CN104052568A - Cooperative multi-point transmission precoding algorithm for timing synchronization reciprocity error - Google Patents

Abstract

The invention provides a cooperative multi-point transmission precoding algorithm for a timing synchronization reciprocity error. According to the cooperative multi-point transmission precoding algorithm, if the timing synchronization reciprocity error approximates a constant application scene, the error is compensated through MMSE channel estimation, RVQ quantification feedback, LS error estimation and linear interpolation when a precoding vector or a matrix is designed; in a real-time change application scene of the timing synchronization reciprocity error, the algorithm averages lower bound of SLNR at a maximum degree through a probability density function of the error to acquire the robust precoding vector or the matrix. In a cooperative multi-point transmission system in a TDD mode, compared with a traditional precoding algorithm, the algorithm can settle orthogonality influence of the timing synchronization reciprocity error on the precoding vector or the matrix, so interference among users or communities is better eliminated, and system capacity is improved.

Description

Cooperative multipoint transmission precoding algorithm for Timing Synchronization reciprocity error

Technical field

The present invention relates to wireless communication field, particularly adopt the cooperation communication system of OFDM technology tdd mode.

Background technology

In order further to improve spectrum efficiency, to improve Cell Edge User throughput, cooperative multipoint transmission (Coordinated Multi-point Transmission, CoMP) becomes communications field study hotspot in recent years.Researcher design and improved a large amount of precoding algorithms, to eliminate completely or to reduce by a relatively large margin the interference between multi-user and between co-frequency cell.Because most of precoding algorithm is all supposed based on ideal communication channel letter (Channel Side Information, CSI), therefore believe that the accuracy of CSI becomes the key that guarantees associating precoding algorithm performance.In CoMP, tdd mode, based on channel reciprocity feature, is estimated to obtain the CSI of down channel by ascending pilot frequency, thereby has avoided extensive quantification feedback overhead and the error of fdd mode.Therefore tdd mode is considered to the important development direction of CoMP.

In actual application, up-downgoing equivalent channel, except comprising aerial transmission channel, also comprises base band and the radio frequency part of transmitting terminal and receiving terminal.Therefore the up-downgoing equivalent channel of tdd mode is generally imperfect reciprocity, thereby the performance of precoding is significantly reduced.The people such as Su Liyan have studied the time variation of equivalent channel.Jose and Ashikhmin have studied pilot pollution and the asymmetric interference of up-downgoing channel.In order to promote the practical application of tdd mode, Alcatel-Lucent company has set up the reciprocity error model of mimo system narrow band channel.Meanwhile, Huang Fan and Shi Jing also carry out modeling analysis to the rf gain reciprocity error of CoMP channel, and have proposed corresponding calibration steps.For frequency selective fading channels, LTE or WiMAX all adopt OFDM with antagonism multipath effect.Introduce OFDM and can to the CoMP system of tdd mode, bring new channel reciprocity error to meeting.This type of channel reciprocity error can cause traditional precoding algorithm performance significantly to reduce.

In literary composition, tiltedly black matrix represents vector or matrix, () ^hwith () ^-1represent respectively conjugate transpose and matrix inversion, || with || represent to get respectively the 2-norm of the modulus of complex number and amount of orientation, for Kronecker product (Kronecker product), diag{} is diagonal matrix, and E{} represents to get desired value, I _xrepresent the unit matrix that order is x.

Summary of the invention

For the tdd mode CoMP system that adopts OFDM, the present invention relates to the imperfect reciprocity error of channel that partially causes when synchronous, and for its characteristic, proposed to resist the precoding algorithm of this reciprocity error.CoMP system be in the nature multi-cell base station cooperation.In supposing the system, have B cooperative base station, n is all assembled in each base station _troot antenna.In supposing the system, have M user, each is with assembling per family single antenna.System adopts OFDM that channel is divided into N sub-channels at frequency domain.At k sub-channels, cooperative base station can be expressed as to the equivalent up-downgoing channel of user m

(1)

Wherein represent respectively the equivalent upstream and downstream channel between cooperative base station b and user m.For convenience of expressing, hereinafter in formula, all omit sub-channel index k.Suppose that total emission power P is averagely allocated to each user, user m can be expressed as at the reception signal of k sub-channels

$r_m=\sqrt{\frac{P}{M}}{H}_{m\_\mathrm{DL}}{v}_m{s}_m+\underset{j=1,j\≠m}{\overset{M}{\mathrm{\Σ}}}\sqrt{\frac{P}{M}}{H}_{m\_\mathrm{DL}}{v}_j{s}_j+n_{\mathrm{noise}}---\left(2\right)$

S wherein _mand s _jfor sending to the signal of user m and user j, v _mand v _jfor the precoding vector of user m and user j, n _noisefor additivity white complex gaussian noise.

