CN114363126A - Space diversity MMSE-RISIC-NP equalization method - Google Patents
Space diversity MMSE-RISIC-NP equalization method Download PDFInfo
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Abstract
The invention belongs to the technical field of troposphere scattering communication and discloses a space diversity MMSE-RISIC-NP equalization method, which comprises the following steps: based on the SC-FDE system, the MIMO-SCFDE system is expanded to a MIMO-single carrier frequency domain equalization MIMO-SCFDE system; and establishing a model of the space diversity MIMO-SCFDE system, and performing space diversity MMSE-RISIC balance and space diversity MMSE-RISIC-NP balance. According to the invention, because the data noise is predicted and removed, the accuracy of the judgment result is improved; on the other hand, the data after being subjected to space diversity MMSE-RISIC equalization algorithm and data separation is used
Derived by making delta estimates
Closer to deltadCompared with the traditional MMSE-RISIC algorithm, the method reduces the extra interference caused by delta estimation.
Description
Technical Field
The invention belongs to the technical field of troposphere scattering communication, and particularly relates to a space diversity MMSE-RISIC-NP equalization method.
Background
At present, the traditional tropospheric scattering communication waveform such as Distortion Adaptive Receiver (DAR) overcomes the effect of multipath propagation by increasing the guard interval of adjacent symbols, however, when the information transmission rate is increased from 2Mb/s to 8Mb/s or even higher, the passive way of increasing the guard interval is no longer feasible, and then the effect of multipath propagation should be actively eliminated by using an equalization way. Equalization is a method of amplitude and phase compensation to minimize the bit error rate degradation due to intersymbol interference. If equalization is performed in the time domain, the equalization is called time domain equalization and is generally realized by adopting a transverse filter, the change of a channel is tracked by changing a tap coefficient, and when the multipath number of the channel is increased, the equalization complexity is in an exponential rising trend. If equalization is performed in the frequency domain, it is called frequency domain equalization, which mainly takes the frequency response into account. The Single-carrier frequency domain equalization (SC-FDE) technology resists frequency selective fading through a frequency domain equalization method, compared with Single-carrier time domain equalization, the method does not need to improve the capacity of resisting intersymbol interference by lengthening a tapped delay line, but directly corrects distortion on a frequency spectrum, so that the complexity of the frequency domain equalization is obviously reduced during large-path time delay; compared with an Orthogonal Frequency Division Multiplexing (OFDM) system, the OFDM system has similar complexity, and retains the advantage of low peak-to-average power ratio (PAPR) of a single carrier signal, thereby reducing sensitivity to phase noise and frequency offset.
The single carrier frequency domain equalization algorithm can be divided into a linear single carrier frequency domain equalization algorithm and a non-linear single carrier frequency domain equalization algorithm according to the existence of feedback.
1. SC-FDE technology
SC-FDE is an effective technique for overcoming ISI in high-rate wireless communication, and fig. 6 is a block diagram of an SC-FDE system. The transmitted binary data is transmitted in a block form after being coded, interleaved and symbol mapped, every N symbols are used as a code block, then a Guard Interval (GI) is inserted between the code blocks, and the length of the guard interval needs to be larger than the maximum time delay extension length of a channel so as to avoid intersymbol interference; and finally, the digital-to-analog conversion is carried out and the data is sent out through a transmitting antenna. The signal reaches the receiving end after wireless channel transmission, and is converted into a digital signal through analog-to-digital conversion, after removing GI, the digital signal is converted into a frequency domain through Fast Fourier Transform (FFT), channel estimation is carried out by using inserted pilot frequency, a channel transfer function obtained by channel estimation is used for frequency domain equalization, an SC-FDE code block is compensated in the frequency domain, the digital signal is converted into a time domain through Inverse Fast Fourier Transform (IFFT), and then corresponding demapping, deinterleaving and decoding are carried out to obtain estimated binary data. For GI of SC-FDE, Cyclic Prefix (CP) may be inserted, that is, the GI is copied from the tail of the code block to the head of the code block for repeated transmission, as shown in fig. 7(a), the CP may be inserted to convert the linear convolution of the transmission code block and the channel impulse response into cyclic convolution, so as to convert the cyclic convolution into a simple frequency domain multiplication operation through FFT, and thus, low-complexity frequency domain equalization may be performed. A known specific sequence may be inserted as GI, that is, a special word (UW) having a small peak-to-average power ratio in the time domain and a nearly constant amplitude-to-frequency characteristic in the frequency domain, as shown in fig. 7(b), a UW may be inserted before the beginning code block and a UW may be inserted between every two remaining code blocks, which may also function as a cyclic prefix, and the UW may also be used as a channel estimation, and when using decision feedback equalization, the influence of error propagation may be reduced.
Taking the insertion UW as an example, assuming that the channel impulse response is not changed in one data block, the data block inserted into UW can be represented as
Where d is a K × 1 data vector and u is a G × 1 UW vector, and the total length N of one data block is K + G.
Data is transmitted through a channel, and after removing the cyclic prefix, the data can be expressed as:
y＝hx+v (2)
wherein the received signal vector y ═ y0,…,yN-1]T，y0,…,yN-1Respectively, the received signal at the nth (N-0, …, N-1) point, v is the mean value 0 where the element variance is
H is an N × N cyclic matrix formed by the channel impulse response, and the first row element of the vector is [ h (0) h (1) … h (L-1) 0 … 0]TL is the number of multipath of the channel, L<N, h (0) h (1) … h (L-1) are channel impulse responses, respectively, and a received signal vector y after FFT can be expressed as:
Y＝Fy
＝F(hx+v)
＝FhFHFx+Fv
＝HX+V (3)
wherein
H＝FhFH (4)
X＝Fx (5)
V＝Fv (6)
Wherein F is an N × N dimensional FFT matrix, FHTranspose matrix for its conjugate:
y, X and V are respectively the frequency domain forms of Y, X and V, H is a frequency domain channel response matrix, H is a diagonal matrix because H is a cyclic matrix, k represents the kth point of the frequency domain, and therefore the frequency domain channel impulse response H of the kth point of the frequency domainkFor the kth diagonal element of H, it is:
let YkRepresenting the received signal at the kth point of the frequency domain, i.e. the kth received signal of the frequency domain, then
Yk＝HkXk+Vk (9)
In the formula, HkIs the frequency domain channel impulse response of the k-th point of the frequency domain, Hk＝[H]kkThat is, the frequency domain channel impulse response of the frequency domain kth point is the kth diagonal element on the frequency domain channel response matrix H; xk，VkA frequency domain transmission signal and a noise signal at the kth point of the frequency domain respectively. At this time, the transmitted data can be restored by frequency domain equalization technology.
2. Linear single carrier frequency domain equalization algorithm
The traditional SC-FDE equalization algorithm comprises ZF equalization and MMSE equalization. ZF equalization is theoretically optimal in eliminating intersymbol interference, but amplifies the influence of noise at the deep fading point of the channel frequency domain, thus deteriorating performance; MMSE equalization aims to minimize the Bit Error Rate (BER), which corresponds to a trade-off between channel noise and intersymbol interference.
(1) ZF equalization
ZF equalization can eliminate ISI to zero, and its equalization matrix can be expressed as:
WZF＝(HHH)-1HH (10)
where H is the channel frequency domain response matrix. Multiplying the equalization matrix W on both sides of equation (3)ZFTo obtain an equalized signal
Comprises the following steps:
as can be seen from equation (11), a frequency-domain transmission signal in which ISI is completely removed can be obtained by ZF equalization, but the noise vector is also multiplied by the frequency-domain equalizationMatrix array
When there is a small channel response value at a deep fading point of the channel frequency domain, i.e. at a certain frequency point, the noise power value at the frequency point is amplified, and the equalization performance is deteriorated.
(2) MMSE equalization
MMSE equalization, which considers ISI cancellation and noise suppression in combination, minimizes the mean square error between the equalized signal and the transmitted signal, and the MMSE equalization matrix can be expressed as:
wherein
Represents the frequency domain transmit signal power value,
representing the noise power level of the received signal, INRepresenting an identity matrix of order N. Multiplying W on both sides of equation (3)MMSEThe equalized signal is:
as can be seen from equation (13), when at the deep fading point of the channel frequency domain, the noise enhancement is suppressed, and at the same time, the ISI suppression performance is reduced, which is equivalent to making a compromise between the channel noise and the intersymbol interference. In general, when the channel has a deep fading point, the error performance of MMSE equalization is better than ZF equalization.
Through the above analysis, the problems and defects of the prior art are as follows: the prior art is interfered by data noise, and the accuracy of a judgment result is reduced.
The difficulty in solving the above problems and defects is: how to design a frequency domain equalization algorithm so as to accurately estimate and remove a noise signal and an intersymbol interference signal in a received signal, and if the estimation of the noise signal and the intersymbol interference signal is not accurate, an accumulated error is easily caused.
The significance of solving the problems and the defects is as follows: the method can accurately estimate the transmitted signal, reduce the influence of the scattering multi-path channel and overcome the frequency selective fading caused by the scattering multi-path channel.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a space diversity MMSE-RISIC-NP equalization method.
