CN107222438A - The simplification BEM channel estimation methods of high-speed mobile SC FDMA systems - Google Patents
The simplification BEM channel estimation methods of high-speed mobile SC FDMA systems Download PDFInfo
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Abstract
The invention belongs to wireless communication technology field, disclose a kind of simplification BEM channel estimation methods of high-speed mobile SC FDMA systems, by estimate base system number required for matrix calculated in advance and store, estimate base system number；Using the characteristic of channel and the transformation relation of time-domain and frequency-domain, the relationship of base system number and domain channel response matrix is derived, the domain channel response for receiving signal is estimated.The present invention determines the number of optimal basic function, to improve estimated accuracy from the minimum complex exponential basis expansion model of model error；By for estimating the frequency domain matrix calculated in advance of base system number and storing, computation complexity is reduced；Using the time-frequency domain characteristic of channel, the relationship of base system number and domain channel response matrix is derived, it is to avoid computation complexity higher channel time-frequency domain transfer process, be easy to receiver docking to collect mail and number carry out a frequency domain equalization processing.
Description
Technical field
The invention belongs to wireless communication technology field, more particularly to a kind of simplified BEM channel estimation methods, it is adaptable at a high speed
Single carrier frequency division multiplexing multiple access SC-FDMA systems under mobile.
Background technology
In broadband wireless communications, when two terminals of communication are moved with faster relative velocity, Doppler is generated
Effect, wireless channel forms varying Channels.Inter-sub-carrier interference ICI and multipath effect are brought caused by varying Channels
Intersymbol interference ISI can cause the rapid deterioration of SC-FDMA systematic functions.So, signal is solved in the receiving terminal of signal
Reconcile before decoding, it is very necessary to carry out dynamic estimation to channel.Existing channel estimation methods are to be based on pilot tone mostly
Auxiliary, pilot frequency information periodically known to insertion, is the letter that first estimation obtains in pilot frequency locations in the data of transmission
Road is responded, and the channel response on Data Position is then obtained using certain processing method.Qingchuan Zhang et al. are in text
Chapter " An Enhanced DFT-Based Channel Estimator for LTE-A Uplink " (IEEE
Transactions on Vehicular Technology 2013) in propose it is a kind of based on discrete Fourier transform DFT's
Channel estimation methods, estimate the channel estimation value of pilot frequency locations first, and the channel estimation values of data symbol positions passes through linear
Interpolation is obtained.The weak point of this method is：In a mobile environment, channel time of origin Selective intensity, linear interpolation side
The estimated accuracy of method drastically declines, it is impossible to ensure the reliable communication of SC-FDMA systems.Method pin based on basis expansion model BEM
Model is set up to varying Channels, using a few parameters with regard to a non-linear fast-changing channel can be stated.Yang Lihua
Et al. in article " Fast Time-Varying Channel Estimation Technique for LTE Uplink in
Proposed in HST Environment " (IEEE Transactions on Vehicular Technology 2012) multinomial
Formula basis expansion model P-BEM improves the estimated accuracy of varying Channels, but the calculation with the method that autoregression model AR is combined
Method is related to various big matrix operation, causes computation complexity high, is not easy to realize, and in a mobile environment, P-BEM models are missed
Error of the difference than complex exponential basis expansion model CE-BEM is big, the precision of influence varying Channels estimation.
In summary, the problem of prior art is present be：It is relatively low to there is estimated accuracy in existing channel estimation methods, calculates
Complexity is high, is not easy to realize.
The content of the invention
The problem of existing for prior art, the invention provides a kind of simplification BEM of high-speed mobile SC-FDMA systems letters
Channel estimation method.
The present invention is achieved in that a kind of simplification BEM channel estimation methods of high-speed mobile SC-FDMA systems, described
The simplification BEM channel estimation methods of high-speed mobile SC-FDMA systems are by the matrix calculated in advance required for estimating base system number and deposit
Storage, estimates base system number；Using the characteristic of channel and the transformation relation of time-frequency domain, base system number and domain channel response are derived
The relationship of matrix, estimates the domain channel response for receiving signal.
Further, the simplification BEM channel estimation methods of the high-speed mobile SC-FDMA systems comprise the following steps：
Step one, conversion domain matrix is obtainedBase station is by local frequency pilot signTransform domain is transformed into, transform domain is obtained
Matrix
Wherein, domain matrix is convertedDimension be N (Q+1) × L (Q+1),Diag () be by
Amount is converted into the computing of diagonal matrix, psIt is the sequence number of local frequency pilot sign, two local frequency pilot sign s=1,2, its serial number
p1=4, p2=11, Q are the number of optimal basic function, IQ+1The unit matrix tieed up for Q+1；For row product code in Crow；FLFor N
The preceding L row of point quick Fourier conversion FFT matrix Fs：
Wherein, WN=e-j2π/N, L is the separable footpath number of varying Channels；
Step 2, based on complex exponential basis expansion model, base station end generation basic function matrix and basic function frequency domain matrix；
Step 3, base station end obtains the frequency domain matrix for estimating base system number, willWithIt is multiplied, obtains base station end use
In the matrix of estimation base system number：Its dimension is N × L (Q+1)；
Step 4, base station carries out Fast Fourier Transform (FFT) to time-domain received signal y and obtains frequency-region signal Y, from frequency-region signal Y
Middle extraction Block-type pilot symbol
Step 5, base station is according to the block frequency pilot sign of receptionAnd matrixEstimate base system number vector；
Step 6, the channel estimation in frequency domain of each single carrier frequency division multiplexed symbols is directly obtained using the base system number estimated
Response.
