CN106488464A - Optimal robustness Poewr control method under non-ideal CSI in two-layer Femtocell network - Google Patents

Abstract

The present invention is claimed the optimal robustness Poewr control method under non-ideal CSI in a kind of two-layer Femtocell network; under the conditions of the method is considered channel estimation errors and is met the interference constraints of macrocell user; by controlling the transmission power of Femtocell user, maximize the total throughout of Femtocell user.For the interference constraints condition of strict protection macrocell user, the thought based on robust optimization and the worst criterion mechanism for the method, the Max Min optimization problem of unlimited constraint is converted into the convex optimization problem of finite constraint.By the optimality condition of convex optimization problem, give the closed solutions of the optimal robustness power of Femtocell user.It is low that the present invention has a computation complexity, can strict guarantee macrocell user QoS, the advantage improving Femtocell user throughput, be particularly suitable for the two-layer Femtocell network under non-ideal CSI.

Description

Optimal robustness Poewr control method under non-ideal CSI in two-layer Femtocell network

Technical field

The present invention relates to the power control techniques field under non-ideal CSI in two-layer Femtocell network, specifically, relate to And based on throughput-maximized optimal robustness Poewr control method in two-layer Femtocell network.

Background technology

With the fast development of Technology of New Generation Mobile Communications, people are to radio communication service service quality (QoS) sum Requirement according to transfer rate increasingly increases.Research shows, more than 90% data communication and more than 67% voice communication are all Complete indoors.But the carrier frequency more and more higher used by radio communication, so that the penetration capacity of ripple is worse and worse, indoor The signal attenuation at family increases, so that high-quality indoor communications service is difficult to.By flying honeycomb (Femtocell) skill Art can expand network coverage, the capacity boost of effectively solving indoor mobile communication network, realizes higher spectrum efficiency, Therefore, it is subject to industry extensive concern in recent years.

Under two-layer Femtocell network, Femtocell user can be connect by the frequency spectrum of shared macrocell user Enter, thus carrying out data transmission.However, which introducing cross-layer interference and with layer interference.Therefore, it is desirable to realize Femtocell's Promote on a large scale, interference management is crucial, and Power Control is the important method solving this key issue.Zheng Z et al. ?《2011IEEE 73rd Vehicular Technology Conference, Yokohama, 2011:1-5.》On deliver Entitled " On uplink power control optimization and distributed resource allocation The article of in femtocell networks ".This article with maximize Femtocell user total throughout as optimization aim, Under the interference restriction of macrocell user, by realizing to the space search of Femtocell user power iterative parameter The power optimization of Femtocell user.Because this algorithm is the communication environment based on imperfect channel state information (CSI), rather than Preferably CSI can affect the power adjustment of user, and this algorithm may reduce network performance in the environment of non-ideal CSI.

At present, Most scholars, when studying the Power Control of two-layer Femtocell network, all assume that in preferable CSI Communication environment in.And in actual wireless communication system, due to the time-varying characteristics of channel, quantization error and time delay etc. Factor, is typically difficult to obtain preferable CSI.

Therefore, for the two-layer Femtocell network that there are channel estimation errors, it is necessary to take into account ensureing macrocellular use Under the qos requirement at family, the optimal robustness Poewr control method based on maximize handling capacity for the research.

Content of the invention

Present invention seek to address that above problem of the prior art.Propose a kind of maximize Femtocell user throughput, The optimal robustness work(of the two-layer Femtocell network that computation complexity is low, channel adaptability is strong, be particularly suitable under non-ideal CSI Rate control method.Technical scheme is as follows：

Optimal robustness Poewr control method under non-ideal CSI in a kind of two-layer Femtocell network, it includes following step Suddenly：

101st, initialization Femtocell user's number, the same layer jamming power upper bound of Femtocell user and The ranking factor of Femtocell user；

102nd, the ranking factor ascending order of Femtocell user is arranged；

103rd, calculate the Lagrangian tolerance factor of each Femtocell user and Lagrange judges the factor；

