 Research
 Open Access
Uplink interference mitigation for heterogeneous networks with userspecific resource allocation and power control
 Wei Xu^{1}Email author and
 Hong Zhang^{1}
https://doi.org/10.1186/16871499201455
© Xu and Zhang; licensee Springer. 2014
 Received: 8 September 2013
 Accepted: 30 March 2014
 Published: 10 April 2014
Abstract
This paper investigates interference mitigation for an uplink heterogeneous network (HetNet) with universal frequency reuse. In this study, we propose a userspecific resource allocation as well as a power control scheme for the uplink HetNet. With this scheme, the mobile users are grouped into two different groups according to their evaluated signaltoleakageplusnoise ratio (SLNR) metric. By dividing users into two groups, the primal nonconvex resource allocation problem can be casted to two subproblems. For the ‘good users’ with high SLNR value, the formulated nonconvex optimization problem which focuses on maximizing the system capacity is transformed into a standard geometric programming (GP) convex power optimization problem. For the other ‘interfering users’ with low SLNR values, we develope a semiorthogonal resource block (RB) allocation strategy for interference control. Simulation results show that most of the severe intercell interference can be removed by the semiorthogonal RB allocation scheme and the optimal power allocation of interfering users contributes to a better overall system capacity.
Keywords
 Heterogeneous network
 Interference mitigation
 Userspecific power control
 Geometric programming
1 Introduction
The spectrum efficiency is significantly improved in longterm evolution (LTE)/LTE Advanced by exploiting universal frequency reuse with multipleinput multipleoutput (MIMO) and orthogonal frequency division multiplexing (OFDM). However, facing the explosive data demands, pure macro coverage can hardly meet the increasing requirements. A latest evolution of cellular networks, namely heterogeneous networks (HetNet), has been well acknowledged as an effective way of balancing the highdata rate requirements with low complexity. A HetNet consists of a large number of small cells, including microcells, picocells, and femtocells underlaying regular macrocells [1, 2]. As macrocells and small cells share the same frequency resource, mobile users who dynamically associate with macro/small cell stations can benefit a lot from small cell deployments.
As the aggressive frequency reuse is used, even in homogeneous LTE cellular systems, intercell interference has been a major factor that limits the entire network performance. A number of ways have been proposed for intercell interference coordination (ICIC) in different systems [3]. In current homogeneous cellular systems, the thirdgeneration partnership project (3GPP) has proposed to balance the network performance and intercell interference by exploiting proper frequency reuse patterns, instead of the universal frequency reuse strategy. Two popular frequency assignment patterns are known as fractional frequency reuse (FFR) [4] and soft frequency reuse (SFR) [5].
HetNet has been a promising technique for future wireless cellular networks. Unfortunately, unplanned small cell deployments lead to the unprecedented challenges in terms of intercell interference control [6]. In a downlink HetNet, for instance, a picocell station causes severe interference to a macrocell user (MUE) in the proximity of the picocell coverage. Similarly for an uplink HetNet, the cochannel interference between macro and small cells also exists, and it becomes an essential concern which limits the entire network performance. In order to deal with the more severe and complicated interference problems, enhanced intercell interference coordination (eICIC) techniques have been proposed by both industrial and academic researchers. In [7], cell range expansion (CRE) is developed for balancing the macro and picocell performance without any new spectrum available. However, the users associated with the picocell in the expanded region suffer severe downlink interference from the macro base station (BS). To mitigate this problem, a specific subframe called almost blank subframe (ABS) is introduced in [8, 9] at the macrocell transmission durations. The duration of ABS is left for picocell stations to schedule its celledge users; hence, the picocell users (PUE) is rarely affected by the macrocell interference. It is obvious that the benefits of PUEs are obtained at a cost of MUE performance. Moreover, in order to maintain the macrocell performance, carrier aggregation (CA)based interference control strategies are proposed by exploiting a new spectrum resource [10].
Most of the abovementioned techniques are specified for downlink HetNets. In a traditional uplink system, fractional power control (FPC) [11] is a typical scheme for uplink channels. However, the FPC is usually applied in homogeneous networks while it is shown not effective enough in HetNets. In [12], a cellspecific power control strategy was proposed for a special kind of uplink HetNet composing of a macrocell and a femtocell. It adaptively chose specified reference power P_{0} for femto stations near or far from the macro station. Differently in [13], opportunistic power control schemes were proposed with both centralized sensing and distributed sensing strategies in order to maintain the outage requirements. The performance was evaluated under different settings of user outage requirements. Both studies [12] and [13] assumed a closed subscriber group which allows access only to a limited number of authorized terminals. For an open accessed uplink HetNet, a closedloop power control scheme as well as cell range expansion was considered in [14] with performance evaluation under different CRE offsets and P_{0} values for FPC.