Further, the step 2 is specifically included：
(1) complex exponential CE basic function numbers Q is determined：
Base station is according to the translational speed v of user, the carrier frequency f of system and a duration T for sending signals=
1ms, obtains basic function number：Wherein, c is the light velocity,It is the computing that rounds up；
(2) basic function matrix is generated
Wherein,It is basic function matrixElement, its utilize complex exponential basis expansion model, given birth to according to below equation
Into：
Wherein, q=0,1 ..., Q, Q are the numbers of basic function, n=0,1 ..., N, and N=256 is that a single carrier frequency division is answered
With the points of the subcarrier number, i.e. Fast Fourier Transform (FFT) of symbol, ns=1,2 ..., NsymbIt is single carrier frequency division multiplexed symbols
Sequence number, Nsymb=14 be the number of single carrier frequency division multiplexed symbols in a transmission block, psIt is the index of local frequency pilot sign
Number, two local frequency pilot sign s=1,2, its call number are p1=4, p2=11；
(3) frequency domain matrix is generatedWith
Wherein,It is q-th of frequency domain matrix, q=0,1 ..., Q, Q is the number of basic function,It is pilot tone
Basic function matrix at symbol, psIt is the sequence number of frequency pilot sign, two local frequency pilot sign s=1,2, its call number are p1=4,
p2=11,It is matrixPreceding L row, F is N point quick Fourier transformation matrixs, ()HIt is the conjugate transposition behaviour of matrix
Make.
Further, the step 4 is specifically included：
(1) Fast Fourier Transform (FFT) is carried out to time-domain received signal y, obtains frequency-domain received signal Y：
Y=Fy；
Wherein, F is N point quick Fourier transformation matrixs；
(2) Block-type pilot symbol is extracted from frequency-domain received signal YThere are 14 single carrier frequency divisions in one transmission block
Multiplexed symbols, wherein the 4th and the 11st is Block-type pilot sign of lambda=1,2, p1=4, p2=11, i.e. frequency-domain received signal Y's
Form is the matrix that a N × 14 are tieed up, and the 4th row and the 11st row of matrix are Block-type pilot symbols, pλWith psIt is equal.
Further, the step 5 is specifically included：
(1) Block-type pilot symbol is set upWith the relation of local frequency pilot signRelational expression be：
Wherein, F is N point quick Fourier transformation matrixs, ()HIt is the conjugate transposition operation of matrix, W is in transmitting procedure
The additive white Gaussian noise being subject to,It is pthλThe time domain channel shock response matrix of individual frequency pilot sign；
(2) time domain channel shock response matrix is represented using basis expansion model
Wherein,It is the basic function matrix of generation, GqIt is q-th of base system matrix number, it is Top's profit that dimension is N × N
Hereby circular matrix：
Wherein, L is the separable footpath number of varying Channels；
(3) relational expression for substituting into basis expansion model expression formula in step (1), is obtained：
Due to GqIt is Teoplitz circular matrix, so making gq=[gq,0,...,gq,l,...,gq,L-1]T, FGqFH=FLgq,
Wherein, FLIt is Fourier transform matrix F preceding L row, above formula can be reduced to：
Wherein,It is frequency domain matrix,g
It is the column vector that dimension is L (Q+1) × 1,It is conversion domain matrix, so far, establishes Block-type pilot symbol
NumberWith matrixAnd the relation between the base system number vector g to be estimated：
(4) two Block-type pilot symbols are utilizedAnd matrixBase system number is gone out using existing Least Square Method
Vector：
Wherein,It is group inverse matrices computing；Base system number vector is represented, it is the column vector of L (Q+1) × 1 dimensions, is had
14 single carrier frequency division multiplexed symbols, wherein the 4th and the 11st is Block-type pilot symbol, i.e. s=λ=1,2, p1=4, p2=
11,It is to receive the 4th column element in signal Y,It is to receive the 11st column element in signal Y, matrixBy matrixExtension is obtained, for the system of fixed Block-type pilot, matrixIt is constant, it is possible to will
Calculated in advance is simultaneously stored.
Further, the step 6 is specifically included：
(1) frequency domain channel matrix of each single carrier frequency division multiplexed symbolsWith time domain channel matrixRelational expression be：
The diagonal element of frequency domain channel matrix is estimated, i.e.,：
Wherein,It is n-thsThe domain channel response matrix of individual single carrier frequency division multiplexed symbols, F is N point quick Fouriers
Transformation matrix, ()HIt is the conjugate transposition operation of matrix,It is n-thsThe time domain channel response of individual single carrier frequency division multiplexed symbols
Matrix；
(2) relational expression of base system number and domain channel response matrix is set up：
By basis expansion model expression formulaIt is updated toIn, obtain：
Due to GqIt is Teoplitz circular matrix, GqFirst is classified as [gq,0,gq,1,…,gq,L-1,0,…,0]T, so making gq
=[gq,0,…,gq,l,…,gq,L-1]T, FGqFH=FLgq, wherein, FLIt is N point Fourier transform matrix F preceding L row, above formula can letter
Turn to：
Wherein,It is the basic function matrix according to generation,It is matrixPreceding L row, Q be basic function
Number, nsIt is the sequence number of single carrier frequency division multiplexed symbols；
(3) the domain channel response matrix of each single carrier frequency division multiplexed symbols is obtained, the base system number estimated is utilized
According to the relationship of the base system number and domain channel response matrix of foundation, n-th is obtainedsIndividual single carrier frequency division multiplexed symbols
Domain channel response matrix：
Wherein,It is the frequency domain matrix of generation.