If the Lagrangian tolerance factor of 104 last Femtocell user be more than it Lagrange judge because Son, then the Lagrange factor of Femtocell user be equal to it Lagrange judge the factor, according to this Lagrange factor, Provide optimal robustness power, terminate；Otherwise jump to step 105；

If 105 last Femtocell user corresponding Lagrange tolerance factor is less than or equal to drawing of it Ge Lang judges the factor, then be zero by the power setting of last Femtocell user, and go to step 104, to other The Lagrangian tolerance factor of Femtocell user and its Lagrange judge that the factor is compared, to the last one The Lagrangian tolerance factor of Femtocell user is more than its Lagrange and judges that factor condition meets, and calculates glug bright Day factor and optimal robustness power.

Further, initialize Femtocell user's number K=n described in step 101, other all of Femtocell use The same layer jamming power upper bound γ to Femtocell user's i receiving terminal for the family j (j=1,2 ..., n, j ≠ i), Femtocell user The ranking factor M of i_i：

Wherein,The estimation channel gain at the i of Femtocell base station servicing to its offer for Femtocell user i,Estimation channel gain for Femtocell user i to macro base station, ε_fRepresent that Femtocell user i provides service to it The normalization uncertainty of the channel gain estimation difference at the i of Femtocell base station, ε_mRepresent Femtocell user i to grand base The normalization uncertainty of the channel gain estimation difference stood, σ²For macrocell user, Femtocell user's receiving terminal is done Disturb power and background noise sum, n is the number of Femtocell user.

Further, in described step 102, the ranking factor ascending order arrangement of Femtocell user is specially：

The sortord of Femtocell user is：M₁≤M₂≤…≤M_K, wherein, M_KSequence for Femtocell user K The factor.

Further, for the Lagrangian tolerance factor of Femtocell user i (i=1 ..., K) in described step 103 α_iValue be：

Wherein, M_iRanking factor for Femtocell user i.

Lagrange for Femtocell user i (i=1 ..., K) judges factor-beta_iValue be：

Wherein, M_jFor Femtocell user j (j=1 ..., ranking factor i),Maximum interference for macrocell user Thresholding.

Further, described step 104 is specially：

If the Lagrangian tolerance factor α of Femtocell user K_KJudge factor-beta more than its Lagrange_K, then The Lagrange factor λ of Femtocell user is：

Wherein, M_iFor the ranking factor of Femtocell user i,Maximum interference threshold for macrocell user；

According to Lagrange factor, then the optimal robustness power of Femtocell user iFor：

Wherein,The estimation channel gain at the i of Femtocell base station servicing to its offer for Femtocell user i,Estimation channel gain for Femtocell user i to macro base station, ε_fRepresent that Femtocell user i provides service to it The normalization uncertainty of the channel gain estimation difference at the i of Femtocell base station, ε_mRepresent Femtocell user i to grand base The normalization uncertainty of the channel gain estimation difference stood, γ represent other all of Femtocell user j (j=1, 2 ..., n, j ≠ i) the same layer jamming power upper bound to Femtocell user's i receiving terminal, σ²For macrocell user pair The jamming power of Femtocell user's receiving terminal and background noise sum, n is the number of Femtocell user, and λ is The Lagrange factor of Femtocell user.

Further, described step 105 is specially：If the Lagrangian tolerance factor α of Femtocell user K_KLess Judge factor-beta in its Lagrange_K, then, the optimal robustness power of Femtocell user K is zero, and K-1 is assigned to K, return to step 104, the Lagrange factor to remaining K Femtocell user and optimal robustness power are configured.

Further, described non-ideal CSI model is not know description method based on spheroid to set up, and model is as follows：

Wherein,Represent Femtocell user i to the estimation channel providing for it at Femtocell base station i of service Gain,Represent Femtocell user i to macro base station estimation channel gain, △ g_i,iWith △ g_i,mCorresponding channel increases respectively Beneficial estimation difference, ε_fAnd ε_mRepresent △ g respectively_i,iWith △ g_i,mNormalization uncertainty, n be Femtocell user number.