The invention is realized in such a way that a space diversity MMSE-RISIC-NP equalization method comprises the following steps:
expanding the system to a multi-input multi-output-single carrier frequency domain equalization MIMO-SCFDE system on the basis of the SC-FDE system; establishing a model of a space diversity MIMO-SCFDE system; the step plays a positive role: and a system framework basis is provided for the subsequent MMSE-RISIC-NP equalization.
And step two, establishing a model of the space diversity MIMO-SCFDE system, and performing space diversity MMSE-RISIC balance and space diversity MMSE-RISIC-NP balance. A space diversity MMSE-RISIC-NP equalization algorithm; the method comprises a space diversity MMSE-RISIC equalization algorithm and a space diversity MMSE-RISIC-NP equalization algorithm, wherein the space diversity MMSE-RISIC-NP equalization algorithm comprises the steps of the space diversity MMSE-RISIC equalization algorithm.
The MMSE-RISIC equalization algorithm has positive effects: firstly, only an MMSE-RISIC equalization algorithm is proposed in the existing document, but the MMSE-RISIC equalization algorithm is not applied to a space diversity MIMO-SCFDE system, so that the space diversity MMSE-RISIC equalization algorithm is firstly proposed; secondly, the defects in the space diversity MMSE-RISIC equalization algorithm can be comparatively analyzed, and the problems and the innovativeness solved by the MMSE-RISIC-NP equalization algorithm are highlighted.
Further, in the second step, the specific process of establishing the MIMO-SCFDE system model is as follows:
combining the STBC with the SC-FDE, and adopting STBC coding with a block as a unit; the frame structure of STBC-SCFDE system is used, the number of transmitting antennas is 2, and the receiving antennas receiveThe number of antennas is nRThen, 2n is realizedRFull diversity gain of; using UW as GI, in order to satisfy orthogonality at receiving end, processing UW;
original data of a sending end is converted into a sending data block after mapping, interweaving and coding, the sending data block is inserted into UW after being coded by STBC, and enters a channel through a transmitting antenna; the STBC encoded transmission data block inserted into the UW may be expressed as follows:
the data in the i +1 th time data block can be obtained by performing reverse order on the data part in the ith time data block and matching with operations such as conjugation, negation and the like, and the transmission data on the two antennas can be represented as:
the received signals at the ith, i +1 th time on the jth receiving antenna after channel transmission can be respectively expressed as:
wherein
Respectively representing the channel matrixes from the mth transmitting antenna to the jth receiving antenna at the ith and the ith +1 time points,
and
is a mean of zero, where the element variance is
White gaussian noiseA sound vector;
the formula (15) is introduced into the formula (16), and for simplification, the symbol (·)(i)Omitted and assuming that the channel impulse response is constant over two consecutive transmission data blocks, i.e. ordered
Equation (16) can be expressed as:
will be provided with
Multiplying by an NxN cyclic shift permutation matrix PKObtaining the replaced reception signal of the jth receiving antenna at the i +1 moment
And use property hj,mP＝Phj,mIs obtained by
For Nx 1 vector r ═ r0 r1…rN-1]TIn the case of a non-woven fabric,
to pair
Is subjected to FFT to obtain
Wherein F is an N × N dimensional FFT matrix
In the second equation of the equation (19),
and
so that the STBC coding loses the orthogonality, therefore, the UW block processing is needed
Wherein
The frequency domain received signal at the i +1 th time on the jth receiving antenna after being processed by the UW block is shown,
in the second term of equation (21), the interference caused by transmitting the UW block is removed and the time reversal UW is reconstructed in the third term; equation (21) is processed as follows:
combining (19) and (22) gives:
in the formula RjRepresenting the frequency-domain received signal at the jth receiving antenna, X1Representing the frequency-domain transmission signal on the first transmit antenna, X2Representing the frequency-domain transmission signal on the second transmitting antenna, H(j)Denotes the jthFrequency domain channel matrix on the receiving antenna, X representing the frequency domain transmission signal on the two transmitting antennas, NjRepresenting the frequency domain noise signal on the jth receiving antenna, RjMultiplying by H(j)HCan decompose X1And X2；
Wherein the content of the first and second substances,
a frequency domain received signal transformed by the equation (24) on the jth receiving antenna at time i; 0N×NA zero matrix representing NxN;
then
Wherein Λ(j)Is an N multiplied by N diagonal matrix, and E {. cndot.) represents the mean value;
will be provided with
And
normalization is performed so that the noise term remains at variance of
Gaussian white noise, equation (24) can be written as:
wherein the content of the first and second substances,
the normalized frequency domain receiving signal on the jth receiving antenna at the time i is shownThe number of the mobile station is,
representing the normalized frequency domain noise signal, Λ, on the jth receiving antenna at time i(j)＝(|H(j,1)|2+|H(j,2)|2)1/2Is an N × N diagonal matrix, and represents the frequency domain channel impulse response on the jth receiving antenna, and the (k, k) th item on the diagonal is equal to (| H)(j,1)(k,k)|2+|H(j,2)(k,k)|2)1/2K itself denotes the kth point of the frequency domain, thus H(j,1)K diagonal element of (2)(j,1)(k, k) and H(j,2)K diagonal element of (2)(j,2)(k, k) respectively represent frequency domain channel impulse responses of frequency domain kth points of a 1 st transmitting antenna, a 2 nd transmitting antenna to a jth receiving antenna,
INrepresenting an N-order identity matrix; equation (25) can be decomposed into two equations:
as can be seen from the formula (26)
And
the method does not interfere with each other, namely STBC decoding is finished, only simple linear processing is carried out during decoding, and then the transmitted signal can be estimated through frequency domain equalization
And
the two equations in equation (26) have the same form and have the same frequency domain channel impulse response Λ(j)Same noise asPower of
Therefore, when frequency domain equalization is performed on the receiving antenna, the equalization can be unified into:
Y(j)＝Λ(j)X(j)+V(j) (27)
in the formula Y(j)For receiving signals, X, in the frequency domain on the jth receiving antenna(j)For the estimated frequency domain transmission signal, V, on the jth receiving antenna(j)Is the frequency domain noise signal on the jth receiving antenna; in frequency domain equalization, n is sent in two timesRThe received STBC-SCFDE system is treated as a single-transmitting and multi-receiving system.
Further, the
Represents a data block of length N transmitted by the mth transmit antenna at time instant i,
respectively indicating transmission data at an nth (N-0, …, N-1) point in the transmission data block,
which represents the data part of the data block sent by the mth transmitting antenna at time i, having a length K,
wherein
Respectively representing the data of 0 th, … th and K-1 th points of the data part in the data block sent by the mth transmitting antenna at the time i;
the length of the UW part in the data block sent by the mth transmitting antenna at time i is G,
wherein u ism,0um,1…um,G-1When the m-th transmitting antenna respectively transmits data of UW part 0, … and G-1 points in the data block at the time i, N is K + G; g is larger than or equal to L to eliminate the interference between blocks, and L is the length of the channel impulse response.
Further, the transmitting antenna for the m (m ═ 1,2) th transmitting antenna,
0G×1、0K×1respectively representing G multiplied by 1 dimension and K multiplied by 1 dimension zero vectors; qKIs an NxN inverse cyclic shift permutation matrix, representing the conjugation, for an Nx1 vector
In the case of a non-woven fabric,
(·)Nrepresenting a modulo N operation.
Further, the
Representing the frequency domain received signal on the jth receive antenna at time i,
representing the frequency domain receiving signal on the jth receiving antenna at the time of i +1 after the replacement; h(j,m)＝Fhj,mFHIs an N × N diagonal matrix with the k (k ═ 0, 1.., N-1) diagonal elements having values of
hj,m(l) Denotes a channel impulse response at an L (L ═ 1., L-1) th path from an m-th transmitting antenna to a j-th receiving antenna,
representing the frequency domain received signal noise on the jth receive antenna at time instant i,
representing the frequency domain received signal noise on the jth receive antenna at time i +1 after the permutation,
further, in the second step, the spatial diversity MMSE-RISIC equalization specifically comprises the following steps:
STBC decoded received signal Y on jth receiving antenna(j),j＝1,2,…,nRMultiplying it by the MMSE equalization coefficient W on this antenna(j)Adding the equalized data of all receiving antennas to obtain a frequency domain receiving signal S after MMSE equalization, performing IFFT transformation to obtain a time domain receiving signal S after MMSE equalization, and subtracting a time domain residual intersymbol interference estimated value obtained in delta estimation from S
Delta is real time domain residual intersymbol interference data, and finally, a data estimation value is obtained through judgment
Further, the frequency domain received signal after MMSE equalization before IFFT can be expressed as:
wherein SkFor the data of the signal S at the k-th frequency point after MMSE equalization, S ═ S0,…,Sk,…,SN-1],S0,…,Sk,…,SN-1Respectively representing the data of the MMSE equalized signal S at 0, …, k, … and N-1 frequency points;
equalization coefficients at the k (k is 0,1, …, N-1) point of the MMSE equalizer on the jth receiving antenna in the frequency domain;
respectively representing frequency domain received signals at 0, …, k, … and N-1 frequency points of a j-th receiving antenna frequency domain; from formula (27):
wherein
Denotes the frequency domain channel impulse response, X, at the 0, …, k, …, N-1 frequency point of the jth receive antennakRepresenting the data of the estimated frequency domain transmission signal at the 0 th, … th, k, … th, N-1 th frequency point on the jth receiving antenna;
for the noise at the kth frequency point on the jth receive antenna, the variance is
Normalizing the power of the data signal to unit 1 for analysis, i.e.