Another object of the present invention is to provide a kind of simplification BEM channels suitable for high-speed mobile SC-FDMA systems to estimate
Meter method.
Advantages of the present invention and good effect are：From the complex exponential basis expansion model that model error is minimum, determine optimal
Basic function number, to improve estimated accuracy；By for estimating the frequency domain matrix calculated in advance of base system number and storing, drop
Low computation complexity；Using the time-frequency domain characteristic of channel, the mathematical relationship of base system number and domain channel response matrix is derived
Formula, it is to avoid computation complexity higher channel time-frequency domain transfer process, is easy to receiver docking to collect mail and number carries out a frequency domain equalization
Processing.It will be appreciated from fig. 6 that method that multinomial model is combined with autoregression model and based on discrete Fourier transform DFT with it is linear
The method that interpolation is combined is when user velocity is 450km/h, and BLER curves are almost without downward trend, and Block Error Rate is all higher than 10-1,
The BLER curves of the present invention can drop to 10-2Hereinafter, have greatly improved；Contrast complex exponential basis expansion model method, the present invention
BLER curves and complex exponential basis expansion model method almost maintain an equal level, without performance loss.As shown in Table 1, the inventive method institute
The computation complexity magnitude needed is 1, and the computation complexity magnitude needed for complex exponential basis expansion model method is 3, and the present invention will
Two magnitudes have dropped in computation complexity.
Brief description of the drawings
Fig. 1 is the simplification BEM channel estimation methods flows of high-speed mobile SC-FDMA systems provided in an embodiment of the present invention
Figure.
Fig. 2 is the realization of the simplification BEM channel estimation methods of high-speed mobile SC-FDMA systems provided in an embodiment of the present invention
Flow chart.
Fig. 3 is the system block diagram provided in an embodiment of the present invention used.
Fig. 4 is the pilot configuration figure provided in an embodiment of the present invention used.
Fig. 5 is the multipath fast time variant of the present invention provided in an embodiment of the present invention and existing channel estimation technique in 330km/h
Performance comparision curve map in channel.
Fig. 6 is the multipath fast time variant of the present invention provided in an embodiment of the present invention and existing channel estimation technique in 450km/h
Performance comparision curve map in channel.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
The application principle of the present invention is explained in detail below in conjunction with the accompanying drawings.
As shown in figure 1, the simplification BEM channel estimation methods of high-speed mobile SC-FDMA systems provided in an embodiment of the present invention
Comprise the following steps：
S101：Matrix of the frequency pilot sign in transform domain is calculated by local frequency pilot sign；
S102：Based on complex exponential basis expansion model, the frequency domain matrix of basic function matrix and basic function is obtained；
S103：The docking collection of letters number carries out a FFT, obtains frequency-domain received signal, is proposed from the reception signal
Block-type pilot symbol；
S104：Go out base system number using the frequency pilot sign of reception and the matrix of transform domain and frequency domain Matrix Estimation；
S105：According to the base system number and the relational expression of domain channel response derived, frequency is gone out using base system number direct estimation
Domain channel response.
The application principle of the present invention is further described below in conjunction with the accompanying drawings.
As shown in figure 3, the communication system that the present invention is used is made up of base station, wireless varying Channels and user；Wherein use
The translational speed at family is v, and the bit stream that user sends is by constellation modulation, subcarrier maps, Fourier transformation and adds before circulation
Sent after a series of processing such as sewing by a transmission antenna, send signal and arrived after varying Channels and noise jamming
Up to base station, base station end two reception antennas of configuration dock the collection of letters number and synchronize, remove cyclic prefix and parallel-serial conversion etc. respectively
After processing, base station carries out channel estimation using local frequency pilot sign and complex exponential basis expansion model to the signal of reception, estimates
Domain channel response matrix, so that base station carries out the processing such as ensuing frequency domain equalization, solution constellation modulation, completes whole system
Communication.
As shown in Fig. 2 mobile SC-FDMA low complex degrees BEM channel estimation methods provided in an embodiment of the present invention include with
Lower step：
Step 1：Obtain conversion domain matrix
Base station is by local frequency pilot signTransform domain is transformed into, obtains converting domain matrix
Wherein, domain matrix is convertedDimension be N (Q+1) × L (Q+1),Diag () be by
Amount is converted into the computing of diagonal matrix, psBe have in the sequence number of local frequency pilot sign, this example two local frequency pilot sign s=1,
2, its serial number p1=4, p2=11, Q are the number of optimal basic function, IQ+1The unit matrix tieed up for Q+1；To arrange product in Crow
Symbol；FLThe preceding L row of FFT matrix Fs are converted for N point quick Fouriers：
Wherein, WN=e-j2π/N, L is the separable footpath number of varying Channels.
Step 2：Based on complex exponential basis expansion model, base station end generation basic function matrix and basic function frequency domain matrix.
