ratio, and the average correct identification probability reaches 1 under the condition of other OFDM blocks. When the number of OFDM blocks is small, if t is too large, the empirical distribution function will be generated

And

the smaller middle element is not beneficial to inhibiting the influence of noise and channel on the empirical distribution function, thereby leading the correct identification probability of ST3-OFDM and ST4-OFDM to be lower, and influencing the average correct probability P_c。

FIG. 9 shows the average correct recognition probability P when the prefix lengths are N/4, N/16, and N/32_cCurve as a function of prefix length. As can be seen from fig. 9, the performance of the algorithm does not vary substantially with the prefix v length, mainly because the prefix length does not change the estimated value of the correlation function nor affect its autocorrelation function X_iAnd thus does not affect the calculation of its empirical distribution function estimate. The prefix length v has substantially no effect on the algorithm.

Claims (3)

1. A method for constructing different distributed signal sequences in an STBC-OFDM system, comprising the steps of: dividing the received signal into two sub-sequences which are overlapped with each other again, calculating the correlation function of the column vector in the two sub-sequences to obtain two received signal sequences which are distributed differently, respectively calculating the time delay correlation functions of the two received signal sequences, analyzing the distribution conditions of the two time delay correlation functions of different STBC, and finally identifying different STBC by adopting a method based on K-S detection;

   the repartitioning of the received signal into two mutually overlapping subsequences is specifically: will receive the signal

   

   Dividing into two mutually overlapping subsequences:

   

   

   wherein the content of the first and second substances,N_Bis the number of OFDM blocks, g_j Representing a single received OFDM block, j ∈ [0, N ∈ >_B-1]T represents the time delay of the correlation function;

   the method based on K-S detection is adopted to identify different STBC as

   

   And

   

   is a vector X₀And X₁Empirical distribution function of (2):

   

   wherein M is a vector X_iI is 0, length of 1; ind (.) is an indicator function, when the input parameter is true, F_i(z) returning a value of 1; when the input parameter is false, F_i(z) returning a value of 0; the maximum distance between the two distribution functions can be expressed as:

   

   wherein the content of the first and second substances,

   

   as a goodness-of-fit statistic value when

   

   Is established, refusing H₀Wherein, in the step (A),

   

   

   for the evaluation of the K-S test, β is the threshold value and α is the confidence interval, which can be expressed as:

   

   wherein the content of the first and second substances,

   
2. 2. the method according to claim 1, wherein said calculating the correlation function of the column vectors in the two subsequences is specifically:

   x_i(k)＝|[R_i(:,2tk)]^TR_i(:,2tk+t)|

   wherein i is 0,1, | represents absolute value, and represents block matrix R_iAll rows of (k ∈ [0, M-1 ]]，

   

   N is the length of the OFDM block.
3. 3. The method according to claim 2, wherein obtaining two received signal sequences with different distributions is specifically: the correlation function values are arranged to obtain two correlation vector sequences:

   X₀＝[x₀(0),x₀(1),…,x₀(M-1)]

   X₁＝[x₁(0),x₁(1),…,x₁(M-1)]。

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