The MMSE equalization coefficient expression can be derived from equation (12):
wherein
the following formula (29) and (30) can be substituted into formula (28) and simplified:
in the formula
Denotes noise data of frequency domain noise at k (k is 0, …, N-1) th frequency point after MMSE equalization, ΔkData representing frequency domain residual intersymbol interference at a k (k is 0, …, N-1) th frequency point after MMSE equalization;
let Delta be [ Delta ]0,…,Δk…,ΔN-1]T，V＝[V0,…,Vk,…,VN-1]T，X＝[X0,…,Xk,…,XN-1]If delta and V are respectively the frequency domain form of RISI and noise after MMSE equalization, X is the frequency domain emission signal vector; s ═ S0,…,Sk,…,SN-1]And S represents an MMSE equalized signal, the relationship between vectors corresponding to equation (32) can be expressed as:
S＝X+Δ+V (35)
the IFFT transformation of equation (35) yields:
s＝x+δ+v (36)
wherein s represents the time domain form of the data after MMSE equalization, δ represents the real time domain residual intersymbol interference data after MMSE equalization, and v represents the time domain form of the noise after MMSE equalization;
the MMSE-RISIC equalization algorithm first performs a delta estimation, which can be derived from equation (33):
in the formula
Represents the data of the estimated post-MMSE frequency-domain residual intersymbol interference at the k (k 0, …, N-1) th frequency point,
data representing the decided frequency domain transmission signal at a k (k-0, …, N-1) th frequency point; namely, the frequency domain form of the estimated residual intersymbol interference is obtained
Then to
IFFT (inverse fast Fourier transform) is carried out to obtain time domain residual intersymbol interference estimation value
Is removed in s
Order to
In the formula
Indicating removal of estimated residueMMSE equalized data with intersymbol interference left, and final pair
Judging; since the RISI is estimated and removed;
from the formulae (36) (38):
due to the formula (37)
Data indicating that estimated post-MMSE frequency-domain residual intersymbol interference is at the k (k 0, …, N-1) th frequency point,
Data representing the decided frequency domain transmission signal at a k (k-0, …, N-1) th frequency point; the frequency domain form of the estimated residual intersymbol interference can be obtained
Then to
IFFT (inverse fast Fourier transform) is carried out to obtain time domain residual intersymbol interference estimation value
δ is the true time domain residual intersymbol interference data.
Further, in the second step, the spatial diversity MMSE-RISIC-NP equalization specifically comprises the following steps:
noise prediction is added on the basis of MMSE-RISIC balance, the UW noise is used for predicting the noise of data and removing the noise before judgment by utilizing the correlation between the UW estimation noise and the data estimation noise, and the precision of delta estimation is also improved because the noise of the data before judgment is removed;
comparison (14) gives:
so that s can be separated into data vectors
And UW vector
An analog formula (36) of
And
is represented as follows:
where d, u denote the data and UW block, respectively, deltadData portion, δ, representing true time-domain residual intersymbol interference datauUW part, v, representing true time-domain residual intersymbol interference datadData portion, v, representing time domain noise after MMSE equalizationuA UW portion representing time domain noise after MMSE equalization;
in addition, the s can obtain a time domain estimation transmitting signal after the space diversity MMSE-RISIC equalization algorithm
One prime in the upper right corner represents the time domain estimated transmitted signal after the space diversity MMSE-RISIC-NP equalization method obtained finally
Distinguishing, estimating the time domain of the transmitted signal after the space diversity MMSE-RISIC equalization algorithm
After data separation, the data part of the transmitted signal is estimated in time domain after space diversity MMSE-RISIC equalization algorithm is obtained
After the UW block is inserted, FFT transformation is carried out, and then delta estimation is carried out to obtain a time domain residual intersymbol interference estimation value of space diversity MMSE-RISIC-NP balance
Spatial diversity MMSE-RISIC-NP equalized time domain residual intersymbol interference estimate since inserted UW block is accurate
May be represented by the following formula:
thus can be used for
Time domain residual intersymbol interference estimate data portion separated into space diversity MMSE-RISIC-NP equalization
Time domain residual intersymbol interference estimate UW portion delta equalized with spatial diversity MMSE-RISIC-NPu；
The noise prediction input vector may be represented as
From the formula (41)
Wherein, the noise prediction input vector is the noise v of UW partuSince u is known, v isuCan be accurately obtained by a receiverOut, vdAs data noise vectors, vdAnd vuLinear transformation from the same noise vector v, and thus correlation; can utilize vuTo predict vd；
By vuTo predict vdThe problem can be converted into a linear optimal filtering problem, the optimization performance is measured by a certain minimum cost function, the mean square value of the estimation error, namely a linear MMSE criterion, is selected as the cost function, the cost function is easy to carry out mathematical processing, and the cost function has a unique minimum value which can uniquely define statistical optimization design;
assuming the linear MMSE prediction matrix is B, then
From the wiener filtering principle, we can obtain:
wherein
Where V denotes the frequency domain form of the noise after MMSE equalization, FdIs the first K columns of the matrix F, FuIs the last G column of matrix F
And
are respectively FdAnd FuThe conjugate transpose of (1); the vector relationship corresponding to the formula (34) can be expressed as
V(j)Representing the frequency domain form of the noise after MMSE equalization on the jth receiving antenna;
bringing equations (45) (46) (47) into equation (44) yields the expression for B:
v is thendPredicted value of (2)
Can be expressed as:
the decided data can be expressed as:
wherein
Represents the data obtained by decision after space diversity MMSE-RISIC-NP equalization,
the predicted data noise is derived from the noise prediction.
Another object of the present invention is to provide a program storage medium for receiving a user input, the stored computer program causing an electronic device to execute the space diversity MMSE-RISIC-NP equalization method comprising the steps of:
expanding the system to a multi-input multi-output-single carrier frequency domain equalization MIMO-SCFDE system on the basis of the SC-FDE system;
and step two, establishing a model of the space diversity MIMO-SCFDE system, and performing space diversity MMSE-RISIC balance and space diversity MMSE-RISIC-NP balance.
It is another object of the present invention to provide a computer program product stored on a computer readable medium, comprising a computer readable program for providing a user input interface to implement the space diversity MMSE-RISIC-NP equalization method when executed on an electronic device.
By combining all the technical schemes, the invention has the advantages and positive effects that: according to the invention, because the data noise is predicted and removed, the accuracy of the judgment result is improved; on the other hand, the data after being subjected to space diversity MMSE-RISIC equalization algorithm and data separation is used
Derived by making delta estimates
Closer to deltadCompared with the traditional MMSE-RISIC algorithm, the method reduces the extra interference caused by delta estimation.
Drawings
Fig. 1 is a flowchart of a space diversity MMSE-RISIC-NP equalization method provided by an embodiment of the present invention.
Fig. 2 is a schematic structural diagram of a space diversity MIMO-SCFDE wireless communication system according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of a frame structure of a UW-based STBC-SCFDE system according to an embodiment of the present invention.
Fig. 4 is a schematic structural diagram of a space diversity MMSE-RISIC equalization algorithm provided by an embodiment of the present invention.
Fig. 5 is a schematic structural diagram of a space diversity MMSE-RISIC-NP equalization algorithm provided by an embodiment of the present invention.
Fig. 6 is a schematic structural diagram of an SC-FDE system according to an embodiment of the present invention.
Fig. 7 is a schematic diagram of the form of inserting GI according to the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Aiming at the problems in the prior art, the invention provides a space diversity MMSE-RISIC-NP equalization method, which is described in detail below with reference to the attached drawings.
The spatial diversity MMSE-RISIC-NP equalization method provided by the present invention can also be implemented by those skilled in the art using other steps, and the spatial diversity MMSE-RISIC-NP equalization method provided by the present invention in fig. 1 is only a specific embodiment.
As shown in fig. 1, a space diversity MMSE-RISIC-NP equalization method provided by an embodiment of the present invention includes:
s101: based on the SC-FDE system, the MIMO-SCFDE system is expanded to a MIMO-single carrier frequency domain equalization MIMO-SCFDE system;
s102: and establishing a model of the space diversity MIMO-SCFDE system, and performing space diversity MMSE-RISIC balance and space diversity MMSE-RISIC-NP balance.