(2.1) complex exponential CE basic function numbers Q is determined：
Base station is according to the translational speed v of user, the carrier frequency f of system and a duration T for sending signals=
1ms, obtains basic function number：Wherein, c is the light velocity,It is the computing that rounds up；
(2.2) basic function matrix is generated
Wherein,It is basic function matrixElement, its utilize complex exponential basis expansion model, given birth to according to below equation
Into：
Wherein, q=0,1 ..., Q, Q are the numbers of basic function, n=0,1 ..., N, and N=256 is that a single carrier frequency division is answered
With the points of the subcarrier number, i.e. Fast Fourier Transform (FFT) of symbol, ns=1,2 ..., NsymbIt is single carrier frequency division multiplexed symbols
Sequence number, Nsymb=14 be the number of single carrier frequency division multiplexed symbols in a transmission block, psIt is the index of local frequency pilot sign
Number, there are two local frequency pilot sign s=1,2 in this example, its call number is p1=4, p2=11；
(2.3) frequency domain matrix is generatedWith
Wherein,It is q-th of frequency domain matrix, q=0,1 ..., Q, Q is the number of basic function,It is to lead
Basic function matrix at frequency symbol, psIt is to have two local frequency pilot sign s=1,2, its rope in the sequence number of frequency pilot sign, this example
Quotation marks are p1=4, p2=11,It is matrixPreceding L row, F is N point quick Fourier transformation matrixs, ()HIt is matrix
Conjugate transposition operation.
Step 3：Base station end obtains the frequency domain matrix for estimating base system number.
Step (2.3) is obtainedObtained with step (1)It is multiplied, obtaining base station end is used to estimate base system number
Matrix：Its dimension is N × L (Q+1).
Step 4：Base station carries out Fast Fourier Transform (FFT) to time-domain received signal y and obtains frequency-region signal Y, from frequency-region signal Y
Middle extraction Block-type pilot symbol
(4.1) Fast Fourier Transform (FFT) is carried out to time-domain received signal y, obtains frequency-domain received signal Y：
Y=Fy；
Wherein, F is N point quick Fourier transformation matrixs；
(4.2) Block-type pilot symbol is extracted from frequency-domain received signal YPilot configuration such as accompanying drawing 3, a transmission block
In have 14 single carrier frequency division multiplexed symbols, wherein the 4th and the 11st is Block-type pilot sign of lambda=1,2, p1=4, p2=11,
That is the form of frequency-domain received signal Y is the matrix that a N × 14 are tieed up, and the 4th row and the 11st row of matrix are Block-type pilot symbols, pλ
With the p in step 2 and step 3sIt is equal.
Step 5：Base station is according to the block frequency pilot sign of receptionAnd matrixEstimate base system number vector.
It is implemented as follows：
(5.1) Block-type pilot symbol is set upWith the relation of local frequency pilot signRelational expression be：
Wherein, F is N point quick Fourier transformation matrixs, ()HIt is the conjugate transposition operation of matrix, W is in transmitting procedure
The additive white Gaussian noise being subject to,It is pthλThe time domain channel shock response matrix of individual frequency pilot sign；
(5.2) time domain channel shock response matrix is represented using basis expansion model
Wherein,It is the basic function matrix of generation in step (2.2), GqIt is q-th of base system matrix number, it is that dimension is N
× N Teoplitz circular matrix：
Wherein, L is the separable footpath number of varying Channels；
(5.3) relational expression for substituting into the basis expansion model expression formula in step (5.2) in step (5.1), is obtained：
Due to GqIt is Teoplitz circular matrix, so making gq=[gq,0,...,gq,l,...,gq,L-1]T, FGqFH=FLgq,
Wherein, FLIt is Fourier transform matrix F preceding L row, above formula can be reduced to：
Wherein,It is the frequency domain matrix in step (2),G is the column vector that dimension is L (Q+1) × 1,It is the change in step (1)
Domain matrix is changed, so far, Block-type pilot symbol is establishedWith matrixAnd the relation between the base system number vector g to be estimated：
(5.4) two Block-type pilot symbols in step 4 are utilizedWith the matrix in step 3Using it is existing most
Small square law estimates base system number vector：
Wherein,It is group inverse matrices computing；Base system number vector is represented, it is the column vector of L (Q+1) × 1 dimensions, this
There are 14 single carrier frequency division multiplexed symbols in example, wherein the 4th and the 11st is Block-type pilot symbol, i.e. s=λ=1,2, p1
=4, p2=11,It is to receive the 4th column element in signal Y,It is to receive the 11st column element in signal Y, matrixBy
MatrixExtension is obtained, for the system of fixed Block-type pilot, matrixIt is constant, it is possible to willCalculated in advance is simultaneously stored, and substantially reduces the computation complexity required for estimation base system number vector, it is easy to actual fortune
With.
Step 6：The channel estimation in frequency domain of each single carrier frequency division multiplexed symbols is directly obtained using the base system number estimated
Response.
(6.1) frequency domain channel matrix of each single carrier frequency division multiplexed symbolsWith time domain channel matrixRelational expression
For：
Ignore the ICI influences inside a symbol, approximate evaluation goes out the diagonal element of frequency domain channel matrix, i.e.,：
Wherein,It is n-thsThe domain channel response matrix of individual single carrier frequency division multiplexed symbols, F is N point quick Fouriers
Transformation matrix, ()HIt is the conjugate transposition operation of matrix,It is n-thsThe time domain channel response of individual single carrier frequency division multiplexed symbols
Matrix.
