CN106534008A - Power compensation MMSE equalization method for wireless multipath channel - Google Patents

Power compensation MMSE equalization method for wireless multipath channel Download PDF

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Publication number
CN106534008A
CN106534008A CN201611060075.4A CN201611060075A CN106534008A CN 106534008 A CN106534008 A CN 106534008A CN 201611060075 A CN201611060075 A CN 201611060075A CN 106534008 A CN106534008 A CN 106534008A
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frequency domain
data
wireless multi
path channels
filter coefficient
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CN106534008B (en
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王西玲
马允龙
杨勇
梁峰
朱广法
张青松
李钧
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Shaanxi Fenghuo Communication Group Co Ltd
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Shaanxi Fenghuo Communication Group Co Ltd
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00Baseband systems
    • H04L25/02Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202Channel estimation
    • H04L25/0204Channel estimation of multiple channels
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00Baseband systems
    • H04L25/02Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202Channel estimation
    • H04L25/024Channel estimation channel estimation algorithms
    • H04L25/0256Channel estimation using minimum mean square error criteria
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00Baseband systems
    • H04L25/02Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006Arrangements for removing intersymbol interference
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00Baseband systems
    • H04L25/02Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006Arrangements for removing intersymbol interference
    • H04L25/03159Arrangements for removing intersymbol interference operating in the frequency domain
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00Baseband systems
    • H04L25/02Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006Arrangements for removing intersymbol interference
    • H04L2025/03433Arrangements for removing intersymbol interference characterised by equaliser structure
    • H04L2025/03439Fixed structures
    • H04L2025/03522Frequency domain

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Cable Transmission Systems, Equalization Of Radio And Reduction Of Echo (AREA)

Abstract

The invention belongs to the wireless communication technology field and discloses a power compensation MMSE equalization method for a wireless multipath channel. The method comprises steps that A/D sampling for data after wireless multipath channel transmission is carried out to acquire the sampling data after reception; MMSE estimation for the wireless multipath channel is carried out to acquire a frequency domain filter coefficient of the wireless multipath channel, and a filter error power spectrum and a compensation direction of MMSE estimation are determined; the frequency domain filter coefficient of the wireless multipath channel is corrected to acquire a frequency domain filter coefficient after error compensation; frequency domain equalization for frequency domain sampling data is carried out according to the frequency domain filter coefficient after error compensation to acquire the data after frequency domain equalization; the actual reception data is acquired. The method is advantaged in that better performance and lower complexity are realized, and the method is easy for engineering realization.

Description

The power back-off MMSE equalization methods of wireless multi-path channels
Technical field
The invention belongs to wireless communication technology field, more particularly to a kind of power back-off MMSE of wireless multi-path channels (Minimum Mean Squared Error, least mean-square error) equalization methods.
Background technology
Traditional mode of operation can only be relied on the Situation Awareness energy of each combat unit itself due to limiting by communication capacity Power, commander's control ability, maneuverability, killing ability, survival ability and quantity are forming its fighting capacity, and network-centric warfare Advanced communication and network technology are then make use of, relies primarily on the cooperation between combat unit and collaboration to produce fighting capacity.Battlefield Situation is fast changing, and amount of communication data is huge, thus combat troop to traditional military communication radio station transfer rate, channel width, The aspects such as communication distance, mobile reception, constructing communication network and capacity of resisting disturbance propose requirements at the higher level.
But width has been had a strong impact on by the symbol crosstalk brought by the frequency selective fading that multipath causes in wireless channel Reliability with radio communication.Broadband high-speed data transmission is very sensitive to the time-varying of channel, and the increase of bandwidth can make sampling Interval this creates the terminal the frequency selective fading under multi-path environment less than the delay spread of channel.Meanwhile, radio communication sets High speed relative movement between standby can cause doppler shift effect, Doppler effect that transmission channel was quickly become with the time Change, so as to cause the time selective fading of channel.Therefore, WiMAX mobile communication system will be double because being subjected to channel time-frequency The impact of Selective intensity and cause intersymbol interference, intersymbol interference can make reception signal deteriorate, the bit error rate increase, systematic function drop It is low, system can be made under serious conditions to continue normal work.