In S102 provided by the embodiment of the present invention, the specific process of establishing the MIMO-SCFDE system model is as follows:
combining the STBC with the SC-FDE, and adopting STBC coding with a block as a unit; the frame structure of STBC-SCFDE system has transmitting antenna number of 2 and receiving antenna number of nRThen, 2n is realizedRFull diversity gain of; using UW as GI, in order to satisfy orthogonality at receiving end, processing UW;
original data of a sending end is converted into a sending data block after mapping, interweaving and coding, the sending data block is inserted into UW after being coded by STBC, and enters a channel through a transmitting antenna; the STBC encoded transmission data block inserted into the UW may be expressed as follows:
wherein
Represents a data block of length N transmitted by the mth transmit antenna at time instant i,
respectively indicating transmission data at an nth (N-0, …, N-1) point in the transmission data block,
which represents the data part of the data block sent by the mth transmitting antenna at time i, having a length K,
wherein
Respectively representing the data of 0 th, … th and K-1 th points of the data part in the data block sent by the mth transmitting antenna at the time i;
the length of the UW part in the data block sent by the mth transmitting antenna at time i is G,
wherein u ism,0um,1…um,G-1When the mth transmitting antenna transmits data at points 0, …, and G-1 in the UW part of the data block at time i, respectively, N is K + G. G is larger than or equal to L to eliminate the interference between blocks, and L is the length of the channel impulse response.
The data in the i +1 th time data block can be obtained by performing reverse order on the data part in the ith time data block and matching with operations such as conjugation, negation and the like, and the transmission data on the two antennas can be represented as:
wherein for the m (m ═ 1,2) th transmit antenna,
0G×1、0K×1respectively representing G multiplied by 1 dimension and K multiplied by 1 dimension zero vectors; qKIs an NxN inverse cyclic shift permutation matrix, representing the conjugation, for an Nx1 vector
In the case of a non-woven fabric,
(·)Nrepresenting a modulo N operation.
The received signals at the ith, i +1 th time on the jth receiving antenna after channel transmission can be respectively expressed as:
wherein
Respectively representing the channel matrixes from the mth transmitting antenna to the jth receiving antenna at the ith and the ith +1 time points,
and
is a mean of zero, where the element variance is
An additive white gaussian noise vector. The formula (15) is introduced into the formula (16), and for simplification, the symbol (·)(i)Omitted and assuming that the channel impulse response is constant over two consecutive transmission data blocks, i.e. ordered
Equation (16) can be expressed as:
will be provided with
Multiplying by an NxN cyclic shift permutation matrix PKObtaining the replaced reception signal of the jth receiving antenna at the i +1 moment
And use property hj,mP＝Phj,mIs obtained by
For Nx 1 vector r ═ r0 r1…rN-1]TIn the case of a non-woven fabric,
to pair
Is subjected to FFT to obtain
Wherein F is an N × N dimensional FFT matrix
Wherein the content of the first and second substances,
representing the frequency domain received signal on the jth receive antenna at time i,
indicating the j receiving antenna at the time of i +1 after the permutationReceiving a signal in the frequency domain; h(j,m)＝Fhj,mFHIs an N × N diagonal matrix with the k (k ═ 0, 1.., N-1) diagonal elements having values of
hj,m(l) Denotes a channel impulse response at an L (L ═ 1., L-1) th path from an m-th transmitting antenna to a j-th receiving antenna,
representing the frequency domain received signal noise on the jth receive antenna at time instant i,
representing the frequency domain received signal noise on the jth receive antenna at time i +1 after the permutation,
in the second equation of the equation (19),
and
so that the STBC coding loses the orthogonality, therefore, the UW block processing is needed;
wherein
The frequency domain received signal at the i +1 th time on the jth receiving antenna after being processed by the UW block is shown,
in the second term of equation (21), the interference caused by transmitting the UW block is removed, and the time reversal UW is reconstructed in the third term. Equation (21) is processed as follows:
combining (19) and (22) gives:
in the formula RjRepresenting the frequency-domain received signal at the jth receiving antenna, X1Representing the frequency-domain transmission signal on the first transmit antenna, X2Representing the frequency-domain transmission signal on the second transmitting antenna, H(j)Representing the frequency domain channel matrix on the jth receive antenna, X representing the frequency domain transmit signal on two transmit antennas, NjRepresenting the frequency domain noise signal on the jth receiving antenna, RjMultiplying by H(j)H type can decompose X1And X2；
Wherein the content of the first and second substances,
a frequency domain received signal transformed by the equation (24) on the jth receiving antenna at time i; 0N×NA zero matrix representing NxN;
then
Wherein Λ(j)Is an N multiplied by N diagonal matrix, and E {. cndot.) represents the mean value.
Will be provided with
And
normalization is performed so that the noise term remains at variance of
Gaussian white noise, equation (24) can be written as:
wherein the content of the first and second substances,
representing the normalized frequency domain received signal on the jth receiving antenna at time i,
representing the normalized frequency domain noise signal, Λ, on the jth receiving antenna at time i(j)＝(|H(j,1)|2+|H(j,2)|2)1/2Is an N × N diagonal matrix, and represents the frequency domain channel impulse response on the jth receiving antenna, and the (k, k) th item on the diagonal is equal to (| H)(j,1)(k,k)|2+|H(j,2)(k,k)|2)1/2K itself denotes the kth point of the frequency domain, thus H(j,1)K diagonal element of (2)(j ,1)(k, k) and H(j,2)K diagonal element of (2)(j,2)(k, k) respectively represent frequency domain channel impulse responses of frequency domain kth points of a 1 st transmitting antenna, a 2 nd transmitting antenna to a jth receiving antenna,
INrepresenting an identity matrix of order N. Equation (25) can be decomposed into two equations:
as can be seen from the formula (26)
And
the method does not interfere with each other, namely STBC decoding is finished, only simple linear processing is carried out during decoding, and then the transmitted signal can be estimated through frequency domain equalization
And
the two equations in equation (26) have the same form and have the same frequency domain channel impulse response Λ(j)Equal noise power
Therefore, when frequency domain equalization is performed on the receiving antenna, the equalization can be unified into:
Y(j)＝Λ(j)X(j)+V(j) (27)
in the formula Y(j)For receiving signals, X, in the frequency domain on the jth receiving antenna(j)For the estimated frequency domain transmission signal, V, on the jth receiving antenna(j)Is the frequency domain noise signal on the jth receive antenna. Thus, when frequency domain equalization is carried out, n is sent out in two timesRThe STBC-SCFDE system of receiving can be regarded as a system of single-sending and multi-receiving for processing.
In S102 provided by the embodiment of the present invention, space diversity MMSE-RISIC equalization specifically includes the following steps:
STBC decoded received signal Y on jth receiving antenna(j),j＝1,2,…,nRMultiplying it by the MMSE equalization coefficient W on this antenna(j)Adding the equalized data of all receiving antennas to obtain a frequency domain receiving signal S after MMSE equalization, performing IFFT conversion to obtain a time domain receiving signal S after MMSE equalization, and performing time domain processing on the time domain receiving signal SSubtracting the time domain residual intersymbol interference estimate from the delta estimate
Delta is real time domain residual intersymbol interference data, and finally, a data estimation value is obtained through judgment
The frequency domain received signal after MMSE equalization before IFFT can be expressed as
Wherein SkFor the data of the signal S at the k-th frequency point after MMSE equalization, S ═ S0,…,Sk,…,SN-1],S0,…,Sk,…,SN-1Respectively representing the data of the MMSE equalized signal S at 0, …, k, … and N-1 frequency points;
equalization coefficients at the k (k is 0,1, …, N-1) point of the MMSE equalizer on the jth receiving antenna in the frequency domain;
respectively representing frequency domain received signals at 0, …, k, … and N-1 frequency points of a j-th receiving antenna frequency domain; from formula (27):
wherein
Denotes the frequency domain channel impulse response, X, at the 0, …, k, …, N-1 frequency point of the jth receive antennakRepresenting the data of the estimated frequency domain transmission signal at the 0 th, … th, k, … th, N-1 th frequency point on the jth receiving antenna;
for the noise at the kth frequency point on the jth receive antenna, the variance is
Normalizing the power of the data signal to unit 1 for analysis, i.e.
The MMSE equalization coefficient expression can be derived from equation (12):
wherein
The following formula (29) and (30) can be substituted into formula (28) and simplified:
in the formula
Denotes noise data of frequency domain noise at k (k is 0, …, N-1) th frequency point after MMSE equalization, ΔkData at the k (k is 0, …, N-1) th frequency point of frequency domain residual intersymbol interference after MMSE equalization is represented.