Further, the thought according to robust optimization and the worst criterion mechanism, in view of channel gain estimation difference In the case of, using the optimal power control under channel gain worst case as the foundation of robust optimization problem, former optimization problem can It is written as a robust and optimizes Power Control Problem, be expressed as follows：

Advantages of the present invention and having the beneficial effect that：

The present invention, in the case of considering channel estimation errors, based on the thought of robust optimization and the worst criterion mechanism, incites somebody to action The Max-Min optimization problem of unlimited constraint is converted into the convex optimization problem of finite constraint, by the optimality bar of convex optimization problem Part, provides the closed solutions of the optimal robustness power of Femtocell user.There is channel estimation by mistake in method provided by the present invention In the case of difference, compare other traditional scheme strict guarantee QoS of macrocell user, strong to channel adaptability, especially suitable Close the two-layer Femtocell network under non-ideal CSI.Because algorithm has analytical expression, therefore execution speed is fast, has relatively Good feasibility and practicality.

Brief description

Fig. 1 is the up-link model that the present invention provides in preferred embodiment two-layer Femtocell network；

Fig. 2 is present invention ε in special screne_fChannel uncertainty ε when=0_mShadow to Femtocell user throughput Ring；

Fig. 3 is present invention ε in special screne_mChannel uncertainty ε when=0_fShadow to Femtocell user throughput Ring；

Fig. 4 is present invention ε in special screne_fChannel uncertainty ε when=0_mThe jamming power that macro base station is received Impact；

Fig. 5 is present invention ε in general scene_fChannel uncertainty ε when=0_mShadow to Femtocell user throughput Ring；

Fig. 6 is the schematic flow sheet of the present invention.

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, detailed Carefully describe.Described embodiment is only a part of embodiment of the present invention.

Technical scheme is as follows：

Optimal robustness Poewr control method under non-ideal CSI in the open two-layer Femtocell network of the present invention, including： Initialization Femtocell user's number, the same layer jamming power upper bound of Femtocell user, the sequence of Femtocell user because Son；Femtocell user is carried out ascending order arrangement by the ranking factor according to Femtocell user；Calculate Femtocell user's Lagrange judges the factor；Relatively the Lagrangian tolerance factor of Femtocell user and Lagrange judge that factor size is closed System, if condition meets, calculates Lagrange factor, provides optimal robustness power, method terminates；Otherwise, by ranking factor Maximum Femtocell user power is set to zero, and other Femtocell users continue according to the 4th step execution, until condition is full Foot, calculates Lagrange factor and the optimal robustness power of Femtocell user.The present invention considers in the worst channel gain Optimal robustness Power Control under estimation difference, sets up Femtocell user throughput and maximizes model, research channel gain is estimated The meter impact to network performance for the error.It is low that the present invention has a computation complexity, and channel adaptability is strong, can strict guarantee macrocellular use Family QoS, the advantage improving Femtocell user's total throughout, it is particularly suitable for the two-layer Femtocell network under non-ideal CSI.