(6.2) relational expression of base system number and domain channel response matrix is set up：
By basis expansion model expression formulaIt is updated in second relational expression in (6.1), obtains：
Due to GqIt is Teoplitz circular matrix, GqFirst is classified as [gq,0,gq,1,…,gq,L-1,0,…,0]T, so making gq
=[gq,0,…,gq,l,…,gq,L-1]T, FGqFH=FLgq, wherein, FLIt is N point Fourier transform matrix F preceding L row, above formula can letter
Turn to：
Wherein,It is the basic function matrix according to the formula generation in step (2.2),It is matrixPreceding L
Row, Q is the number of basic function, nsIt is the sequence number of single carrier frequency division multiplexed symbols.So far, base system number g and frequency domain channel are established
Response matrixRelationship.
(6.3) the domain channel response matrix of each single carrier frequency division multiplexed symbols is obtained
Utilize the base system number estimated in step 5According to the base system number set up in (6.2) and domain channel response matrix
Relationship, obtain n-thsThe domain channel response matrix of individual single carrier frequency division multiplexed symbols：
Wherein,It is the frequency domain matrix of generation in step (2.2).
The application effect of the present invention is explained in detail with reference to emulation.
1. simulated conditions
The communication system such as Fig. 3 used is emulated, SC-FDMA transmission standard is multiplexed using the single carrier frequency division of 3GPP standards,
Subcarrier number N=256, i.e., converted using 256 point fast Fouriers, and cyclic prefix is 18 points, and data use QPSK modulation methods
Formula, sample frequency 3.84MHz, carrier frequency 3.6GHz, subcarrier spacing 15KHz.
Pilot configuration such as Fig. 4, there is 14 single carrier frequency division multiplexed symbols in a transmission block, wherein there is two bulks to lead
Frequency symbol is located on the 4th and the 11st symbol.
User velocity is set to 330km/h, 450km/h in emulation, and piece transmission antenna of user configuring, base station configures two piece-root graftings
Receive antenna, wireless channel uses the extension vehicle channel model E VA in 3GPP standards, wherein, the time delay of multipath channel for [0,
30,50,310,370,710,1090,1730,2510] ns, the power attenuation in its each footpath for [0.0, -1.5, -1.4, -3.6, -
0.6, -9.1, -7.0, -12.0, -16.9] dB.The separable footpath number L of channel is set to 10 in emulation, obtains the flat of simulation curve
Equal number of times is 100000 times.
Emulating the method used has 4 kinds：1st, the inventive method, 2, based on discrete Fourier transform DFT and linear interpolation knot
The method of conjunction, 3, complex exponential basis expansion model method, 4, the method that is combined with autoregression model of multinomial model.
2. emulation content and result
Emulation 1
System block error rate BLER performance when user velocity is 330km/h is emulated with of the invention and above-mentioned 3 kinds of existing methods,
Simulation result is as shown in Figure 5.
As shown in Figure 5, the method that BLER performance comparisons multinomial model of the invention is combined with autoregression model has 4dB's
Performance boost；The method combined with linear interpolation based on discrete Fourier transform DFT is 10 in BLER-1When there is error floor,
And the BLER curve continuous decreases of the present invention, 10 can be dropped to-5；Complex exponential basis expansion model method is contrasted, BLER of the invention is bent
Line and the BLER curves of complex exponential basis expansion model method almost maintain an equal level, without performance loss.
Emulation 2
System block error rate BLER performance when user velocity is 450km/h is emulated with of the invention and above-mentioned 3 kinds of existing methods,
Simulation result is as shown in Figure 6.
It will be appreciated from fig. 6 that method that multinomial model is combined with autoregression model and based on discrete Fourier transform DFT and line
Property the method that combines of interpolation when user velocity is 450km/h, BLER curves are almost without downward trend, and Block Error Rate is all higher than
10-1, BLER curves of the invention can drop to 10-2Hereinafter, have greatly improved；Complex exponential basis expansion model method is contrasted, this
The BLER curves and complex exponential basis expansion model method of invention almost maintain an equal level, without performance loss.
The computation complexity and the computation complexity of existing complex exponential basis expansion model method of the present invention are contrasted, tied
Fruit such as table 1.
The computation complexity of the present invention of table 1 and complex exponential basis expansion model method are contrasted
| Computation complexity | Complex exponential basis expansion model method | The inventive method |
| Complex multiplication | ο(N2L+N3) | ο(NL) |
| Complex addition | ο(N2(L-1)+N2(N-1)) | ο((N-1)L) |
Wherein, ο is the order of magnitude of computation complexity, and N is the points of Fourier transformation, and L is the separable footpath of multipath channel
Number.
As shown in Table 1, the computation complexity magnitude needed for the inventive method is 1, and complex exponential basis expansion model method institute
The computation complexity magnitude needed is 3, and computation complexity has been dropped two magnitudes by the present invention.
The above results show that the present invention not only increases estimated accuracy compared with prior art, and than prior art tool
There is the advantage that computation complexity is lower.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention
Any modifications, equivalent substitutions and improvements made within refreshing and principle etc., should be included in the scope of the protection.
Claims (7)
1. a kind of simplification BEM channel estimation methods of high-speed mobile SC-FDMA systems, it is characterised in that the high-speed mobile SC-
The simplification BEM channel estimation methods of FDMA systems are by the matrix calculated in advance required for estimating base system number and store, and estimate base
Coefficient；Using the characteristic of channel and the transformation relation of time-frequency domain, derive that the mathematics of base system number and domain channel response matrix is closed
It is formula, direct estimation goes out to receive the domain channel response of signal.