Let Delta be [ Delta ]0,…,Δk…,ΔN-1]T，V＝[V0,…,Vk,…,VN-1]T，X＝[X0,…,Xk,…,XN-1]Then, Δ and V are frequency domain forms of RISI and noise after MMSE equalization, respectively, and X is a frequency domain transmit signal vector. S ═ S0,…,Sk,…,SN-1]And S represents an MMSE equalized signal, the relationship between vectors corresponding to equation (32) can be expressed as:
S＝X+Δ+V (35)
the IFFT transformation of equation (35) yields:
s＝x+δ+v (36)
wherein s represents the time domain form of the data after MMSE equalization, δ represents the real time domain residual intersymbol interference data after MMSE equalization, and v represents the time domain form of the noise after MMSE equalization;
the MMSE-RISIC equalization algorithm first performs a delta estimation, which can be derived from equation (33):
in the formula
Denotes the estimated post-MMSE frequency domain residual intersymbol interference at k (k)0, …, N-1) data at frequency points,
data representing the decided frequency domain transmission signal at a k (k-0, …, N-1) th frequency point; namely, the frequency domain form of the estimated residual intersymbol interference is obtained
Then to
IFFT (inverse fast Fourier transform) is carried out to obtain time domain residual intersymbol interference estimation value
Is removed in s
Order to
In the formula
MMSE equalized data representing the removed estimated residual intersymbol interference, and finally
And (6) making a decision. Since the RISI is estimated and removed;
from the formulae (36) (38):
due to the formula (37)
Indicating that the estimated post-MMSE frequency-domain residual intersymbol interference is at the k (k 0, …, N-1) th frequency binThe data of (A),
Data representing the decided frequency domain transmission signal at a k (k-0, …, N-1) th frequency point; the frequency domain form of the estimated residual intersymbol interference can be obtained
Then to
IFFT (inverse fast Fourier transform) is carried out to obtain time domain residual intersymbol interference estimation value
δ is the true time domain residual intersymbol interference data.
In S102 provided by the embodiment of the present invention, space diversity MMSE-RISIC-NP is balanced, and the specific process is as follows:
noise prediction is added on the basis of MMSE-RISIC balance, the UW noise is used for predicting the noise of data and removing the noise before judgment by utilizing the correlation between the UW estimation noise and the data estimation noise, and the precision of delta estimation is also improved because the noise of the data before judgment is removed;
comparison (14) gives:
so that s can be separated into data vectors
And UW vector
An analog formula (36) of
And
is represented as follows:
where d, u denote the data and UW block, respectively, deltadData portion, δ, representing true time-domain residual intersymbol interference datauUW part, v, representing true time-domain residual intersymbol interference datadData portion, v, representing time domain noise after MMSE equalizationuRepresenting the UW portion of the MMSE equalized time domain noise.
In addition, the s can obtain a time domain estimation transmitting signal after the space diversity MMSE-RISIC equalization algorithm
One prime in the upper right corner represents the time domain estimated transmitted signal after the space diversity MMSE-RISIC-NP equalization method obtained finally
Distinguishing, estimating the time domain of the transmitted signal after the space diversity MMSE-RISIC equalization algorithm
After data separation, the data part of the transmitted signal is estimated in time domain after space diversity MMSE-RISIC equalization algorithm is obtained
After the UW block is inserted, FFT transformation is carried out, and then delta estimation is carried out to obtain a time domain residual intersymbol interference estimation value of space diversity MMSE-RISIC-NP balance
Spatial diversity MMSE-RISIC-NP equalized time domain residual intersymbol interference estimate since inserted UW block is accurate
May be represented by the following formula:
thus can be used for
Time domain residual intersymbol interference estimate data portion separated into space diversity MMSE-RISIC-NP equalization
Time domain residual intersymbol interference estimate UW portion delta equalized with spatial diversity MMSE-RISIC-NPu。
The noise prediction input vector may be represented as
From formula (41):
wherein, the noise prediction input vector is the noise v of UW partuSince u is known, v isuV can be accurately calculated by a receiverdAs data noise vectors, vdAnd vuLinear transformation from the same noise vector v and thus correlation. Can utilize vuTo predict vd。
By vuTo predict vdThe problem can be converted into a linear optimal filtering problem, the optimization performance is measured by a certain minimum cost function, the mean square value of the estimation error, namely a linear MMSE criterion, is selected as the cost function, the cost function is easy to carry out mathematical processing, and the cost function has a unique minimum value which can uniquely define statistical optimization design;
assuming the linear MMSE prediction matrix is B, then
From the wiener filtering principle, we can obtain:
wherein
Where V denotes the frequency domain form of the noise after MMSE equalization, FdIs the first K columns of the matrix F, FuThe last G column of the matrix F,
and
are respectively FdAnd FuThe conjugate transpose of (c). The vector relationship corresponding to equation (34) can be expressed as:
V(j)representing the frequency domain version of the MMSE equalized noise on the jth receive antenna.
Bringing equations (45) (46) (47) into equation (44) yields the expression for B:
v is thendPredicted value of (2)
Can be expressed as:
the decided data can be expressed as:
wherein
Represents the data obtained by decision after space diversity MMSE-RISIC-NP equalization,
the predicted data noise is derived from the noise prediction.
The technical solution of the present invention will be described in detail with reference to the following specific examples.
1. Establishing a space diversity MIMO-SCFDE system model
In the space diversity MIMO-SCFDE system, when the MIMO coding mode is space-time block code (STBC) and space-time trellis code (STTC), full diversity gain can be obtained, and the rate at this time is the same as that of a single-input single-output (SISO) system. The STTC coding can also obtain coding gain, but the coding complexity is complex, the coding complexity is raised exponentially when the rate is raised, and the STBC decoding can be completed only by simple linear processing.
Fig. 2 shows a MIMO-SCFDE system model based on spatial diversity. The STBC and the SC-FDE are combined, and STBC coding is performed in units of blocks, as shown in fig. 3, which shows a frame structure of the STBC-SCFDE system used in the present invention. The number of transmitting antennas is 2, and the number of receiving antennas is nRWhen 2n can be realizedRFull diversity gain of. Here, using UW as the GI requires UW processing later in order to satisfy orthogonality at the receiving end.
Original data of a sending end is converted into a sending data block after mapping, interweaving and coding, the sending data block is inserted into UW after being coded by STBC, and enters a channel through a transmitting antenna. The STBC encoded transmission data block inserted into the UW may be expressed as follows:
wherein
Represents a data block of length N transmitted by the mth transmit antenna at time instant i,
respectively indicating transmission data at an nth (N-0, …, N-1) point in the transmission data block,
which represents the data part of the data block sent by the mth transmitting antenna at time i, having a length K,
wherein
Respectively representing the data of 0 th, … th and K-1 th points of the data part in the data block sent by the mth transmitting antenna at the time i;
the length of the UW part in the data block sent by the mth transmitting antenna at time i is G,
wherein u ism,0um,1…um,G-1When the mth transmitting antenna transmits data at points 0, …, and G-1 in the UW part of the data block at time i, respectively, N is K + G. G is larger than or equal to L to eliminate the interference between blocks, and L is the length of the channel impulse response.
As shown in fig. 3, the data in the data block at the i +1 th time can be obtained by performing reverse order on the data part in the data block at the i-th time and combining conjugation, negation, and the like, so that the transmission data on the two antennas can be represented as:
wherein for the m (m ═ 1,2) th transmit antenna,
0G×1、0K×1respectively representing G multiplied by 1 dimension and K multiplied by 1 dimension zero vectors; qKIs an NxN inverse cyclic shift permutation matrix, representing the conjugation, for an Nx1 vector
In the case of a non-woven fabric,
(·)Nrepresenting a modulo N operation.
The received signals at the ith, i +1 th time on the jth receiving antenna after channel transmission can be respectively expressed as:
wherein
Respectively representing the channel matrixes from the mth transmitting antenna to the jth receiving antenna at the ith and the ith +1 time points,
and
is a mean of zero, where the element variance is
An additive white gaussian noise vector. General formula(15) With the formula (16), to simplify the representation, the superscript (.)(i)Omitted and assuming that the channel impulse response is constant over two consecutive transmission data blocks, i.e. ordered
Equation (16) can be expressed as:
will be provided with
Multiplying by an NxN cyclic shift permutation matrix PKObtaining the replaced reception signal of the jth receiving antenna at the i +1 moment
And use property hj,mP＝Phj,mThe following can be obtained:
for Nx 1 vector r ═ r0 r1…rN-1]TIn the case of a non-woven fabric,
to pair
Is subjected to FFT to obtain
Wherein F is an N × N dimensional FFT matrix
Wherein the content of the first and second substances,
representing the frequency domain received signal on the jth receive antenna at time i,
representing the frequency domain receiving signal on the jth receiving antenna at the time of i +1 after the replacement; h(j,m)＝Fhj,mFHIs an N multiplied by N diagonal matrix, the k (k is 0,1, …, N-1) diagonal elements of which have the value
hj,m(l) Denotes a channel impulse response at an L (L ═ 1., L-1) th path from an m-th transmitting antenna to a j-th receiving antenna,
representing the frequency domain received signal noise on the jth receive antenna at time instant i,
representing the frequency domain received signal noise on the jth receive antenna at time i +1 after the permutation,
in the second equation of the equation (19),
and
so that the STBC coding loses the orthogonality, therefore, the UW block processing is needed
Wherein
The frequency domain received signal at the i +1 th time on the jth receiving antenna after being processed by the UW block is shown,
in the second term of equation (21), the interference caused by transmitting the UW block is removed, and the time reversal UW is reconstructed in the third term. Equation (21) is processed as follows:
combining (19) and (22) gives:
in the formula RjRepresenting the frequency-domain received signal at the jth receiving antenna, X1Representing the frequency-domain transmission signal on the first transmit antenna, X2Representing the frequency-domain transmission signal on the second transmitting antenna, H(j)Representing the frequency domain channel matrix on the jth receive antenna, X representing the frequency domain transmit signal on two transmit antennas, NjRepresenting the frequency domain noise signal on the jth receiving antenna, RjMultiplying by H(j)HCan decompose X1And X2
Wherein the content of the first and second substances,
a frequency domain received signal transformed by the equation (24) on the jth receiving antenna at time i; 0N×NA zero matrix representing NxN;
then
Wherein Λ(j)Is an N multiplied by N diagonal matrix, and E {. cndot.) represents the mean value.