The content of the invention
The present invention provides a kind of power back-off MMSE equalization methods of wireless multi-path channels, with better performance, lower Complexity and be easy to Project Realization.
To reach above-mentioned purpose, the present invention is adopted the following technical scheme that and is achieved.
A kind of power back-off MMSE equalization methods of wireless multi-path channels, methods described comprise the steps:
Step 1, obtains the intermediate frequency data for needing to send, and the intermediate frequency data is transmitted through wireless multi-path channels, to passing through Data after wireless multi-path channels transmission carry out A/D samplings, obtain the sampled data for receiving;
The wireless multi-path channels are carried out MMSE estimations using training sequence by step 2, obtain the wireless multi-path channels Frequency domain filter coefficient, according to the frequency domain filter coefficient of the wireless multi-path channels, determine that the wave filter that MMSE estimates is missed Difference power spectrum and compensation direction;
Step 3, according to the filter error power spectrum and compensation direction, the frequency domain filtering to the wireless multi-path channels Device coefficient is modified, and obtains the frequency domain filter coefficient after error compensation;
Step 4, carries out fast Fourier transform to the sampled data for receiving, and obtains frequency domain sample data, and root According to the frequency domain filter coefficient after the error compensation, frequency domain equalization is carried out to the frequency domain sample data, frequency domain equalization is obtained Data afterwards;
Data after the frequency domain equalization are carried out inverse Fourier transform, obtain time domain sampled data by step 5, so as to To actual receiving data.
The characteristics of technical solution of the present invention and further it is improved to:
(1) in step 1,
Obtain the intermediate frequency data { a for needing to sendk, the intermediate frequency data is transmitted through wireless multi-path channels, to process nothing Data after line multi-path channel transmission carry out A/D samplings, obtain the sampled data { r for receivingm};And:
Wherein, k=0,1 ..., (M1- 1), M1For the points after if sampling;M=0,1 ..., (M-1), M is adopted for A/D The points of sample, and M=M1;Shock responses of the h (i) for wireless multi-path channels, n (i) are additive noise, and T is the if sampling cycle.
(2) the frequency domain filter coefficient W in step 3 after error compensationlFor:
Wherein, l=0,1,2 ..., (M2- 1), M2For the number of frequency domain filter coefficient, and M2=M,For filter error power spectrum,For HlConjugation, SNR For signal to noise ratio, σ2For the variance of additive noise, h represents the shock response of wireless multi-path channels,Represent wireless multi-path channels The average of the radian value of shock response, Expression is askedValue of symbol,'s It is worth for -1 or 1, represents compensation direction.
(3), in step 5, obtain actual receiving data { zmBe:
Wherein, RlFor frequency domain sample data, WlFor the frequency domain filter coefficient after error compensation.
The present invention proposes a kind of power back-off MMSE equalization methods of wireless multi-path channels, carries out letter using training sequence Estimate, calculate the power error value and compensation direction of MMSE, equalizing coefficient is updated in road.Equilibrium side proposed by the present invention Method performance compared with existing equalization methods is more preferable, complexity is low, and be easy to Project Realization.
Description of the drawings
In order to be illustrated more clearly that the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing Accompanying drawing to be used needed for having technology description is briefly described, it should be apparent that, drawings in the following description are only this Some embodiments of invention, for those of ordinary skill in the art, on the premise of not paying creative work, can be with Other accompanying drawings are obtained according to these accompanying drawings.