2. the simplification BEM channel estimation methods of high-speed mobile SC-FDMA systems as claimed in claim 1, it is characterised in that institute
The simplification BEM channel estimation methods for stating high-speed mobile SC-FDMA systems comprise the following steps：
Step one, conversion domain matrix is obtainedBase station is by local frequency pilot signTransform domain is transformed into, obtains converting domain matrix
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Wherein, domain matrix is convertedDimension be N (Q+1) × L (Q+1),Diag () is to turn vector
Change the computing of diagonal matrix, p intosIt is the sequence number of local frequency pilot sign, two local frequency pilot sign s=1,2, its serial number p1=
4, p2=11, Q are the number of optimal basic function, IQ+1The unit matrix tieed up for Q+1；For row product code in Crow；FLIt is fast for N points
The preceding L row of fast Fourier transformation FFT matrix Fs：
Wherein, WN=e-j2π/N, L is the separable footpath number of varying Channels；
Step 2, based on complex exponential basis expansion model, base station end generation basic function matrix and basic function frequency domain matrix；
Step 3, base station end obtains the frequency domain matrix for estimating base system number, willWithIt is multiplied, obtaining base station end is used to estimate
Count the matrix of base system number：Its dimension is N × L (Q+1)；
Step 4, base station carries out Fast Fourier Transform (FFT) to time-domain received signal y and obtains frequency-region signal Y, is carried from frequency-region signal Y
Take Block-type pilot symbol
Step 5, base station is according to the block frequency pilot sign of receptionAnd matrixEstimate base system number vector；
Step 6, the channel estimation in frequency domain for directly obtaining each single carrier frequency division multiplexed symbols using the base system number estimated rings
Should.
3. the simplification BEM channel estimation methods of high-speed mobile SC-FDMA systems as claimed in claim 2, it is characterised in that institute
Step 2 is stated to specifically include：
(1) complex exponential CE basic function numbers Q is determined：
Base station is according to the translational speed v of user, the carrier frequency f of system and a duration T for sending signals=1ms, is obtained
To basic function number：Wherein, c is the light velocity,It is the computing that rounds up；
(2) basic function matrix is generated
<mrow>
<msubsup>
<mi>D</mi>
<mi>q</mi>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msubsup>
<mo>=</mo>
<mi>d</mi>
<mi>i</mi>
<mi>a</mi>
<mi>g</mi>
<mo>{</mo>
<mo>&lsqb;</mo>
<msubsup>
<mi>b</mi>
<mi>q</mi>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msubsup>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msubsup>
<mi>b</mi>
<mi>q</mi>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msubsup>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msubsup>
<mi>b</mi>
<mi>q</mi>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msubsup>
<mrow>
<mo>(</mo>
<mi>N</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>}</mo>
<mo>;</mo>
</mrow>
Wherein,It is basic function matrixElement, its utilize complex exponential basis expansion model, generated according to below equation：
<mrow>
<msubsup>
<mi>b</mi>
<mi>q</mi>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msubsup>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mn>2</mn>
<mi>&pi;</mi>
<mo>(</mo>
<mrow>
<mi>q</mi>
<mo>-</mo>
<mi>Q</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
<mo>(</mo>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mi>N</mi>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
<mo>/</mo>
<mi>N</mi>
<mo>*</mo>
<msub>
<mi>N</mi>
<mrow>
<mi>s</mi>
<mi>y</mi>
<mi>m</mi>
<mi>b</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
1
Wherein, q=0,1 ..., Q, Q are the numbers of basic function, n=0,1 ..., N, and N=256 is a single carrier frequency division multiplexing symbol
Number subcarrier number, i.e. Fast Fourier Transform (FFT) points, ns=1,2 ..., NsymbIt is the sequence of single carrier frequency division multiplexed symbols
Number, Nsymb=14 be the number of single carrier frequency division multiplexed symbols in a transmission block, psIt is the call number of local frequency pilot sign, two
Individual local frequency pilot sign s=1,2, its call number are p1=4, p2=11；
(3) frequency domain matrix is generatedWith
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<mi>&Delta;</mi>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msup>
<mo>=</mo>
<mo>&lsqb;</mo>
<msubsup>
<mi>&Delta;</mi>
<mn>0</mn>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msubsup>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msubsup>
<mi>&Delta;</mi>
<mi>q</mi>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msubsup>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msubsup>
<mi>&Delta;</mi>
<mi>Q</mi>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msubsup>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mi>&Psi;</mi>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msup>
<mo>=</mo>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<msubsup>
<mi>FD</mi>
<mn>0</mn>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msubsup>
<mrow>
<mo>(</mo>
<mi>L</mi>
<mo>)</mo>
</mrow>
<mo>,</mo>
<msubsup>
<mi>FD</mi>
<mn>1</mn>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msubsup>
<mrow>
<mo>(</mo>
<mi>L</mi>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<msubsup>
<mi>FD</mi>
<mi>Q</mi>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msubsup>
<mrow>
<mo>(</mo>
<mi>L</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>;</mo>
</mrow>
Wherein,It is q-th of frequency domain matrix, q=0,1 ..., Q, Q is the number of basic function,It is frequency pilot sign
The basic function matrix at place, psIt is the sequence number of frequency pilot sign, two local frequency pilot sign s=1,2, its call number are p1=4, p2=
11,It is matrixPreceding L row, F is N point quick Fourier transformation matrixs, ()HIt is the conjugate transposition operation of matrix.