Will be provided with
And
normalization is performed so that the noise term remains at variance of
Gaussian white noise, equation (24) can be written as:
wherein the content of the first and second substances,
representing the normalized frequency domain received signal on the jth receiving antenna at time i,
representing the normalized frequency domain noise signal, Λ, on the jth receiving antenna at time i(j)＝(|H(j,1)|2+|H(j,2)|2)1/2Is an N × N diagonal matrix, and represents the frequency domain channel impulse response on the jth receiving antenna, and the (k, k) th item on the diagonal is equal to (| H)(j,1)(k,k)|2+|H(j,2)(k,k)|2)1/2K itself denotes the kth point of the frequency domain, thus H(j,1)K diagonal element of (2)(j ,1)(k, k) and H(j,2)K diagonal element of (2)(j,2)(k, k) denotes frequency domain kth point from 1 st transmitting antenna, 2 nd transmitting antenna to jth receiving antennaThe frequency-domain channel impulse response is,
INrepresenting an identity matrix of order N. Equation (25) can be decomposed into two equations:
as can be seen from the formula (26)
And
the method does not interfere with each other, namely STBC decoding is finished, only simple linear processing is carried out during decoding, and then the transmitted signal can be estimated through frequency domain equalization
And
the two equations in equation (26) have the same form and have the same frequency domain channel impulse response Λ(j)Equal noise power
Therefore, when frequency domain equalization is performed on the receiving antenna, the equalization can be unified into:
Y(j)＝Λ(j)X(j)+V(j) (27)
in the formula Y(j)For receiving signals, X, in the frequency domain on the jth receiving antenna(j)For the estimated frequency domain transmission signal, V, on the jth receiving antenna(j)Is the frequency domain noise signal on the jth receive antenna. Thus, when frequency domain equalization is carried out, n is sent out in two timesRThe STBC-SCFDE system of receiving can be regarded as a system of single-sending and multi-receiving for processing.
2. Space diversity MMSE-RISIC equalization
FIG. 4 is a structural diagram of space diversity MMSE-RISIC equalization algorithm, wherein the received signal Y after STBC decoding is carried out on the jth receiving antenna(j),j＝1,2,…,nRMultiplying it by the MMSE equalization coefficient W on this antenna(j)Adding the equalized data of all receiving antennas to obtain a frequency domain receiving signal S after MMSE equalization, performing IFFT transformation to obtain a time domain receiving signal S after MMSE equalization, and subtracting a time domain residual intersymbol interference estimated value obtained in delta estimation from S
Delta is real time domain residual intersymbol interference data, and finally, a data estimation value is obtained through judgment
The specific implementation of the delta estimation will be described later.
The frequency domain received signal after MMSE equalization before IFFT can be expressed as:
wherein SkFor the data of the signal S at the k-th frequency point after MMSE equalization, S ═ S0,…,Sk,…,SN-1],S0,…,Sk,…,SN-1Respectively representing the data of the MMSE equalized signal S at 0, …, k, … and N-1 frequency points;
equalization coefficients at the k (k is 0,1, …, N-1) point of the MMSE equalizer on the jth receiving antenna in the frequency domain;
respectively, the frequency domain received signals at 0, …, k, …, N-1 frequency points of the j-th receiving antenna frequency domain. From formula (27):
wherein
Denotes the frequency domain channel impulse response, X, at the 0, …, k, …, N-1 frequency point of the jth receive antennakRepresenting the data of the estimated frequency domain transmission signal at the 0 th, … th, k, … th, N-1 th frequency point on the jth receiving antenna;
for the noise at the kth frequency point on the jth receive antenna, the variance is
Normalizing the power of the data signal to unit 1 for ease of analysis, i.e.
The MMSE equalization coefficient expression can be derived from equation (12):
wherein
The following formula (29) and (30) can be substituted into formula (28) and simplified:
in the formula
Denotes noise data of frequency domain noise at k (k is 0, …, N-1) th frequency point after MMSE equalization, ΔkData at the k (k is 0, …, N-1) th frequency point of frequency domain residual intersymbol interference after MMSE equalization is represented.
Let Delta be [ Delta ]0,…,Δk…,ΔN-1]T，V＝[V0,…,Vk,…,VN-1]T，X＝[X0,…,Xk,…,XN-1]Then, Δ and V are frequency domain forms of RISI and noise after MMSE equalization, respectively, and X is a frequency domain transmit signal vector. S ═ S0,…,Sk,…,SN-1]And S denotes an MMSE equalized signal, the relationship between vectors corresponding to equation (32) can be expressed as
S＝X+Δ+V (35)
The IFFT transformation of equation (35) yields:
s＝x+δ+v (36)
wherein s represents the time domain form of the data after MMSE equalization, δ represents the real time domain residual intersymbol interference data after MMSE equalization, and v represents the time domain form of the noise after MMSE equalization.
The traditional MMSE equalization directly judges s, and the formula shows that delta and v still exist in s, so that the judgment precision is influenced. The MMSE-RISIC equalization algorithm first performs a delta estimation, which can be derived from equation (33):
in the formula
Represents the data of the estimated post-MMSE frequency-domain residual intersymbol interference at the k (k 0, …, N-1) th frequency point,
and represents data of the decided frequency domain transmission signal at the k (k-0, …, N-1) th frequency point. The frequency domain form of the estimated residual intersymbol interference can be obtained
Then to
IFFT (inverse fast Fourier transform) is carried out to obtain time domain residual intersymbol interference estimation value
Is removed in s
Order to
In the formula
MMSE equalized data representing the removed estimated residual intersymbol interference, and finally
And (6) making a decision. As RISI is estimated and removed, MMSE-RISIC equalization algorithm improves in accuracy over MMSE, but is derived from equations (36) (38):
due to the formula (37)
Data indicating that estimated post-MMSE frequency-domain residual intersymbol interference is at the k (k 0, …, N-1) th frequency point,
And represents data of the decided frequency domain transmission signal at the k (k-0, …, N-1) th frequency point. The frequency domain form of the estimated residual intersymbol interference can be obtained
Then to
IFFT (inverse fast Fourier transform) is carried out to obtain time domain residual intersymbol interference estimation value
δ is the true time domain residual intersymbol interference data.
As can be seen from the formula (39)
The noise interference v still exists in the judgment result, so that the judgment result is influenced; and the default decision is correct in delta estimation, so the estimation is obtained
There is a deviation from δ, which further causes additional interference. When the signal-to-noise ratio is low, the extra interference increases, degrading system performance, although MMSE-RISIC equalization can improve accuracy by iteration, but this will cause the counter to be lowThe calculated amount is multiplied.
3. Space diversity MMSE-RISIC-NP equalization
Fig. 5 is a structure of a space diversity MMSE-RISIC-NP equalization algorithm, which adds noise prediction based on MMSE-RISIC equalization, and predicts the noise of data by using the correlation between UW estimation noise and data estimation noise, and removes the noise of the data before decision, because the data before decision removes the noise, the precision of δ estimation is also improved.
Obtained by comparison of formula (14)
So that s can be separated into data vectors
And UW vector
An analog formula (36) of
And
is represented as follows:
where d, u denote the data and UW block, respectively, deltadData portion, δ, representing true time-domain residual intersymbol interference datauUW part, v, representing true time-domain residual intersymbol interference datadData portion, v, representing time domain noise after MMSE equalizationuRepresenting the UW portion of the MMSE equalized time domain noise.