Fig. 1 is that a kind of flow process of the power back-off MMSE equalization methods of wireless multi-path channels provided in an embodiment of the present invention is shown It is intended to;
Fig. 2 is the schematic block diagram of the equalization methods based on CPM modulated signals provided in an embodiment of the present invention;
Fig. 3 is the method to set up of Chu synchronizing sequences provided in an embodiment of the present invention;
Fig. 4 is that Chu synchronizing sequences provided in an embodiment of the present invention and CPM modulated signals carry out the Frame after data recombination Structural representation;
Fig. 5 is the simulation result schematic diagram one under SUI6 channels provided in an embodiment of the present invention;
Fig. 6 is the simulation result schematic diagram two under SUI6 channels provided in an embodiment of the present invention;
Fig. 7 is the simulation result schematic diagram three under SUI6 channels provided in an embodiment of the present invention;
Fig. 8 is error code of the power back-off MMSE equalization methods provided in an embodiment of the present invention under different Doppler frequency shifts Can schematic diagram.
Specific embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete Site preparation is described, it is clear that described embodiment is only a part of embodiment of the invention, rather than the embodiment of whole.It is based on Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under the premise of creative work is not made Embodiment, belongs to the scope of protection of the invention.
Two kinds of mode of operations, i.e. training mode and tracking mould are generally comprised based on the adaptive equalizer of pilot training sequence Formula.In training mode, traditional method be transmitting terminal launch one known to, the pilot training sequence of fixed length, so as to receiving terminal Equalizer passes through the reception signal for having distorted and known transmission signal calculates channel estimation value, is adjusted according to channel estimation value The coefficient of equalization filter is implemented around the compensation to channel distortions to optimum.Typical pilot training sequence is one two and enters Pseudo-random sequence processed or a string preassigned data bit, what is transmitted after pilot training sequence is number of users According to.When pilot training sequence is designed, it is desirable to which, even if accomplishing under worst channel condition, equalizer can also pass through this sequence Obtain correct filter coefficient.So ensure that the filter coefficient of equalizer connects after pilot training sequence is received Nearly optimum.From adjusting parameter to convergence is formed, the time span of whole process is equalizer algorithm, structure and channel to equalizer The function of rate of change.In order to guarantee to effectively eliminate intersymbol interference, equalizer needs periodically to train.Tracing mode is Real user data is received, starts the transmission of the useful information of communicating pair, this method is referred to as skilled self adaptation It is balanced.However, being particularly in wireless mobile communications in actual applications, the change of the characteristic of channel is often very violent, in order to Enable equalizer the change of the characteristic of channel be tracked always so as to effectively eliminate intersymbol interference, have to every one in transmitting terminal The section time just periodically sends training sequence.
Considered based on each side such as the performance requirement of communication system, the characteristic of channel, implementation complexity combined factors, in reality Using in, adaptive equalizer is typically from ZF (Zero-Forcing, ZF) equalization algorithm and the MMSE equalization algorithms for simplifying.
In existing technical scheme, when the frequency decline relatively flat time of channel, ZF equilibriums and MMSE portfolio effects It is more or less the same.But, when channel has the deep fade limit on frequency domain, ZF equilibriums amplify can noise, and MMSE equilibriums will not Interchannel noise is made excessively to be amplified, performance is better than zero forcing equalization.However, after MMSE is balanced, can there is part residual intersymbol interference, If the intersymbol interference of residual is eliminated, the bit error rate can be further reduced, improve performance.MMSE-RISIC(Residual ISI Cancellation) algorithm utilizes feedback op, and the intersymbol interference of residual can be effectively removed, increase is disadvantageous in that Computational complexity.
A kind of power back-off MMSE equalization methods of wireless multi-path channels are embodiments provided, as shown in figure 1, institute The method of stating comprises the steps:
Step 1, obtains the intermediate frequency data for needing to send, and the intermediate frequency data is transmitted through wireless multi-path channels, to passing through Data after wireless multi-path channels transmission carry out A/D samplings, obtain the sampled data for receiving.
In step 1, the intermediate frequency data { a for needing to send is obtainedk, the intermediate frequency data is transmitted through wireless multi-path channels, A/D samplings are carried out to the data after wireless multi-path channels are transmitted, the sampled data { r for receiving is obtainedm};And:
Wherein, k=0,1 ..., (M1- 1), M1For the points after if sampling;M=0,1 ..., (M-1), M is adopted for A/D The points of sample, and M=M1;Shock responses of the h () for wireless multi-path channels, n () are additive noise, and T is if sampling week Phase.