The present embodiment is the optimal robustness power control scheme under non-ideal CSI in two-layer Femtocell network, at one In up two-layer Femtocell network, comprise 1 macro base station being located at macro cells center (0,0), 1 macrocellular is used Family, 5 are located at (120,70) respectively, (150, -120), (- 100, -200), (- 150,80), the Femtocell of (- 20,300) Base station, each Femtocell base station services 1 Femtocell user respectively.Macrocell user is randomly dispersed in macro base station In the range of 500m, Femtocell user is randomly dispersed in be provided in the range of the 30m of the base station of service for it, wherein, Femtocell user is accessed by the frequency spectrum of shared macrocell user.The tolerable maximum interference threshold of macrocell user isMacrocell user is to the jamming power of Femtocell user's i receiving terminal and background noise sum σ 2=10- 10W.Femtocell user i provides the average channel gain of Femtocell base station i of service to be to for it Femtocell user i to the average channel gain at macrocell base stations isWherein, | | represent absolute value, d_i,iAnd d_i,mBeing respectively Femtocell user i provides the Femtocell base station i of service and arrives to for it The distance of macro base station, h_i,iAnd h_i,mTo meet zero-mean, variance be respectively 1dB and 0.5dB multiple Gauss distribution, indoor path loss because Sub- α_i=3, the indoor path loss factor-alpha to outdoor_io=4, indoor linkFixing propagation loss κ_i=37dB, with f_MHzRelated κ_ioRepresent indoor and outdoor linkFixing propagation loss, f_MHz=2000MHz, κ_io=30log₁₀(f_MHz) -71dB, interior is arrived Outdoor subregion loss ξ=5dB.

With reference to above-mentioned instantiation to non-ideal CSI in a kind of two-layer Femtocell network of offer of the present invention Under elaborated based on the optimal robustness Poewr control method of robust optimization, the worst criterion mechanism and convex optimization thought：

(1) assume, in the case of preferable CSI, to meet the qos requirement of macrocell user so that Femtocell user handles up Measure maximized Power Control optimization method to be expressed as below：

Wherein, p_iFor the transmission power of Femtocell user i, p_jFor Femtocell user j (j=1,2 ..., n, j ≠ i) Transmission power, g_i,iFor the channel gain at Femtocell user i to the Femtocell base station i of its offer service, g_i,mFor Femtocell user i is to the channel gain of macro base station, g_j,iArrive for Femtocell user j (j=1,2 ..., n, j ≠ i) Channel gain at the i of Femtocell base station, σ²For macrocell user to the jamming power of Femtocell user's receiving terminal and the back of the body Scape noise sum,For the tolerable maximum interference threshold of macrocell user, n is the number of Femtocell user.Constraints In, C1 ensures that the QoS of macrocell user, C2 represent the nonnegativity of transmission power.

(2) in actual wireless communication system, typically it is difficult to obtain preferable CSI, need to consider that channel gain is estimated by mistake Difference.Because actual channel gain is typically in the uncertain region of some bounded, therefore, description is not known based on spheroid Method, sets up non-ideal CSI model as follows：

Wherein,Represent Femtocell user i to the estimation channel providing for it at Femtocell base station i of service Gain,Represent Femtocell user i to macro base station estimation channel gain, △ g_i,iWith △ g_i,mCorresponding channel increases respectively Beneficial estimation difference, ε_fAnd ε_mRepresent △ g respectively_i,iWith △ g_i,mNormalization uncertainty, n be Femtocell user number.

Meanwhile, other all of Femtocell user j (j=1,2 ..., n, j ≠ i) are to Femtocell user's i receiving terminal Jamming powerIt is in the interval of bounded, that is,Wherein, γ represents that other are all of The same layer jamming power upper bound to Femtocell user's i receiving terminal for the Femtocell user j (j=1,2 ..., n, j ≠ i).

In the uncertain regional extent of channel gain, handling capacity that Femtocell user calculates there is also not true Qualitative.Therefore, the thought according to robust optimization and the worst criterion mechanism, in the case of in view of channel gain estimation difference, Using the optimal power control under channel gain worst case as the foundation of robust optimization problem, former optimization problem can be written as one Robust optimizes Power Control Problem, is expressed as follows：

(3) robust based on the worst criterion mechanism optimizes thought, not true using same layer jamming power upper bound γ and normalization Surely spend ε_f、ε_m, below equation can be obtained：

Therefore, substitute into above equation, the problems referred to above can one finite constraint of conversion of equal value optimization problem, be expressed as follows：

Wherein,

Obviously, the object function in above-mentioned equation group is one with regard to p_iIncreasing function, so, the optimum of this optimization problem Value should be equal to maximum interference threshold in Femtocell user to the jamming power of macrocell userWhen obtain, therefore, above-mentioned Optimization problem is equivalent to following problem：

OrderOptimization problem of equal value as follows can be obtained：

Above-mentioned object function is with regard to p_iConvex function, meanwhile, constraints is linear constraints, it follows that Optimization problem of equal value is a convex optimization problem.Therefore, optimization problem of equal value can by lagrangian optimization method Lai Maximize following Lagrangian：

Wherein, λ and μ_iIt is the Lagrange factor under constraints.