The FFT window starting point of OFDM is positioned at the Cyclic Prefix (Cyclic Prefix, CP) without intersymbol interference, and Timing Synchronization error d meets L-N _cP≤ d≤0(is L wherein, N _cPrepresent respectively maximum multipath time delay and CP length).This Timing Synchronization error d causes phase rotating exp (j2 π kd/N).At k sub-channels, cooperative base station b can be expressed as to the up-downgoing equivalent channel of user m

$h_{\mathrm{mb}\_\mathrm{UL}}=h_{\mathrm{mb}}\×e^{-j2\mathrm{\πk}{d}_{\mathrm{mb}.\mathrm{UL}}/N}$ (3)

$h_{\mathrm{mb}\_\mathrm{DL}}=h_{\mathrm{mb}}\×e^{-j2\mathrm{\πk}{d}_{\mathrm{mb}.\mathrm{DL}}/N}$

D wherein _mb.ULand d _mb.DLrepresent respectively up and descending Timing Synchronization error, and represent the aerial transmission channel between cooperative base station b and user m, meet desirable reciprocity.Ignore path fading and the shadow fading of channel, only consider Rayleigh fading, h _mbin each element separate, and equal multiple Gaussian Profile CN (0,1) of obedience standard.By formula (3), the up-downgoing equivalent channel relation between cooperative base station b and user m can be expressed as

$h_{\mathrm{mb}\_\mathrm{DL}}=h_{\mathrm{mb}\_\mathrm{UL}}{e}^{-j2\mathrm{\πk}(d_{\mathrm{mb}.\mathrm{DL}}-d_{\mathrm{mb}.\mathrm{UL}})/N}---\left(4\right)$

Definition φ _mb=-2 π k Δ d _mb/ N is the Timing Synchronization reciprocity error of up-downgoing equivalent channel between cooperative base station b and user m, wherein Δ d _mb=(d _mb.DL-d _mb.UL).Descending equivalent channel between cooperative base station and user m can be expressed as again the product of up channel and Timing Synchronization reciprocity error

H _{m_DL}＝H _{m_UL}Φ _m (5)

Wherein ${\mathrm{\Φ}}_m=\mathrm{diag}\{e^{j{\mathrm{\φ}}_{m1}},...e^{j{\mathrm{\φ}}_{\mathrm{mB}}}\}\⊗I_{n_t}.$

For multi-multipoint CoMP system, Timing Synchronization reciprocity error can cause traditional precoding performance significantly to reduce.For Timing Synchronization reciprocity error characteristics, the present invention proposes the precoding algorithm of this error of antagonism.The CoMP system applies scene different according to two classes, the precoding algorithm that the precoding algorithm that the present invention proposes can be divided into again the precoding algorithm based on estimation compensation and distribute based on error.As Timing Synchronization reciprocity error φ in CoMP system _mbin time domain, change slowly, approximately constant, can adopt the precoding algorithm based on estimation compensation.Take user m as example, and the production process of the precoding vector of this algorithm comprises the following steps:

(1), according to the channel condition between send and receive antenna, choose the antenna p of user m and the antenna q of base station b as with reference to antenna pair.Antenna is better than other antennas pair to the standard of choosing for the channel condition between this antenna pair, ${\left|h_{\mathrm{mb}}^{\mathrm{pq}}{s}_m\right|}^2/\left|n_{\mathrm{noise}}^{\mathrm{pq}}\right|>{\left|h_{\mathrm{mb}}^{\mathrm{jl}}{s}_m\right|}^2/\left|n_{\mathrm{noise}}^{\mathrm{jl}}\right|.$

(2) choosing n sub-channels is that more with reference to number of sub-channels, Timing Synchronization reciprocity estimation error is more accurate with reference to subchannel, but corresponding feedback overhead is also larger with it.

(3), for subchannel k, by ascending pilot frequency, estimate up channel h _{pmqb_UL}(k), by user, quantize feedback and obtain down channel pilot tone estimates to adopt MMSE, quantizes feedback and adopts RVQ.