The wireless multi-path channels are carried out MMSE estimations using training sequence by step 2, obtain the wireless multi-path channels Frequency domain filter coefficient, according to the frequency domain filter coefficient of the wireless multi-path channels, determine that the wave filter that MMSE estimates is missed Difference power spectrum and compensation direction.
Step 3, according to the filter error power spectrum and compensation direction, the frequency domain filtering to the wireless multi-path channels Device coefficient is modified, and obtains the frequency domain filter coefficient after error compensation.
Frequency domain filter coefficient W in step 3 after error compensationlFor:
Wherein, l=0,1,2 ..., (M2- 1), M2For the number of frequency domain filter coefficient, and M2=M, For filter error power spectrum, For HlConjugation, SNR is signal to noise ratio, σ2For additivity The variance of noise, h represent the shock response of wireless multi-path channels,Represent the radian value of the shock response of wireless multi-path channels Average,Expression is askedValue of symbol,Value be -1 or 1, represent Compensation direction.
Step 4, carries out fast Fourier transform to the sampled data for receiving, and obtains frequency domain sample data, and root According to the frequency domain filter coefficient after the error compensation, frequency domain equalization is carried out to the frequency domain sample data, frequency domain equalization is obtained Data afterwards.
Data after the frequency domain equalization are carried out inverse Fourier transform, obtain time domain sampled data by step 5, so as to To actual receiving data.
In step 5, actual receiving data { z is obtainedmBe:
Wherein, RlFor frequency domain sample data, WlFor the frequency domain filter coefficient after error compensation.
Exemplary, technical solution of the present invention is illustrated below by way of instantiation emulation.
Original based on the equalization methods of Continuous Phase Modulation CPM (Continue Phase Modulation) signal modulation Reason block diagram is as shown in Fig. 2 Chu sequences are mainly used in the estimation of estimation, equilibrium, frequency deviation and the skew of wireless multi-path channels.
First, the Chu sequences in the present embodiment are illustrated:
Chu sequences belong to CAZAC (Constant Amplitude Zero Auto-Correlation) sequence, that is, possess Permanent width, the nonbinary sequence of complex numbers of the good characteristic of zero auto-correlation.CAZAC sequences have relevant peaks sharp, and secondary lobe is Zero the characteristics of.CAZAC sequences are usually used in the synchronized algorithm in communication system.CAZAC sequences have the property that:
Permanent envelope trait:The CAZAC sequence constant amplitudes of random length.
Preferable cycle autocorrelation performance:Arbitrarily behind CAZAC sequential shift n positions, n is not the whole of the cycle of CAZAC sequences During several times, the sequence after displacement is uncorrelated to former sequence.
Good cross correlation:Cross-correlation and partial correlation values are close to 0.
Low peak average ratio characteristic:The signal that arbitrarily CAZAC sequences are constituted, its peak value are very low with the ratio of its average.
CAZAC sequences are remained after Fourier transformation:Arbitrarily CAZAC sequences are remained after the positive anti-change of Fourier CAZAC sequences.The Chu synchronizing sequences adopted by the embodiment of the present invention for:
The set-up mode of Chu synchronizing sequences is as shown in figure 3, the set-up mode of Chu synchronizing sequences is to utilize this herein Two training sequences carry out channel estimation, it is ensured that do not receive other information signal before and after receiving the two sequences in signal The impact of multipath extension.Transmitting terminal and receiving terminal are to work independently, so transmiting data to the reception end up to receiving terminal It is not aware that, receiving terminal will obtain transmiting data to the moment up to receiving terminal by processing.
Such that it is able to utilize two training symbols before every frame to obtain time synchronization information.Carrying out time synchronized estimation When can be obtained by the time domain estimated value of channel, the frequency domain value of channel estimation is just obtained after carrying out FFT.Using channel Data after elapsed time and carrier wave frequency deviation correction are carried out channel equalization to offset channel to letter by the frequency domain value of estimation in frequency domain Number impact.