Further, the Karush-Kuhn-Tucker condition of maximization Lagrangian problem is：

Obtain the closed solutions of Femtocell user's optimal robustness power by above-mentioned equation：

Wherein, There is provided at the Femtocell base station i of service to it for Femtocell user i Estimate channel gain,Estimation channel gain for Femtocell user i to macro base station, ε_fRepresent that Femtocell user i arrives It provides the normalization uncertainty of the channel gain estimation difference at the Femtocell base station i of service, ε_mRepresent To the normalization uncertainty of the channel gain estimation difference of macro base station, γ represents that other are all of to Femtocell user i The same layer jamming power upper bound to Femtocell user's i receiving terminal for the Femtocell user j (j=1,2 ..., n, j ≠ i), σ²For Macrocell user to the jamming power of Femtocell user's receiving terminal and background noise sum, n be Femtocell user Number, λ is the Lagrange factor of Femtocell user.

The Lagrange factor λ of Femtocell user is calculated from following equation：

Algorithm terminates.

In the present embodiment, Fig. 1 provides the up-link mould in preferred embodiment two-layer Femtocell network for the present invention Type, the frequency spectrum of in figure n Femtocell users to share macrocell user, macrocell user passes through to limit Femtocell user's Total interference to ensure the QoS of itself.Fig. 2 ε in special screne_fIt is respectively adopted Poewr control method and the basis of non-robust when=0 The Femtocell user throughput curve chart that embodiment method obtains；Fig. 3 gives ε in special screne_mAdopt respectively when=0 The Femtocell user throughput curve chart being obtained with Poewr control method and the present embodiment method of non-robust；Fig. 4 is in spy ε in different scene_fIt is respectively adopted reception at the macro base station that the Poewr control method of non-robust and the present embodiment method obtain when=0 Jamming power curve chart；Fig. 5 is ε in general scene_fChannel uncertainty ε when=0_mTo Femtocell user throughput curve Figure.From Fig. 2 and Fig. 3：Under special screne (γ=0), two methods obtain Femtocell user throughput all with Uncertainty ε_mOr ε_fIncrease and reduce, with ε_mOr ε_fIncrease, two methods obtain Femtocell user throughput Interval be gradually increased.As seen from Figure 4：Under special screne, institute's extracting method can be strict compared with the Poewr control method of non-robust Ensure the QoS of macrocell user, with ε_fIncrease, the interference receiving at the macro base station that the Poewr control method of non-robust obtains Power is gradually increased, and has exceeded maximum interference threshold.As seen from Figure 5：Under general scene (γ ≠ 0), institute's extracting method obtains Femtocell user throughput with uncertainty ε_mIncrease and reduce, this is identical with the trend in special screne, with When, the Femtocell user throughput that institute's extracting method obtains reduces with the increase of γ.Because institute's extracting method can obtain The closed solutions of Femtocell user's optimal robustness power, institute's extracting method can efficiently solve base in two-layer Femtocell network In relevant issues such as throughput-maximized robust power controls.

The above embodiment is interpreted as being merely to illustrate the present invention rather than limits the scope of the invention.? After the content of the record having read the present invention, technical staff can make various changes or modifications to the present invention, these equivalent changes Change and modify and equally fall into the scope of the claims in the present invention.