4. the simplification BEM channel estimation methods of high-speed mobile SC-FDMA systems as claimed in claim 2, it is characterised in that institute
Step 4 is stated to specifically include：
(1) Fast Fourier Transform (FFT) is carried out to time-domain received signal y, obtains frequency-domain received signal Y：
Y=Fy；
Wherein, F is N point quick Fourier transformation matrixs；
(2) Block-type pilot symbol is extracted from frequency-domain received signal YThere are 14 single carrier frequency division multiplexings in one transmission block
Symbol, wherein the 4th and the 11st is Block-type pilot sign of lambda=1,2, p1=4, p2=11, i.e. frequency-domain received signal Y form
It is the matrix that a N × 14 are tieed up, the 4th row and the 11st row of matrix are Block-type pilot symbols, pλWith psIt is equal.
5. the simplification BEM channel estimation methods of high-speed mobile SC-FDMA systems as claimed in claim 2, it is characterised in that institute
Step 5 is stated to specifically include：
(1) Block-type pilot symbol is set upWith the relation of local frequency pilot signRelational expression be：
<mrow>
<msup>
<mi>Y</mi>
<msub>
<mi>p</mi>
<mi>&lambda;</mi>
</msub>
</msup>
<mo>=</mo>
<msup>
<mi>Fh</mi>
<msub>
<mi>p</mi>
<mi>&lambda;</mi>
</msub>
</msup>
<msup>
<mi>F</mi>
<mi>H</mi>
</msup>
<msup>
<mi>X</mi>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msup>
<mo>+</mo>
<mi>W</mi>
<mo>;</mo>
</mrow>
Wherein, F is N point quick Fourier transformation matrixs, ()HThe conjugate transposition operation of matrix, W be in transmitting procedure by
Additive white Gaussian noise,It is pthλThe time domain channel shock response matrix of individual frequency pilot sign；
(2) time domain channel shock response matrix is represented using basis expansion model
<mrow>
<msup>
<mi>h</mi>
<msub>
<mi>p</mi>
<mi>&lambda;</mi>
</msub>
</msup>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>Q</mi>
</munderover>
<msubsup>
<mi>D</mi>
<mi>q</mi>
<msub>
<mi>p</mi>
<mi>&lambda;</mi>
</msub>
</msubsup>
<msub>
<mi>G</mi>
<mi>q</mi>
</msub>
<mo>;</mo>
</mrow>
Wherein,It is the basic function matrix of generation, GqIt is q-th of base system matrix number, it is that the Teoplitz that dimension is N × N is followed
Ring matrix：
Wherein, L is the separable footpath number of varying Channels；
(3) relational expression for substituting into basis expansion model expression formula in step (1), is obtained：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<mi>Y</mi>
<msub>
<mi>p</mi>
<mi>&lambda;</mi>
</msub>
</msup>
<mo>=</mo>
<mi>F</mi>
<mrow>
<mo>(</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>Q</mi>
</munderover>
<msubsup>
<mi>D</mi>
<mi>q</mi>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msubsup>
<msub>
<mi>G</mi>
<mi>q</mi>
</msub>
<mo>)</mo>
</mrow>
<msup>
<mi>F</mi>
<mi>H</mi>
</msup>
<msup>
<mi>X</mi>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msup>
<mo>+</mo>
<mi>W</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>Q</mi>
</munderover>
<msubsup>
<mi>FD</mi>
<mi>q</mi>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msubsup>
<msup>
<mi>F</mi>
<mi>H</mi>
</msup>
<msub>
<mi>FG</mi>
<mi>q</mi>
</msub>
<msup>
<mi>F</mi>
<mi>H</mi>
</msup>
<msup>
<mi>X</mi>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msup>
<mo>+</mo>
<mi>W</mi>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>;</mo>
</mrow>
Due to GqIt is Teoplitz circular matrix, so making gq=[gq,0,...,gq,l,...,gq,L-1]T, FGqFH=FLgq, its
In, FLIt is Fourier transform matrix F preceding L row, above formula can be reduced to：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<mi>Y</mi>
<msub>
<mi>p</mi>
<mi>&lambda;</mi>
</msub>
</msup>
<mo>=</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>Q</mi>
</munderover>
<msubsup>
<mi>FD</mi>
<mi>q</mi>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msubsup>
<msup>
<mi>F</mi>
<mi>H</mi>
</msup>
<mi>d</mi>
<mi>i</mi>
<mi>a</mi>
<mi>g</mi>
<mrow>
<mo>{</mo>
<msup>
<mi>X</mi>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msup>
<mo>}</mo>
</mrow>
<msub>
<mi>F</mi>
<mi>L</mi>
</msub>
<msub>
<mi>g</mi>
<mi>q</mi>
</msub>
<mo>+</mo>
<mi>W</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<msubsup>
<mi>&Delta;</mi>
<mn>0</mn>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>&Delta;</mi>
<mn>1</mn>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msubsup>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<msubsup>
<mi>&Delta;</mi>
<mi>Q</mi>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msubsup>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<msub>
<mi>I</mi>
<mrow>
<mi>Q</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&CircleTimes;</mo>
<mrow>
<mo>(</mo>
<mrow>
<msubsup>
<mi>X</mi>
<mi>D</mi>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msubsup>
<msub>
<mi>F</mi>
<mi>L</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mi>g</mi>
<mo>+</mo>
<mi>W</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<msup>
<mi>&Delta;</mi>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msup>
<msup>
<mi>S</mi>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msup>
<mi>g</mi>
<mo>+</mo>
<mi>W</mi>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>;</mo>
</mrow>
Wherein,It is frequency domain matrix,G is dimension
Spend for L (Q+1) × 1 column vector,It is conversion domain matrix, so far, establishes Block-type pilot symbolWith matrixAnd the relation between the base system number vector g to be estimated：
<mrow>
<msup>
<mi>Y</mi>
<msub>
<mi>p</mi>
<mi>&lambda;</mi>
</msub>
</msup>
<mo>=</mo>
<msup>
<mi>A</mi>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
</msup>
<mi>g</mi>
<mo>+</mo>
<mi>W</mi>
<mo>;</mo>
</mrow>
(4) two Block-type pilot symbols are utilizedAnd matrixBase system number vector is gone out using existing Least Square Method：
Wherein,It is group inverse matrices computing；Base system number vector is represented, it is the column vector of L (Q+1) × 1 dimensions, there are 14
Single carrier frequency division multiplexed symbols, wherein the 4th and the 11st is Block-type pilot symbol, i.e. s=λ=1,2, p1=4, p2=11,It is to receive the 4th column element in signal Y,It is to receive the 11st column element in signal Y, matrixBy matrixExtension is obtained, for the system of fixed Block-type pilot, matrixIt is constant, it is possible to will
Calculated in advance is simultaneously stored.