In addition, the s can obtain a time domain estimation transmitting signal after the space diversity MMSE-RISIC equalization algorithm
One prime in the upper right corner represents the time domain estimated transmitted signal after the space diversity MMSE-RISIC-NP equalization method obtained finally
Distinguishing, estimating the time domain of the transmitted signal after the space diversity MMSE-RISIC equalization algorithm
After data separation, the data part of the transmitted signal is estimated in time domain after space diversity MMSE-RISIC equalization algorithm is obtained
After the UW block is inserted, FFT transformation is carried out, and then delta estimation is carried out to obtain a time domain residual intersymbol interference estimation value of space diversity MMSE-RISIC-NP balance
Spatial diversity MMSE-RISIC-NP equalized time domain residual intersymbol interference estimate since inserted UW block is accurate
May be represented by the following formula:
thus can be used for
Time domain residual intersymbol interference estimate data portion separated into space diversity MMSE-RISIC-NP equalization
Time domain residual intersymbol interference estimate UW portion delta equalized with spatial diversity MMSE-RISIC-NPu。
Noise prediction is known from FIG. 5The input vector can be represented as
From formula (41):
wherein, the noise prediction input vector is the noise v of UW partuSince u is known, v isuV can be accurately calculated by a receiverdAs data noise vectors, vdAnd vuLinear transformation from the same noise vector v and thus correlation. Can utilize vuTo predict vd。
By vuTo predict vdThe problem of (2) can be converted into a linear optimal filtering problem, the optimization performance is measured by a certain minimum cost function, the method selects a mean square value of estimation errors, namely a linear MMSE (minimum mean square error) criterion, as the cost function, the cost function is easy to carry out mathematical processing, and the cost function has a unique minimum value which can uniquely define a statistical optimization design.
Assuming the linear MMSE prediction matrix is B, then
From the wiener filtering principle, we can obtain:
wherein
Where V denotes the frequency domain form of the noise after MMSE equalization, FdIs the first K columns of the matrix F, FuThe last G column of the matrix F,
and
are respectively FdAnd FuThe conjugate transpose of (c). The vector relationship corresponding to the formula (34) can be expressed as
V(j)Representing the frequency domain version of the MMSE equalized noise on the jth receive antenna.
Bringing equations (45) (46) (47) into equation (44) yields the expression for B:
v is thendPredicted value of (2)
Can be expressed as:
from fig. 5, the decided data can be represented as:
wherein
Represents the data obtained by decision after space diversity MMSE-RISIC-NP equalization,
the predicted data noise is derived from the noise prediction. Because the data noise is predicted and removed, the accuracy of the judgment result is improved; on the other hand, the data after being subjected to space diversity MMSE-RISIC equalization algorithm and data separation is used
Derived by making delta estimates
Closer to deltadCompared with the traditional MMSE-RISIC algorithm, the method reduces the extra interference caused by delta estimation.
It should be noted that the embodiments of the present invention can be realized by hardware, software, or a combination of software and hardware. The hardware portion may be implemented using dedicated logic; the software portions may be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or specially designed hardware. Those skilled in the art will appreciate that the apparatus and methods described above may be implemented using computer executable instructions and/or embodied in processor control code, such code being provided on a carrier medium such as a disk, CD-or DVD-ROM, programmable memory such as read only memory (firmware), or a data carrier such as an optical or electronic signal carrier, for example. The apparatus and its modules of the present invention may be implemented by hardware circuits such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of hardware circuits and software, e.g., firmware.
The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.
Claims (10)
1. A space diversity MMSE-RISIC-NP equalization method, characterized in that the space diversity MMSE-RISIC-NP equalization method comprises:
expanding the system to a multi-input multi-output-single carrier frequency domain equalization MIMO-SCFDE system on the basis of the SC-FDE system;
and step two, establishing a model of the space diversity MIMO-SCFDE system, and performing space diversity MMSE-RISIC balance and space diversity MMSE-RISIC-NP balance.
2. The space diversity MMSE-RISIC-NP equalization method of claim 1, wherein in said step two, the MIMO-SCFDE system model establishment specific process is:
combining the STBC with the SC-FDE, and adopting STBC coding with a block as a unit; the frame structure of STBC-SCFDE system has transmitting antenna number of 2 and receiving antenna number of nRThen, 2n is realizedRFull diversity gain of; using UW as GI, in order to satisfy orthogonality at receiving end, processing UW;
original data of a sending end is converted into a sending data block after mapping, interweaving and coding, the sending data block is inserted into UW after being coded by STBC, and enters a channel through a transmitting antenna; the STBC encoded transmission data block inserted into the UW may be expressed as follows:
the data in the data block at the ith time can be obtained by performing reverse order on the data part in the data block at the ith time and matching with operations such as conjugation, negation and the like, and the transmission data on the two antennas is represented as:
the received signals at the ith and i +1 th time on the jth receiving antenna after channel transmission are respectively represented as:
wherein
Respectively representing the channel matrixes from the mth transmitting antenna to the jth receiving antenna at the ith and the ith +1 time points,
and
is a mean of zero, where the element variance is
An additive white gaussian noise vector of (1);
the formula (15) is introduced into the formula (16), and for simplification, the symbol (·)(i)Omit and make the channel impulse response constant on two consecutive transmission data blocks
Equation (16) is then expressed as:
will be provided with
Multiplying by an NxN cyclic shift permutation matrix PKObtaining the replaced reception signal of the jth receiving antenna at the i +1 moment
And use property hj,mP＝Phj,mObtaining:
for Nx 1 vector r ═ r0 r1…rN-1]TIn the case of a non-woven fabric,
to pair
Performing FFT to obtain:
wherein, F is an N × N dimensional FFT matrix:
in the second equation of the equation (19),
and
so that the STBC coding loses the orthogonality, the UW block processing is required:
wherein
Indicating the second after processing of UW blockThe frequency domain received signal at time i +1 on the j receive antennas,
in the second term of equation (21), the interference caused by transmitting the UW block is removed and the time reversal UW is reconstructed in the third term; equation (21) is processed as follows:
combining (19) and (22) to obtain:
in the formula RjRepresenting the frequency-domain received signal at the jth receiving antenna, X1Representing the frequency-domain transmission signal on the first transmit antenna, X2Representing the frequency-domain transmission signal on the second transmitting antenna, H(j)Representing the frequency domain channel matrix on the jth receive antenna, X representing the frequency domain transmit signal on two transmit antennas, NjRepresenting the frequency domain noise signal on the jth receiving antenna, RjMultiplying by H(j)HThe above formula decomposes to X1And X2；
Wherein the content of the first and second substances,
a frequency domain received signal transformed by the equation (24) on the jth receiving antenna at time i; 0N×NA zero matrix representing NxN;
then
Wherein Λ(j)Is an N multiplied by N diagonal matrix, and E {. cndot.) represents the mean value;
will be provided with
And
normalization is performed so that the noise term remains at variance of
Gaussian white noise of (24) is written as:
wherein the content of the first and second substances,
representing the normalized frequency domain received signal on the jth receiving antenna at time i,
representing the normalized frequency domain noise signal, Λ, on the jth receiving antenna at time i(j)＝(|H(j,1)|2+|H(j,2)|2)1/2Is an N × N diagonal matrix, and represents the frequency domain channel impulse response on the jth receiving antenna, and the (k, k) th item on the diagonal is equal to (| H)(j,1)(k,k)|2+|H(j,2)(k,k)|2)1/2K itself denotes the kth point of the frequency domain, thus H(j,1)K diagonal element of (2)(j,1)(k, k) and H(j,2)The k thDiagonal element H(j,2)(k, k) respectively represent frequency domain channel impulse responses of frequency domain kth points of a 1 st transmitting antenna, a 2 nd transmitting antenna to a jth receiving antenna,
INrepresenting an N-order identity matrix; equation (25) can be decomposed into two equations:
as can be seen from the formula (26)
And
the method does not interfere with each other, namely STBC decoding is finished, only simple linear processing is carried out during decoding, and then the transmitted signal can be estimated through frequency domain equalization
And
the two equations in equation (26) have the same form and have the same frequency domain channel impulse response Λ(j)Equal noise power
Therefore, when frequency domain equalization is performed on the receiving antenna, the equalization can be unified into:
Y(j)＝Λ(j)X(j)+V(j) (27)
in the formula Y(j)For receiving signals, X, in the frequency domain on the jth receiving antenna(j)For the estimated frequency domain transmission signal, V, on the jth receiving antenna(j)For the frequency domain on the jth receiving antennaA noise signal; in frequency domain equalization, n is sent in two timesRThe received STBC-SCFDE system is treated as a single-transmitting and multi-receiving system.
3. The space diversity MMSE-RISIC-NP equalization method of claim 2, wherein said method of spatial diversity MMSE-RISIC-NP equalization
Represents a data block of length N transmitted by the mth transmit antenna at time instant i,
respectively indicating transmission data at an nth (N-0, …, N-1) point in the transmission data block,
which represents the data part of the data block sent by the mth transmitting antenna at time i, having a length K,
wherein
Respectively representing the data of 0 th, … th and K-1 th points of the data part in the data block sent by the mth transmitting antenna at the time i;
the length of the UW part in the data block sent by the mth transmitting antenna at time i is G,
wherein u ism,0um,1…um,G-1When the m-th transmitting antenna respectively transmits data of UW part 0, … and G-1 points in the data block at the time i, N is K + G; g is larger than or equal to L to eliminate the interference between blocks, and L is the length of the channel impulse response.