Claims (8)

1. the optimal robustness Poewr control method under non-ideal CSI in a kind of two-layer Femtocell network is it is characterised in that wrap Include following steps：

101st, initialize Femtocell user's number, the same layer jamming power upper bound of Femtocell user and Femtocell use The ranking factor at family；

102nd, the ranking factor ascending order of Femtocell user is arranged；

103rd, calculate the Lagrangian tolerance factor of each Femtocell user and Lagrange judges the factor；

If the Lagrange that the Lagrangian tolerance factor of 104 last Femtocell user is more than it judges the factor, Then the Lagrange factor of Femtocell user is equal to its Lagrange judgement factor, according to this Lagrange factor, is given Optimal robustness power, terminates；Otherwise jump to step 105；

If the glug that 105 last Femtocell user corresponding Lagrange tolerance factor is less than or equal to it is bright Day judge the factor, be then zero by the power setting of last Femtocell user, and go to step 104, to other The Lagrangian tolerance factor of Femtocell user and its Lagrange judge that the factor is compared, to the last one The Lagrangian tolerance factor of Femtocell user is more than its Lagrange and judges that factor condition meets, and calculates glug bright Day factor and optimal robustness power.

2. the optimal robustness Power Control side under non-ideal CSI in two-layer Femtocell network according to claim 1 Method is it is characterised in that initialize Femtocell user's number K=n, other all of Femtocell user j described in step 101 (j=1,2 ..., n, j ≠ i) same layer jamming power upper bound γ to Femtocell user's i receiving terminal, Femtocell user i's Ranking factor M_i：

$M_i=\frac{{\stackrel{\‾}{g}}_{i,m}(1+{\mathrm{\ϵ}}_m)(\mathrm{\γ}+{\mathrm{\σ}}^2)}{{\stackrel{\‾}{g}}_{i,i}(1-{\mathrm{\ϵ}}_f)},(i=1,2...,n)$

Wherein,The estimation channel gain at the i of Femtocell base station servicing to its offer for Femtocell user i,For Femtocell user i is to the estimation channel gain of macro base station, ε_fRepresent that Femtocell user i provides service to it The normalization uncertainty of the channel gain estimation difference at the i of Femtocell base station, ε_mRepresent Femtocell user i to grand base The normalization uncertainty of the channel gain estimation difference stood, σ²For macrocell user, Femtocell user's receiving terminal is done Disturb power and background noise sum, n is the number of Femtocell user.

3. the optimal robustness Power Control side under non-ideal CSI in two-layer Femtocell network according to claim 2 Method is it is characterised in that be specially the ranking factor ascending order arrangement of Femtocell user in described step 102：

The sortord of Femtocell user is：M₁≤M₂≤…≤M_K, wherein, M_KRanking factor for Femtocell user K.

4. the optimal robustness Power Control side under non-ideal CSI in two-layer Femtocell network according to claim 2 Method is it is characterised in that for the Lagrangian tolerance factor α of Femtocell user i (i=1 ..., K) in described step 103_i Value be：

${\mathrm{\α}}_i=\frac{1}{ln2M_i}$

Wherein, M_iRanking factor for Femtocell user i.

Lagrange for Femtocell user i (i=1 ..., K) judges factor-beta_iValue be：

${\mathrm{\β}}_i=\frac{i}{ln2(I_m^{th}+{\mathrm{\Σ}}_{j=1}^i{M}_j)}$

Wherein, M_jFor Femtocell user j (j=1 ..., ranking factor i),Maximum interference threshold for macrocell user.