Further, as shown in figure 4, for Chu sequences and CPM modulated signals carry out the data frame structure after data recombination with And the simulation parameter of the present embodiment, each Frame is changing by two Chu synchronizing symbols, two data symbols and 200us Frequency protection composition, and Chu synchronizing symbols and data symbol have the Cyclic Prefix of 22.22us, for anti-multipath time delay.
Obtain the intermediate frequency data { a for needing to sendk, the intermediate frequency data is transmitted through wireless multi-path channels, to process nothing Data after line multi-path channel transmission carry out A/D samplings, obtain the sampled data { r for receivingm};And:
Wherein, k=0,1 ..., (M1- 1), M1For the points after if sampling;M=0,1 ..., (M-1), M is adopted for A/D The points of sample, and M=M1;Shock responses of the h () for wireless multi-path channels, n () are additive noise, and T is if sampling week Phase.
Due to there is Cyclic Prefix, it can be assumed that { akWith periodically, for any integer L, there is ak=ak±LM, while For shock response also has h (mT)=h ((m ± LM) T).In discrete domain, formula (2) is represented by:
Rl=Hl4l+Vl, l=0,1,2 ..., (M-1) (3)
In formula (3):
After frequency domain equalization, the output signal of time domain is:
WhereinThat is RlIt is to receive signal { rmFFT.
According to zero forcing equalization, then the coefficient of wave filter can be obtained by following formula:
According to least mean-square error (MMSE) criterion, then the coefficient of wave filter can be obtained by following formula
According to traditional MMSE algorithms, then existError power is composed, therefore MMSE can be calculated Method does an improvement, and the filter coefficient after improvement is:
Expression is askedValue of symbol,Value be -1 or 1, determined with it MMSE algorithms miss The direction of difference power spectrum compensation.
All emulation of the embodiment of the present invention are all based on the data frame structure shown in Fig. 4, emulation channel model used It is based primarily upon multi-path Fading Channel+Gaussian noise.Multi-path Fading Channel model is SUI 6 (Strong hilly): Tau=[0 14,000 20000] * 1e-9, pdb=[0-10-14].Wherein tao is that path delay is vectorial, and pdb declines for amplitude Subtract vector, following simulation result is all based on the various equalization algorithms emulation of sui6 channels.
Fig. 5 is the simulation result (frequency deviation 150Hz) under SUI6 channels, and Fig. 6 is the simulation result (frequency deviation under SUI6 channels 100Hz), Fig. 7 is the simulation result (frequency deviation 50Hz) under SUI6 channels;Can be seen that in the bit error rate from Fig. 5, Fig. 6 and Fig. 7 and be 10-2During rank, zero forcing equalization, MMSE equalization algorithms and the present invention's is all had necessarily based on the MMSE equalization algorithms of power back-off Anti-multipath and Doppler frequency shift function, MMSE algorithms probably have the error code gain of 3dB compared with zero forcing equalization performance, this Bright improved power error compensates the error code gain for having 8dB more general than zero forcing equalization of MMSE equalization algorithms, it can be seen that right MMSE equalization algorithms carry out effective power error compensation, can be good at resisting the multipath fading and Doppler frequency shift of channel.
Power error compensation error code of the MMSE equalization algorithms under different Doppler frequency shifts that Fig. 8 is provided for the present invention Can, can see that from the simulation result of Fig. 8 improved for CPM signals MMSE equalization algorithms maximum can resist that 100Hz's is more General Le frequency displacement.
Above-described embodiment is in existing least mean-square error (Minimum Mean Squared Error, MMSE) equilibrium skill A kind of power spectrum based on Continuous Phase Modulation (Continue Phase Modulation, CMP) signal is proposed on the basis of art The new single carrier frequency domain equalization algorithm of compensation, on the basis of MMSE equalization algorithms, estimates channel, root using known training sequence MMSE power error values, and the direction of error amount are determined according to channel estimation value, update coefficient of equalizing wave filter, eliminate residual intersymbol Interference;Can effectively remove remaining intersymbol interference, improve demodulation performance, and have that simple, computation complexity is low, be easy to engineering reality Existing the advantages of.