With the abovementioned works, however, few has considered designing adaptive interference control for different users. This could be an essential problem especially for HetNets. In a HetNet, users generally experience a large variety of interference levels depending on their associations, locations, and adjacent traffic loads for the uplinks. Therefore, it is natural to consider userspecified interference control strategies for an uplink HetNet. In this paper, we study a userspecific resource allocation as well as power control scheme based on user grouping to mitigate uplink interference in HetNets. With this method, all users in each cell are divided into groups according to a signaltoleakageplusnoise ratio (SLNR) metric [15, 16], that is, the users are labelled as cellcenter users and celledge users. The power control optimization problem for cellcenter users is transformed to a geometric program (GP) formulation. While for the celledge users from different cells, they share a δsemiorthogonal resource blocks (RBs) assignment with fixed power control. A system level simulator is constructed to verify the proposed scheme. This userspecific resource allocation as well as power control scheme is shown effective in mitigating the intercell interference and improving the entire network performance.
The remainder of this paper is organized as follows: Section 2 briefly reviews the existing mechanism of FPC for uplink power control. Section 3 describes the HetNet under consideration, and then Section 4 presents the proposed power control and resource allocation strategy. In Section 5, computer simulation results are provided. Finally, conclusions are drawn in Section 6.
2 Review of FPC mechanism
where P_{max} is the maximum transmit power allowed at user k, P_{0} is a target UE received power, α is the path loss compensate factor, P_{loss,k} is the estimated downlink path loss from the user k to its serving BS, and N_{ l } is the number of RBs assigned to the kth uplink user in a cell l. According to [18], P_{0} is an integral value selected from the set {−126,…,24 dBm} and a typical value of α is within the set of {0.4,0.5,0.6,0.7,0.9,1.0}.
The FPC has been proven effective in conventional uplink homogeneous networks. In an uplink HetNet, however, the FPC strategy is not always suitable due to the randomly deployed small cells underlaying the macro coverage. If an MUE at the cell edge adjusts its transmit power according to the FPC rule, the users associated with nearby small cells can be severely influenced due to the increased cochannel interference. Moreover, since the CRE is used in HetNet for a balanced user association, the FPC does not work well for all users due to their cell associations with different tiers of cells and respective CRE bias values. Therefore, to enhance the throughput performance of the uplink HetNet, in the following, we will consider the uplink interference control by developing a userspecific resource allocation as well as power control strategy.
3 System model and problem formulation
where w_{ l } is the weighting factor with respect to the achievable rate corresponding to different cells and N_{ l }=⌈N/K_{ l }⌉, ∀l∈{0,1,…,L} is the maximum allowed number of RBs allocated to each user in the lth cell. Note that the first constraint of problem (4) assumes for simplicity that the maximum power spectrum of a single user is uniformly constrained with ${P}_{\text{max}}^{l}$ across the allocated RBs. We let ${P}_{\text{max}}^{l}={P}_{\text{max}}/{N}_{l}$ so that the total power constraint of P_{max} is always satisfied.
Although with the above assumption, the problem (4) is inherently a nonconvex problem with integer constraints. Generally, it is not easy to handle the integer constraints with globally optimal solution using linear complexity. Moreover, the sum rate maximization object depends on a complex variable in terms of the SINR. The SINR as shown in (2) and (3) is a coupled function with respect to not only the power and RB allocation to the user itself but the resources allocated to other users. In order to make the problem tractable with reasonably good solutions, in the following, we will simplify the problem by presenting a userspecific power and RB allocation algorithm for the HetNet.
4 Userspecific resource allocation and power control
It has been stated that the primal problem of (4) is difficult to solve with efficient approaches, especially in largescale HetNet with both macrocells and a number of pico/femtocells. To deal with the problem, the main job is to handle the intercell interference and to find a balance between the complexity of interference control and entire network performance. In this section, we resort to solving (4) via decomposing the problem into two subproblems under different user experiences. Then, we can address the uplink interference problem via designing a userspecific power and resource allocation strategy.
As for the users suffering severe interference from adjacent cells, the power control itself with full frequency reuse may not be suitable for well controlling the interference. Meanwhile, if the user’s uplink transmission causes severe interference to other user channels, the interfering user may also need to use an orthogonal frequency band instead of sharing with others. Otherwise, if the user is in the proximity of its serving cell station, it can share the allocated frequency band with other users since the mutual interference could be ignorable. The basic idea of our proposed algorithm is outlined as follows:

In the HetNet, each user is specified with both the interference it suffers and its caused interference to others. According to the evaluation, the users will be classified as ‘good users’ and ‘interfering users’.

For the good users, a specified power allocation scheme is presented via using geometric programming (GP) [19] as well as a universal frequency reuse strategy.

For the interfering users, frequency reuse may not be able to achieve better performance than regular frequency partition approach, especially when there are a large number of interfering users around. A δsemiorthogonal RB assignment is thus presented for these interfering users while letting them use an aggressive maximum transmit power.
With the above strategy applied, all users are classified into two groups referred to as good users and interfering users. This kind of user classification is different from the user classification in homogeneous multicell networks in that both its suffered interference and the interference it caused to other users are taken into account. In the following, the metric and procedure of the user grouping are firstly detailed, and then the details of the userspecific resource allocation and power control strategy are elaborated.
4.1 User classification under HetNet
Note that when we evaluate the SLNR metric ${\eta}_{k}^{l}$ for a user k associated with cell l, the initially allocated power ${p}_{k}^{l}$ can be chosen by the conventional uplink power control formula or just simply ${P}_{\text{max}}^{l}$. Given a predetermined value ε_{ l } as the SLNR threshold for users in the lth cell, users are then classified into two different groups.

For users with ${\eta}_{k}^{l}\ge {\epsilon}_{l}$: All these users can be treated as good users within the lth cell. The good users have good enough signal power while causing very limited intercell interference, hence resulting in a large SLNR value. Specifically for the good users, we let all cells share the same RBs for them due to their low intercell interference and relatively large signal strength. Note that we set different SLNR thresholds for different kinds of cells, i.e., macro and picocells. This configuration is reasonable and necessary for a practical HetNet because the transmit power and user topology of users are quite different for a macrocell user and a pico/femtocell user.