(4) utilize Timing Synchronization reciprocity error at each with reference to the linear relationship on subchannel, by least square (Least Squares, LS) from n up-downgoing with reference to the Timing Synchronization reciprocity error obtaining subchannel between subchannel k user m and base station b estimate.

(5) in like manner, obtain the Timing Synchronization reciprocity estimation error of subchannel k user m and other base stations ${\widehat{\mathrm{\Φ}}}_m=\mathrm{diag}\{e^{j{\widehat{\mathrm{\φ}}}_{m,1}},...e^{j{\widehat{\mathrm{\φ}}}_{m,B}}\}\⊗I_{N_t}.$

(6) at precoding vector place, Timing Synchronization reciprocity error is compensated, the precoding vector of subchannel k user m can be expressed as

$w_m~\max .\mathrm{eigenvector}\left({({\mathrm{\σ}}_{\mathrm{noise}}^{2}I+\underset{\text{n=1,n\≠m}}{\overset{\text{M}}{\mathrm{\Σ}}}{\mathrm{\Ω}}_n)}^{-1}{\mathrm{\Ω}}_m\right)---\left(6\right)$

Wherein ${\mathrm{\Ω}}_n={\widehat{\mathrm{\Φ}}}_n^H{H}_{n\_\mathrm{UL}}^H{H}_{n\_\mathrm{UL}}{\widehat{\mathrm{\Φ}}}_n,$ ${\mathrm{\Ω}}_m={\widehat{\mathrm{\Φ}}}_m^H{H}_{m\_\mathrm{UL}}^H{H}_{m\_\mathrm{UL}}{\widehat{\mathrm{\Φ}}}_m,$

As Timing Synchronization reciprocity error φ in CoMP system _mbin time domain, change rapidly, be difficult to estimate and follow the trail of, adopt the precoding algorithm distributing based on error.The k sub-channels precoding vector of user m can be expressed as:

v _m～max.eigenvector(E{M _m} ^-1E{Q _m}) （7）

w _m＝v _m/||v _m||

Wherein

H _{m_UL}can estimate to obtain by ascending pilot frequency, pilot tone estimates to adopt MMSE,

$E\left\{{\mathrm{\Φ}}_m^H{H}_{m\_\mathrm{UL}}^H{H}_{m\_\mathrm{UL}}{\mathrm{\Φ}}_m\right\}\≈E\left\{{\mathrm{\Φ}}_m^H\right\}{H}_{m\_\mathrm{UL}}^H{H}_{m\_\mathrm{UL}}E\left\{{\mathrm{\Φ}}_m\right\}---\left(8\right)$

Wherein $E\left\{{\mathrm{\Φ}}_m\right\}=\mathrm{diag}\left\{E\right\{e^{j{\mathrm{\φ}}_{m,1}}\},...E\{e^{j{\mathrm{\φ}}_{m,B}}\left\}\right\}\⊗I_{n_t},$ $E\left\{e^{j{\mathrm{\φ}}_{m,b}}\right\}=E\left\{\cos {\mathrm{\φ}}_{m,b}\right\}+\mathrm{jE}\left\{\sin {\mathrm{\φ}}_{m,b}\right\}$

According to the probability distribution of the Timing Synchronization heterogeneite error of user m, just can pass through φ _m,bprobability density function and functional integration obtain E{ Φ _m.

Accompanying drawing explanation

Fig. 1 is tdd mode cooperative multicast system, is practical application scene of the present invention.The equivalent up-downgoing channel architecture that has also comprised base station b and user m in Fig. 1.

Fig. 2 be under desirable channel reciprocity condition and Timing Synchronization reciprocity error condition under the simulation result of the average achievable rate of user and its theory lower-bound.By simulation result, can find that Timing Synchronization reciprocity error significantly reduces precoding performance, make the average achievable rate of user interference-limited.

Fig. 3 is for adopting the multi-base station cooperative downlink transfer structured flowchart of precoding algorithm of the present invention.According to the type of Timing Synchronization reciprocity error, in two class precoding algorithms, select.