5. the optimal robustness Power Control side under non-ideal CSI in two-layer Femtocell network according to claim 4 Method is it is characterised in that described step 104 is specially：

If the Lagrangian tolerance factor α of Femtocell user K_KJudge factor-beta more than its Lagrange_K, then The Lagrange factor λ of Femtocell user is：

$\mathrm{\λ}=\frac{K}{ln2(I_m^{th}+{\mathrm{\Σ}}_{i=1}^K{M}_i)}$

Wherein, M_iFor the ranking factor of Femtocell user i,Maximum interference threshold for macrocell user；

According to Lagrange factor, then the optimal robustness power of Femtocell user iFor：

$p_i^{*}=\frac{1}{ln2\mathrm{\λ}{\stackrel{\‾}{g}}_{i,m}(1+{\mathrm{\ϵ}}_m)}-\frac{\mathrm{\γ}+{\mathrm{\σ}}^2}{{\stackrel{\‾}{g}}_{i,i}(1-{\mathrm{\ϵ}}_f)},(i=1,...,n)$

Wherein,The estimation channel gain at the i of Femtocell base station servicing to its offer for Femtocell user i,For Femtocell user i is to the estimation channel gain of macro base station, ε_fRepresent that Femtocell user i provides service to it The normalization uncertainty of the channel gain estimation difference at the i of Femtocell base station, ε_mRepresent Femtocell user i to grand base The normalization uncertainty of the channel gain estimation difference stood, γ represent other all of Femtocell user j (j=1, 2 ..., n, j ≠ i) the same layer jamming power upper bound to Femtocell user's i receiving terminal, σ²For macrocell user pair The jamming power of Femtocell user's receiving terminal and background noise sum, n is the number of Femtocell user, and λ is The Lagrange factor of Femtocell user.

6. the optimal robustness Power Control side under non-ideal CSI in two-layer Femtocell network according to claim 4 Method is it is characterised in that described step 105 is specially：If the Lagrangian tolerance factor α of Femtocell user K_KIt is not more than Its Lagrange judges factor-beta_K, then, the optimal robustness power of Femtocell user K is zero, and K-1 is assigned to K, Return to step 104, the Lagrange factor to remaining K Femtocell user and optimal robustness power are configured.

7. the optimal robustness Power Control side under non-ideal CSI in two-layer Femtocell network according to claim 1 , it is characterised in that described non-ideal CSI model is not know description method based on spheroid to set up, model is as follows for method：

$g_{i,i}={\stackrel{\‾}{g}}_{i,i}+{\mathrm{\Δg}}_{i,i},\left|{\mathrm{\Δg}}_{i,i}\right|\≤{\mathrm{\ϵ}}_f{\stackrel{\‾}{g}}_{i,i},(i=1,...n)$

$g_{i,m}={\stackrel{\‾}{g}}_{i,m}+{\mathrm{\Δg}}_{i,m},\left|{\mathrm{\Δg}}_{i,m}\right|\≤{\mathrm{\ϵ}}_m{\stackrel{\‾}{g}}_{i,m},(i=1,...n)$

Wherein,Represent Femtocell user i to the estimation channel gain providing for it at Femtocell base station i of service,Represent Femtocell user i to macro base station estimation channel gain, △ g_i,iWith △ g_i,mCorresponding channel gain is estimated respectively Meter error, ε_fAnd ε_mRepresent △ g respectively_i,iWith △ g_i,mNormalization uncertainty, n be Femtocell user number.

8. the optimal robustness Power Control side under non-ideal CSI in two-layer Femtocell network according to claim 7 Method it is characterised in that according to the thought of robust optimization and the worst criterion mechanism, in the situation in view of channel gain estimation difference Under, using the optimal power control under channel gain worst case as the foundation of robust optimization problem, former optimization problem can be written as One robust optimizes Power Control Problem, is expressed as follows：

$\max \min \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\log }_2\left(1+\frac{p_i\left({\stackrel{\‾}{g}}_{i,i}+{\mathrm{\Δg}}_{i,i}\right)}{\underset{j=1,j\≠i}{\overset{n}{\mathrm{\Σ}}}{p}_j{g}_{j,i}+{\mathrm{\σ}}^2}\right)$

$s.t.\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{p}_i({\stackrel{\‾}{g}}_{i,m}+{\mathrm{\Δg}}_{i,m})\≤I_m^{th}$

$p_i\≥0,\∀i\∈\{1,2...,n\}.$