For users with ${\eta}_{k}^{l}\le {\epsilon}_{l}$: These users are treated differently as interfering users. The low SLNR evaluation implies that the users have either or both of the two characterizations: (1) experiencing low useful signal strength due to large distance between the user and its associated cell station; (2) causing severe interference to adjacent cells.
4.2 Userspecific heuristic RB allocation
Given the users have been classified as two groups, we divide the entire frequency band into two orthogonal parts dedicated for the user groups. More specifically, the first part of the overall spectrum is reserved for the good users, while the rest part of the spectrum is reserved for the interfering users. Specified for the good users, the dedicated frequency spectrum in terms of RBs is equally assigned to the users within each cell. Meanwhile for the interfering users, the users from different cells will be paired as a δelement group which has no more than δ users sharing the same RB among all, and the RBs will be allocated to the δelement user group in a sequential way.
 1.
Initialize ${P}_{\text{max}}^{l}={P}_{\text{max}}/{N}_{l}$, where N _{ l } is the average number of RBs assigned to a single user, i.e., the number of RBs reserved for interfering users divided by the number of interfering users in the lth cell.
 2.
For each cell l, we first select a subset of users which have the least number of assigned RBs in the lth cell, and this user subset may have one or more users according to the selection criterion. Subsequently, we choose the user with the maximum SLNR value from the user subset. The user is denoted by k ^{ l }. Initialize the user group with $\mathcal{\mathcal{M}}=\left\{{k}^{l}\right\}$; the corresponding cells with users selected in is initialized by $\mathcal{\mathcal{L}}=\left\{l\right\}$.
 3.Calculate the current achievable rate as${R}_{M}=log\left(1+\frac{{P}_{\text{max}}^{l}{h}_{{k}^{l}}^{l}}{{\sigma}^{2}}\right).$
 4.If the cardinality $\left\mathcal{\mathcal{M}}\right<\delta $ or equivalently $\left\mathcal{\mathcal{L}}\right<\delta $, find the least interfered cell c according to$c=arg\phantom{\rule{1em}{0ex}}\underset{c\in {\mathcal{\mathcal{L}}}^{\perp}}{\text{min}}\sum _{u\in \mathcal{\mathcal{M}}}{g}_{u}^{c}$
where ${\mathcal{\mathcal{L}}}^{\perp}$ represents the complementary set of cells in , and ${g}_{u}^{c}$ denotes the interference channel from user u to cell c. Else, stop.
 5.For each user u in cell c, calculate the updated achievable rate with user u involved in the group. It gives${R}_{u}=\sum _{i\in \mathcal{\mathcal{M}}\cup \left\{u\right\}}log\left(1+\frac{{P}_{\text{max}}^{l}{h}_{i}}{{\sum}_{k\in \mathcal{\mathcal{M}}\cup \left\{u\right\},k\ne i}{P}_{\text{max}}^{l}{g}_{k}^{i}+{\sigma}^{2}}\right).$
 6.
If R _{ u }≥R _{ M } for any user u in cell c, update $\mathcal{\mathcal{M}}=\mathcal{\mathcal{M}}\cup \left\{u\right\}$, the corresponding , and the achievable rate R _{ M }=R _{ u }. Else, stop.
 7.
Go back to step 4.
4.3 Userspecific power control under fixed RB allocation
where the user index k corresponds to the assigned user in cell l at the nth RB. From the above formulation, it is readily observed that the problem is still difficult to solve due to its nonconvexity. Actually, even the problem of power control for a simple singlecell interference channel has not been well investigated with efficient solution. In order to make the problem tractable, we recall the above design philosophy with userspecific power control strategies.
Thus far, the above problem is a standard GP which definitely is a convex optimization problem. Hence, it is easy to achieve the optimal power control solution via efficient computations like interior point method [21]. Note that some popular optimization tools including cvx [22] and sedumi [23] can be directly utilized for solving the convex optimization problems GP very efficiently.
5 Simulation results
In this section, we constructed a system level simulator for evaluating the performance of our proposed resource allocation as well as power control strategy for the uplink HetNet. Detailed system parameters of our simulator is summarized in Table 1. Moreover, for comparison, we tested four different strategies as follows:

Scheme (1): With this scheme, all cells share the entire frequency band and each user transmits with its maximum allowed power P_{max}. It is referred to as ‘Pmax’.

Scheme (2): This is a benchmark scheme for our study, namely the traditional uplink power control referred to as ‘FPC’.

Scheme (3): In order to focus on the advantage of our proposed resource allocation scheme. We tested the third scheme as our proposed RB allocation strategy while using the traditional FPC for the uplink power control of all users. This scheme is referred to as ‘ProposedFPC’.

Scheme (4): This scheme is our proposed interference control strategy in this work. Userspecific resource allocation strategy is presented with GPbased power control. The scheme is referred to as ‘ProposedGP’.
Simulation parameters
Cell type  