Fig. 4 is 2 base station 2 users' cooperative multicast system scene, and the Performance Ratio of the precoding that traditional SLNR precoding algorithm and the present invention propose.By the cumulative distribution function curve of power system capacity, can find that traditional SLNR is very responsive to Timing Synchronization reciprocity error, being subject to it to affect power system capacity significantly reduces, and 2 kinds of precoding algorithms that the present invention proposes all in various degree slowed down the performance loss that this error causes, promoted precoding performance.

Fig. 5 is 3 base station 3 users' cooperative multicast system scene, and the Performance Ratio of the precoding that traditional SLNR precoding algorithm and the present invention propose.

Embodiment

The invention will be further described with example by reference to the accompanying drawings, and embodiments of the present invention include but not limited to following example.As shown in Figure 1, make cooperative base station number B=2, number of users M=2, cooperative base station antenna number nt=2, user is single antenna.The sub-carrier number of OFDM is N=1024, and circulating prefix-length is N _cp=144, maximum path time delay is L=(N _cp/ 2).

User, to the up channel of cooperative base station, carries out MMSE by the block pilot tone in the detection reference signal (Sounding Reference Signal, SRS) that user is sent and estimates to obtain.Cooperative base station, to user's down channel, supposes that user can obtain desirable down channel, quantizes (Random Vector Quantization, RVQ) simultaneously down channel is quantized to feedback by random vector.With cooperative base station 1,, 2 to user 1 down channels for example, quantize code book C by 2 ^tthe multiple unit vector of individual 4 dimension forms wherein T is for quantizing number of bits of feedback, and T is larger, and quantification feedback error is less, conventionally makes T=8.The selection that quantizes feedback vector based on

${\hat{H}}_{1\_\mathrm{DL}}~\arg \underset{j=1,...,2^T}{\max }\left|H_{1\_\mathrm{DL}}{\hat{H}}_j^H\right|---\left(9\right)$

Cooperative base station, after obtaining up-downgoing channel, just can calculate channel reciprocity error phase in the situation of change of time domain.As shown in Figure 4, if its error at time domain approximately constant, adopts the precoding algorithm based on estimation compensation, if its error in time domain real-time change, adopts the precoding algorithm distributing based on error.

For the precoding algorithm based on estimation compensation, first antenna of selecting collaboration base station is reference antenna, choose n sub-channels as with reference to channel, by least-squares estimation (Least quare, LS) at frequency domain the reciprocity error by other subchannel of reciprocity estimation error with reference to subchannel.If with reference to number of subchannels n=2, the Timing Synchronization reciprocity error of k subcarrier between user 1 and base station 1 can be expressed as

$e^{j{\widehat{\mathrm{\φ}}}_{11}={\left(\frac{{\hat{h}}_{11\_\mathrm{DL}}\left(c_2\right)h_{11\_\mathrm{UL}}\left(c_1\right)}{h_{11\_\mathrm{UL}}\left(c_2\right){\hat{h}}_{11\_\mathrm{DL}}\left(c_1\right)}\right)}^{k/(c_2-c_1)}---\left(10\right)}$

User 1 can be expressed as at the precoding vector of subchannel k

$w_1~\max .\mathrm{eigenvector}\left({({\mathrm{\σ}}_{\mathrm{noise}}^{2}I+{\mathrm{\Ω}}_2)}^{-1}{\mathrm{\Ω}}_1\right)---\left(11\right)$

Wherein ${\mathrm{\Ω}}_1={\widehat{\mathrm{\Φ}}}_1^H{H}_{1\_\mathrm{UL}}^H{H}_{1\_\mathrm{UL}}{\widehat{\mathrm{\Φ}}}_1,$

${\widehat{\mathrm{\Φ}}}_1=\mathrm{diag}\{e^{j{\widehat{\mathrm{\φ}}}_{11}},...e^{j{\widehat{\mathrm{\φ}}}_{12}}\}\⊗I_2,$ ${\widehat{\mathrm{\Φ}}}_2=\mathrm{diag}\{e^{j{\widehat{\mathrm{\φ}}}_{21}},...e^{j{\widehat{\mathrm{\φ}}}_{22}}\}\⊗I_2.$

For the precoding algorithm distributing based on error, suppose the Timing Synchronization error of the up-downgoing equivalent channel between cooperative base station b and user m obedience is uniformly distributed U (Z _mb, 0), Z wherein _mb=N _cP-L _mb.By deriving, the Timing Synchronization reciprocity error phase φ between base station b and user m _mbprobability density function can be expressed as