6. the simplification BEM channel estimation methods of high-speed mobile SC-FDMA systems as claimed in claim 2, it is characterised in that institute
Step 6 is stated to specifically include：
(1) frequency domain channel matrix of each single carrier frequency division multiplexed symbolsWith time domain channel matrixRelational expression be：
<mrow>
<msup>
<mi>H</mi>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msup>
<mo>=</mo>
<msup>
<mi>Fh</mi>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msup>
<msup>
<mi>F</mi>
<mi>H</mi>
</msup>
<mo>;</mo>
</mrow>
The diagonal element of frequency domain channel matrix is estimated, i.e.,：
<mrow>
<msup>
<mi>H</mi>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msup>
<mo>=</mo>
<mi>d</mi>
<mi>i</mi>
<mi>a</mi>
<mi>g</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>Fh</mi>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msup>
<msup>
<mi>F</mi>
<mi>H</mi>
</msup>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Wherein,It is n-thsThe domain channel response matrix of individual single carrier frequency division multiplexed symbols, F is the conversion of N point quick Fouriers
Matrix, ()HIt is the conjugate transposition operation of matrix,It is n-thsThe time domain channel response square of individual single carrier frequency division multiplexed symbols
Battle array；
(2) relational expression of base system number and domain channel response matrix is set up：
By basis expansion model expression formulaIt is updated toIn, obtain：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<mi>H</mi>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msup>
<mo>=</mo>
<mi>d</mi>
<mi>i</mi>
<mi>a</mi>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>F</mi>
<mo>(</mo>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>Q</mi>
</munderover>
<msubsup>
<mi>D</mi>
<mi>q</mi>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msubsup>
<msub>
<mi>G</mi>
<mi>q</mi>
</msub>
</mrow>
<mo>)</mo>
<msup>
<mi>F</mi>
<mi>H</mi>
</msup>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<mi>d</mi>
<mi>i</mi>
<mi>a</mi>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>Q</mi>
</munderover>
<msubsup>
<mi>FD</mi>
<mi>q</mi>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msubsup>
<msup>
<mi>F</mi>
<mi>H</mi>
</msup>
<msub>
<mi>FG</mi>
<mi>q</mi>
</msub>
<msup>
<mi>F</mi>
<mi>H</mi>
</msup>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>;</mo>
</mrow>
Due to GqIt is Teoplitz circular matrix, GqFirst is classified as [gq,0,gq,1,…,gq,L-1,0,…,0]T, so making gq=
[gq,0,…,gq,l,…,gq,L-1]T, FGqFH=FLgq, wherein, FLIt is N point Fourier transform matrix F preceding L row, above formula can simplify
For：
Wherein,It is the basic function matrix according to generation,It is matrixPreceding L row, Q is the number of basic function, nsIt is
The sequence number of single carrier frequency division multiplexed symbols；
(3) the domain channel response matrix of each single carrier frequency division multiplexed symbols is obtained, the base system number estimated is utilizedAccording to
The base system number of foundation and the relationship of domain channel response matrix, obtain n-thsThe frequency domain of individual single carrier frequency division multiplexed symbols
Channel response matrix：
<mrow>
<msup>
<mover>
<mi>H</mi>
<mo>^</mo>
</mover>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msup>
<mo>=</mo>
<msup>
<mi>&Psi;</mi>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</msup>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mo>;</mo>
</mrow>
Wherein,It is the frequency domain matrix of generation.
7. a kind of simplification BEM channel estimation sides of high-speed mobile SC-FDMA systems described in application claim 1~6 any one
The single carrier frequency division multiplexing multiple access SC-FDMA systems of method.
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| CN201710365688.7A Active CN107222438B (en) | 2017-05-23 | 2017-05-23 | Simplified BEM channel estimation method of high-speed mobile SC-FDMA system |
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