Macrocell  Picocell  
Cellular layout  1 macrocell site  4 picocells per cell 
without sectorization  
Macrocell radius (ISD)  500 m  
Bandwidth  50 RBs (10 MHz)  50 RBs (10 MHz) 
Carrier frequency  2.0 GHz  2.0 GHz 
Path loss  128.1+37.6 log10(d) dB  140.7+36.7 log10(d) dB 
Shadowing deviation  8 dB  10 dB 
Fast fading  Rayleigh fading  Rayleigh fading 
Noise figure  5 dB  13 dB 
Antenna gain  14 dBi  5 dBi 
Antenna type  Omnidirectional  Omnidirectional 
UE configuration  30 UEs per cell  10/20 UEs per cell 
Uniformly dropped  Uniformly dropped  
eNB Tx power  46 dBm  30 dBm 
UE Tx power P_{max}  23 dBm  23 dBm 
Traffic model  Full buffer  Full buffer 
Cell association  Biasbased cell range expansion  Biasbased cell range expansion 
Bias value  0 dB  4 dB 
Simulation loops  20 drops  20 drops 
500 loops per drop  500 loops per drop  
Fractional  P_{0}=−80 dBm  P_{0}=−60 dBm 
Power control  α=0.8  α=0.6 
UEspecific joint  RBs reserved for good users (70%)  
RB allocation and  RBs reserved for interfering users (30%)  
power control  User classification: SLNR threshold selected  
(proposed scheme)  according to the percentage 70%/30% 
Before presenting the simulation results, we first give a brief elaboration on system level simulation. For simplicity, we focused on the performance of a macrocell with four pico stations randomly located within the macro coverage. Generally, in order to evaluate the average user performance, the simulation results are collected from 20 drops and averaging over 500 loops within each drop. For each drop test, a number of users (10 users or 20 users as specified) are uniformly located within the cell coverage. Under this circumstance of a single drop, the user performance is evaluated using four different resource allocation and power control schemes for comparison. The user performance is obtained via MonteCarlo simulation for 500 channel realizations, commonly say 500 loops. In particular for each loop, we generate channel coefficients according to the Rayleigh fading distribution for each and every link between UE terminals and macro/pico stations. Note that the user performance is averaged over 500 channel realizations to remove the fluctuation due to fast fading. Finally, the user CDF is evaluated for all PUEs and MUEs for 20 drops. In this way, the performance by different schemes can be fairly compared under different user locations.
Performance comparison with 10 PUEs
Scheme  

(1)  (2)  (3)  (4)  
Macrocell (Mbps)  Cell capacity  13.8  6.8  11.6  10.3 
Cell coverage  0.0122  0.0067  0.0076  0.0094  
Picocell (Mbps)  Cell capacity  74.7  79.6  80.3  85.4 
Cell coverage  1.88  2.61  2.22  2.07  
All cells (Mbps)  Cell capacity  312.4  329.6  332.8  352.3 
Gain  0%  5.2%  6.5%  12.8% 
Performance comparison with 20 PUEs
Scheme  

(1)  (2)  (3)  (4)  
Macrocell (Mbps)  Cell capacity  10.9  5.7  13.2  14.6 
Cell coverage  0.0087  0.0039  0.0068  0.0073  
Picocell (Mbps)  Cell capacity  80.2  87.3  90.1  96.6 
Cell coverage  1.55  2.14  1.14  0.78  
All cells (Mbps)  Cell capacity  331.7  354.9  373.6  401.0 
Gain  0%  7.0%  12.6%  20.9% 
Performance with different goodtointerfering user ratios for 10 PUEs
Scheme  