The above, the only specific embodiment of the present invention, but protection scope of the present invention is not limited thereto, any Those familiar with the art the invention discloses technical scope in, change or replacement can be readily occurred in, should all be contained Cover within protection scope of the present invention.Therefore, protection scope of the present invention should be defined by the scope of the claims.

Claims (4)

1. power back-off MMSE equalization methods of a kind of wireless multi-path channels, it is characterised in that methods described comprises the steps:
Step 1, obtains the intermediate frequency data for needing to send, and the intermediate frequency data is transmitted through wireless multi-path channels, wireless to process Data after multi-path channel transmission carry out A/D samplings, obtain the sampled data for receiving;
The wireless multi-path channels are carried out MMSE estimations using training sequence by step 2, obtain the frequency of the wireless multi-path channels Domain filter coefficient, according to the frequency domain filter coefficient of the wireless multi-path channels, determines the filter error work(that MMSE estimates Rate is composed and compensation direction;
Step 3, according to the filter error power spectrum and compensation direction, the frequency domain filter system to the wireless multi-path channels Number is modified, and obtains the frequency domain filter coefficient after error compensation;
Step 4, carries out fast Fourier transform to the sampled data for receiving, and obtains frequency domain sample data, and according to institute The frequency domain filter coefficient after error compensation is stated, frequency domain equalization is carried out to the frequency domain sample data, after obtaining frequency domain equalization Data;
Data after the frequency domain equalization are carried out inverse Fourier transform, obtain time domain sampled data by step 5, so as to obtain reality The receiving data on border.
2. a kind of power back-off MMSE equalization methods of wireless multi-path channels according to claim 1, it is characterised in that step In rapid 1,
Obtain the intermediate frequency data { a for needing to sendk, the intermediate frequency data is transmitted through wireless multi-path channels, to through wireless multi-path Data after transmission carry out A/D samplings, obtain the sampled data { r for receivingm};And:
r m = Σ k = 0 M 1 - 1 a k h ( m T - k T ) + n ( m T )
Wherein, k=0,1 ..., (M1- 1), M1For the points after if sampling;M=0,1 ..., (M-1), M is A/D samplings Points, and M=M1;Shock responses of the h () for wireless multi-path channels, n () are additive noise, and T is the if sampling cycle.
3. a kind of power back-off MMSE equalization methods of wireless multi-path channels according to claim 2, it is characterised in that step Frequency domain filter coefficient W in rapid 3 after error compensationlFor:
W l = H l * | H l | 2 + 1 / S N R - s i g n ( ∠ h ‾ ) * σ 2 | H l | 2 + 1 / S N R , l = 0 , 1 , 2 , ... , M 2 - 1
Wherein, l=0,1,2 ..., (M2- 1), M2For the number of frequency domain filter coefficient, and M2=M,For filter Ripple device error power is composed, For HlConjugation, SNR is signal to noise ratio, σ2For additive noise Variance, h represents the shock response of wireless multi-path channels,Represent wireless multi-path channels shock response radian value it is equal Value, Expression is askedValue of symbol,Value be -1 or 1, represent compensation Direction.
4. a kind of power back-off MMSE equalization methods of wireless multi-path channels according to claim 3, it is characterised in that step In rapid 5, actual receiving data { z is obtainedmBe:
z m = 1 M Σ l = 0 M - 1 W l R l exp ( - j 2 π m l M )
Wherein, RlFor frequency domain sample data, WlFor the frequency domain filter coefficient after error compensation.
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CN111239705A (en) * 2020-02-12 2020-06-05 北京未感科技有限公司 Signal processing method, device and equipment of laser radar and storage medium
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CN108600126A (en) * 2018-01-18 2018-09-28 北京大学 A kind of dual user down space division multiple access technology
CN110213184A (en) * 2019-06-03 2019-09-06 北京理工大学 A kind of adaptive channel blind equalization method based on amendment cost function
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CN111726306A (en) * 2020-05-11 2020-09-29 北京大学 Full duplex system phase noise suppression method based on two-stage adaptive filtering
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