$f\left({\mathrm{\&phi;}}_{\mathrm{mb}}\right)=\left\{\begin{array}{cc}\mathrm{\&rho;}\frac{-\mathrm{\&rho;}{\mathrm{\&phi;}}_{\mathrm{mb}}+Z_{\mathrm{mb}}}{Z_{\mathrm{mb}}^2}& \mathrm{if}0<{\mathrm{\&phi;}}_{\mathrm{mb}}\&le;\frac{Z_{\mathrm{mb}}}{\mathrm{\&rho;}}\\ \mathrm{\&rho;}\frac{\mathrm{\&rho;}{\mathrm{\&phi;}}_{\mathrm{mb}}+Z_{\mathrm{mb}}}{Z_{\mathrm{mb}}^2}& \mathrm{if}\frac{Z_{\mathrm{mb}}}{\mathrm{\&rho;}}<\mathrm{\&Delta;}{d}_{\mathrm{mb}}\&le;0\end{array}\right.---\left(12\right)$

ρ=N/2 π k wherein.According to this error, distribute, user 1 k sub-channels precoding vector can be expressed as:

v ₁～max.eigenvector(E{M ₁} ^-1E{Q ₁}) （13）

w ₁＝v ₁/||v ₁||

Wherein

$E\left\{M_1\right\}={\mathrm{\&sigma;}}_{\mathrm{noise}}^{2}I+E\left\{Q_2\right\}$

$E\left\{Q_1\right\}=E\left\{H_{1\_\mathrm{DL}}^H{H}_{1\_\mathrm{DL}}\right\}=E\left\{{\mathrm{\&Phi;}}_1^H{H}_{1\_\mathrm{UL}}^H{H}_{1\_\mathrm{UL}}{\mathrm{\&Phi;}}_1\right\}\&ap;E\left\{{\mathrm{\&Phi;}}_1^H\right\}{H}_{1\_\mathrm{UL}}^H{H}_{1\_\mathrm{UL}}E\left\{{\mathrm{\&Phi;}}_1\right\}.$

Again

$E\left\{{\mathrm{\&Phi;}}_1\right\}=\mathrm{diag}\left\{E\right\{e^{j{\mathrm{\&phi;}}_{11}}\},E\{e^{j{\mathrm{\&phi;}}_{12}}\left\}\right\}\&CircleTimes;I_2,$ $E\left\{e^{j{\mathrm{\&phi;}}_{11}}\right\}=E\left\{\cos {\mathrm{\&phi;}}_{11}\right\}+\mathrm{jE}\left\{\sin {\mathrm{\&phi;}}_{11}\right\},$

$E\left\{e^{j{\mathrm{\&phi;}}_{12}}\right\}=E\left\{\cos {\mathrm{\&phi;}}_{12}\right\}+\mathrm{jE}\left\{\sin {\mathrm{\&phi;}}_{12}\right\}$

Make Z ₁₁=Z ₁₂=Z,

E{sinφ ₁₁}＝E{sinφ ₁₂}＝0

$E\left\{\cos {\mathrm{\&phi;}}_{11}\right\}=E\left\{\cos {\mathrm{\&phi;}}_{12}\right\}=\frac{2{\mathrm{\&rho;}}^2}{Z^2}(1-\cos \left(\frac{Z}{\mathrm{\&rho;}}\right))$

Claims (7)

1. the present invention proposes the cooperative multipoint transmission downlink precoding algorithm for Timing Synchronization reciprocity error, it is characterized by the cooperative multicast system of tdd mode, by estimation compensation or based on error, distribute, design downlink precoding vector or matrix, reduce the impact of Timing Synchronization reciprocity error on orthogonality between precoding vector or matrix, eliminate the interference of user or minizone, capacity.

2. the cooperative multicast system of tdd mode according to claim 1, it is characterized by and adopt OFDM with opposing multipath fading, OFDM symbol cyclic prefix length is greater than maximum multipath time delay, and the FFT starting point of OFDM is positioned at the Cyclic Prefix without intersymbol interference, i.e. relative timing synchronous error is remaining (T _srepresent sampling period) meet (L represents maximum multipath time delay, N _cPrepresent circulating prefix-length), the remaining d of this Timing Synchronization only causes phase rotating exp (j2 π kd/N).

3. according to the cooperative multicast system of claim 1 and tdd mode claimed in claim 2, it is characterized by between each base station and each user and have the different path delays of time, up-downgoing channel exists different Timing Synchronizations remaining.