4. Such asThe space diversity MMSE-RISIC-NP equalization method of claim 2, wherein for the m (1, 2) th transmit antenna,
0G×1、0K×1respectively representing G multiplied by 1 dimension and K multiplied by 1 dimension zero vectors; qKIs an NxN inverse cyclic shift permutation matrix, representing the conjugation, for an Nx1 vector
In the case of a non-woven fabric,
(·)Nrepresenting a modulo N operation.
5. The space diversity MMSE-RISIC-NP equalization method of claim 2, wherein said method of spatial diversity MMSE-RISIC-NP equalization
Representing the frequency domain received signal on the jth receive antenna at time i,
representing the frequency domain receiving signal on the jth receiving antenna at the time of i +1 after the replacement; h(j,m)＝Fhj,mFHIs an N × N diagonal matrix with the k (k ═ 0, 1.., N-1) diagonal elements having values of
hj,m(l) Denotes a channel impulse response at an L (L ═ 1., L-1) th path from an m-th transmitting antenna to a j-th receiving antenna,
representing the frequency domain received signal noise on the jth receive antenna at time instant i,
representing the frequency domain received signal noise on the jth receive antenna at time i +1 after the permutation,
6. the space diversity MMSE-RISIC-NP equalization method of claim 1, wherein in said step two, the space diversity MMSE-RISIC equalization specifically comprises the following processes:
STBC decoded received signal Y on jth receiving antenna(j),j＝1,2,…,nRMultiplying it by the MMSE equalization coefficient W on this antenna(j)Adding the equalized data of all receiving antennas to obtain a frequency domain receiving signal S after MMSE equalization, performing IFFT transformation to obtain a time domain receiving signal S after MMSE equalization, and subtracting a time domain residual intersymbol interference estimated value obtained in delta estimation from S
Delta is real time domain residual intersymbol interference data, and finally, a data estimation value is obtained through judgment
7. The space diversity MMSE-RISIC-NP equalization method of claim 6, wherein the MMSE equalized frequency domain received signal before IFFT can be expressed as:
wherein SkFor the data of the signal S at the k-th frequency point after MMSE equalization, S ═ S0,…,Sk,…,SN-1],S0,…,Sk,…,SN-1Respectively representing the data of the MMSE equalized signal S at 0, …, k, … and N-1 frequency points;
equalization coefficients at the k (k is 0,1, …, N-1) point of the MMSE equalizer on the jth receiving antenna in the frequency domain;
respectively representing frequency domain received signals at 0, …, k, … and N-1 frequency points of a j-th receiving antenna frequency domain; from formula (27):
wherein
Denotes the frequency domain channel impulse response, X, at the 0, …, k, …, N-1 frequency point of the jth receive antennakRepresenting the data of the estimated frequency domain transmission signal at the 0 th, … th, k, … th, N-1 th frequency point on the jth receiving antenna;
for the noise at the kth frequency point on the jth receive antenna, the variance is
Normalizing the power of the data signal to unit 1 for analysis, i.e.
The MMSE equalization coefficient expression can be derived from equation (12):
wherein
the following formula (29) and (30) can be substituted into formula (28) and simplified:
in the formula
Denotes noise data of frequency domain noise at k (k is 0, …, N-1) th frequency point after MMSE equalization, ΔkData representing frequency domain residual intersymbol interference at a k (k is 0, …, N-1) th frequency point after MMSE equalization;
let Delta be [ Delta ]0,…,Δk…,ΔN-1]T，V＝[V0,…,Vk,…,VN-1]T，X＝[X0,…,Xk,…,XN-1]If delta and V are respectively the frequency domain form of RISI and noise after MMSE equalization, X is the frequency domain emission signal vector; s ═ S0,…,Sk,…,SN-1]And S represents an MMSE equalized signal, the relationship between vectors corresponding to equation (32) can be expressed as:
S＝X+Δ+V (35)
the IFFT transformation of equation (35) yields:
s＝x+δ+v (36)
wherein s represents the time domain form of the data after MMSE equalization, δ represents the real time domain residual intersymbol interference data after MMSE equalization, and v represents the time domain form of the noise after MMSE equalization;
the MMSE-RISIC equalization algorithm first performs a delta estimation, which can be derived from equation (33):
in the formula
Represents the data of the estimated post-MMSE frequency-domain residual intersymbol interference at the k (k 0, …, N-1) th frequency point,
data representing the decided frequency domain transmission signal at a k (k-0, …, N-1) th frequency point; namely, the frequency domain form of the estimated residual intersymbol interference is obtained
Then to
IFFT (inverse fast Fourier transform) is carried out to obtain time domain residual intersymbol interference estimation value
Is removed in s
Order:
in the formula
MMSE equalized data representing the removed estimated residual intersymbol interference, and finally
Judging; since the RISI is estimated and removed;
from the formulae (36) (38):
due to the formula (37)
Data indicating that estimated post-MMSE frequency-domain residual intersymbol interference is at the k (k 0, …, N-1) th frequency point,
Indicating that the decided frequency domain transmission signal is at k (k 0, …)N-1) data at frequency points; the frequency domain form of the estimated residual intersymbol interference can be obtained
Then to
IFFT (inverse fast Fourier transform) is carried out to obtain time domain residual intersymbol interference estimation value
δ is the true time domain residual intersymbol interference data.
8. The space diversity MMSE-RISIC-NP equalization method of claim 1, wherein in said step two, the space diversity MMSE-RISIC-NP equalization specifically comprises the following steps:
noise prediction is added on the basis of MMSE-RISIC balance, the UW noise is used for predicting the noise of data and removing the noise before judgment by utilizing the correlation between the UW estimation noise and the data estimation noise, and the precision of delta estimation is also improved because the noise of the data before judgment is removed;
comparison (14) gives:
so that s can be separated into data vectors
And UW vector
An analog formula (36) of
And
is represented as follows:
where d, u denote the data and UW block, respectively, deltadData portion, δ, representing true time-domain residual intersymbol interference datauUW part, v, representing true time-domain residual intersymbol interference datadData portion, v, representing time domain noise after MMSE equalizationuA UW portion representing time domain noise after MMSE equalization;
in addition, the s can obtain a time domain estimation transmitting signal after the space diversity MMSE-RISIC equalization algorithm
One prime in the upper right corner represents the time domain estimated transmitted signal after the space diversity MMSE-RISIC-NP equalization method obtained finally
Distinguishing, estimating the time domain of the transmitted signal after the space diversity MMSE-RISIC equalization algorithm
After data separation, the data part of the transmitted signal is estimated in time domain after space diversity MMSE-RISIC equalization algorithm is obtained
After the UW block is inserted, FFT transformation is carried out, and then delta estimation is carried out to obtain a time domain residual intersymbol interference estimation value of space diversity MMSE-RISIC-NP balance
Spatial diversity MMSE-RISIC-NP equalized time domain residual intersymbol interference estimate since inserted UW block is accurate
May be represented by the following formula:
thus can be used for
Time domain residual intersymbol interference estimate data portion separated into space diversity MMSE-RISIC-NP equalization
Time domain residual intersymbol interference estimate UW portion delta equalized with spatial diversity MMSE-RISIC-NPu；
The noise prediction input vector may be represented as
From the formula (41)
Wherein, the noise prediction input vector is the noise v of UW partuSince u is known, v isuV can be accurately calculated by a receiverdAs data noise vectors, vdAnd vuLinear transformation from the same noise vector v, and thus correlation; can utilize vuTo predict vd；
By vuTo predict vdThe problem can be converted into a linear optimal filtering problem, the optimization performance is measured by a certain minimum cost function, the mean square value of the estimation error, namely a linear MMSE criterion, is selected as the cost function, the cost function is easy to carry out mathematical processing, and the cost function has a unique minimum value which can uniquely define statistical optimization design;
assuming the linear MMSE prediction matrix is B, then
From the wiener filtering principle, we can obtain:
wherein
Where V denotes the frequency domain form of the noise after MMSE equalization, FdIs the first K columns of the matrix F, FuThe last G column of the matrix F,
and
are respectively FdAnd FuThe conjugate transpose of (1); the vector relationship corresponding to the formula (34) can be expressed as
V(j)Representing the frequency domain form of the noise after MMSE equalization on the jth receiving antenna;
bringing equations (45) (46) (47) into equation (44) yields the expression for B:
v is thendPredicted value of (2)
Expressed as:
the decided data is expressed as:
wherein
Represents the data obtained by decision after space diversity MMSE-RISIC-NP equalization,
the predicted data noise is derived from the noise prediction.
9. A program storage medium for receiving a user input, the stored computer program causing an electronic device to execute the space diversity MMSE-RISIC-NP equalization method of any one of claims 1-8, comprising the steps of:
expanding the system to a multi-input multi-output-single carrier frequency domain equalization MIMO-SCFDE system on the basis of the SC-FDE system;
and step two, establishing a model of the space diversity MIMO-SCFDE system, and performing space diversity MMSE-RISIC balance and space diversity MMSE-RISIC-NP balance.
10. A computer device, characterized in that the computer device comprises a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the steps of the space diversity MMSE-RISIC-NP equalization method according to any one of claims 1 to 8.
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