4. Timing Synchronization reciprocity error according to claim 1, the subchannel of take on k subcarrier is example, between base station b and user m, the Timing Synchronization reciprocity error character of up-downgoing channel is φ _mb=-2 π k Δ d _mb/ N, wherein Δ d _mb=(d _mb.DL-d _mb.UL), d _mb.ULand d _mb.DLthe Timing Synchronization that represents respectively up channel and down channel is remaining.

5. the estimation compensation to Timing Synchronization reciprocity error according to claim 1, is characterized by Timing Synchronization reciprocity error φ _mbat time domain approximately constant, the precoding algorithm of user m based on estimation compensation comprises the following steps:

(1) choose the antenna p of user m and the antenna q of base station b as with reference to antenna,

(2) choosing n sub-channels is with reference to subchannel,

(3), for subchannel k, by ascending pilot frequency, estimate up channel h _{pmqb_UL}(k), by user, quantize feedback and obtain down channel h _{pmqb_DL}(k),

(4) utilize Timing Synchronization reciprocity error at each with reference to the linear relationship on subchannel, by estimation error, obtain

(5) use above-mentioned same method, obtain the Timing Synchronization reciprocity estimation error between user m and other base stations for Kronecker product (Kronecker product),

(6) the precoding vector of k sub-channels user m can be expressed as

$w_m~\max .\mathrm{eigenvector}\left({({\mathrm{\&sigma;}}_{\mathrm{noise}}^{2}I+\underset{\text{n=1,n\&NotEqual;m}}{\overset{\text{M}}{\mathrm{\&Sigma;}}}{\mathrm{\&Omega;}}_n)}^{-1}{\mathrm{\&Omega;}}_m\right)---\left(1\right)$

Wherein ${\mathrm{\&Omega;}}_n={\widehat{\mathrm{\&Phi;}}}_n^H{H}_{n\_\mathrm{UL}}^H{H}_{n\_\mathrm{UL}}{\widehat{\mathrm{\&Phi;}}}_n,$ ${\mathrm{\&Omega;}}_m={\widehat{\mathrm{\&Phi;}}}_m^H{H}_{m\_\mathrm{UL}}^H{H}_{m\_\mathrm{UL}}{\widehat{\mathrm{\&Phi;}}}_m,$

6. the Precoding Design distributing based on Timing Synchronization reciprocity error according to claim 1, is characterized in that the k sub-channels precoding vector of user m can be expressed as

v _m～max.eigenvector(E{M _m} ^-1E{Q _m}) （2）

w _m＝v _m/||v _m||

Wherein $Q_m=H_{m\_\mathrm{Dl}}^H{H}_{m\_\mathrm{DL}},$ $M_m={\mathrm{\&sigma;}}_{\mathrm{noise}}^{2}I+\underset{n=1,n\&NotEqual;m}{\overset{M}{\mathrm{\&Sigma;}}}{Q}_n.$

7. Timing Synchronization reciprocity error according to claim 6 distributes, and it is characterized in that the Timing Synchronization reciprocity error phase φ between base station b and user m _mbprobability density function can be expressed as

$f\left({\mathrm{\&phi;}}_{\mathrm{mb}}\right)=\left\{\begin{array}{cc}\mathrm{\&rho;}\frac{-\mathrm{\&rho;}{\mathrm{\&phi;}}_{\mathrm{mb}}+Z_{\mathrm{mb}}}{Z_{\mathrm{mb}}^2}& \mathrm{if}0<{\mathrm{\&phi;}}_{\mathrm{mb}}\&le;\frac{Z_{\mathrm{mb}}}{\mathrm{\&rho;}}\\ \mathrm{\&rho;}\frac{\mathrm{\&rho;}{\mathrm{\&phi;}}_{\mathrm{mb}}+Z_{\mathrm{mb}}}{Z_{\mathrm{mb}}^2}& \mathrm{if}\frac{Z_{\mathrm{mb}}}{\mathrm{\&rho;}}<\mathrm{\&Delta;}{d}_{\mathrm{mb}}\&le;0\end{array}\right.---\left(3\right)$

ρ=N/2 π k wherein, N is subchannel sum, Z _mb=N _cP-L _mb, N _cPfor circulating prefix-length, L _mbfor maximum multipath time delay between base station b and user m.