(1)  (2)  (3)  (4)  
90%/10%  MUE average (Mbps)  0.471  0.023  0.142  0.137 
PUE average (Mbps)  7.465  7.956  8.332  8.804  
80%/20%  MUE average (Mbps)  0.471  0.023  0.262  0.214 
PUE average (Mbps)  7.465  7.956  8.134  8.640  
70%/30%  MUE average (Mbps)  0.471  0.023  0.387  0.346 
PUE average (Mbps)  7.465  7.956  8.016  8.501  
60%/40%  MUE average (Mbps)  0.471  0.023  0.643  0.616 
PUE average (Mbps)  7.465  7.956  7.570  7.932  
50%/50%  MUE average (Mbps)  0.471  0.023  0.801  0.787 
PUE average (Mbps)  7.465  7.956  7.338  7.445 
6 Conclusions
In this paper, an uplink interference mitigation with userspecific power control and RB allocation scheme is presented for uplink heterogeneous networks. The entire user pool is classified as two groups, and each group of users is specified with optimized RB allocation as well as power control strategy for interference control. Simulation results verify that the proposed scheme can achieve a better performance in terms of both the entire network throughput and the cell edge performance. Our proposed scheme is effective in noticeably improving the picocell performance especially when there are a large number of users suffering severe mutual interference.
Appendix
At this step, by applying some basic manipulations, the above problem can be finally casted to a standard form of GP which is readily (8) as desired.
Declarations
Acknowledgements
The authors would like to thank the reviewers for their helpful comments which have greatly improve the quality of this paper. This work was supported by the 973 Program under 2013CB329204, the NSFC under 61101087, the SRFDP under 20110092120011, and the Important National Science & Technology Specific Projects 2013ZX03003016.
Authors’ Affiliations
References
 A Damnjanovic: A survey on 3GPP heterogeneous networks. IEEE Wireless Commun 2011, 18(3):1021.View ArticleGoogle Scholar
 V Chandrasekhar: Femtocell networks: a survey. IEEE Commun. Mag 2008, 46(9):5967.View ArticleGoogle Scholar
 B Soret: CRS interference cancellation in heterogeneous networks for LTEadvanced downlink. In Proceedings of the IEEE International Conference on Communications (ICC). IEEE, Piscataway 2012; June 2012:67976801.Google Scholar
 M AlShalash: Interference constrained soft frequency reuse for uplink ICIC in LTE networks. In Proceedings of the IEEE International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC). IEEE, Piscataway; 2010:18821887.View ArticleGoogle Scholar
 F Wamser: Soft frequency reuse in the uplink of an OFDMA network. In Proceedings of the IEEE Vehicular Technology Conference (VTCSpring). IEEE, Piscataway; 2010:15.Google Scholar
 V Pauli: Heterogeneous LTE networks and intercell interference coordination. Nomor Research Whitepapers Dec 2010 . Accessed 1 June 2013 http://www.nomor.de/uploads/a4/81/a4815c4dc585be33c81f0ec7a15deed7/201012WhitePaper_LTE_HetNet_ICIC.pdfGoogle Scholar
 İ Güvenc: Capacity and fairness analysis of heterogeneous networks with range expansion and interference coordination. IEEE Commun. Lett 2011, 15(10):10841087.View ArticleGoogle Scholar
 J Pang: Optimized timedomain resource partitioning for enhanced intercell interference coordination in heterogeneous networks. In Proceedings of the IEEE Wireless Communication and Networking Conference (WCNC). IEEE Piscataway; 2012:16131617.Google Scholar
 G de la Roche, D LópezPérez: Enhanced intercell interference coordination challenges in heterogeneous networks. IEEE Wireless Commun. Mag 2011, 18(3):2230.View ArticleGoogle Scholar
 GX Yuan: Carrier aggregation for LTEadvanced mobile communication systems. IEEE Commun. Mag 2010, 48(2):8893.View ArticleGoogle Scholar
 A Simonsson: Uplink power control in LTE  overview and performance, subtitle: principles and benefits of utilizing rather than compensating for SINR variations. In Proceedings of the IEEE Vehicular Technology Conference (VTCFall). IEEE, Piscataway; 2008:15.Google Scholar
 J Gora: Cellspecific uplink power control for heterogeneous networks in LTE. In Proceedings of the IEEE Vehicular Technology Conference (VTCFall). IEEE Piscataway; 2010:15.Google Scholar
 MS Jin: Per cluster based opportunistic power control for heterogeneous networks. In Proceedings of the IEEE Vehicular Technology Conference (VTCSpring). IEEE, Piscataway; 2011:15.Google Scholar
 A Morimoto: Investigation on transmission power control in heterogeneous network employing cell range expansion for LTEAdvanced uplink. In European Wireless Conference. Poznan: IEEE, Piscataway; 2012.Google Scholar
 M Sadek: A leakagebased precoding scheme for downlink multiuser MIMO channels. IEEE Trans. Wireless Commun 2007, 6(5):17111721.View ArticleGoogle Scholar
 H Shen: Joint transmit and receive beamforming for MIMO downlinks with channel uncertainty. IEEE Trans. Veh. Tech 2013, PP(99):1.Google Scholar
 3GPP: EUTRAphysical layer procedures. TS 36.213 v8.8.0., European Telecommunications Standards Institute 2009, 178.Google Scholar
 3GPP: EUTRA–MAC protocol specification. TS 36.321 v9.0.0., European Telecommunications Standards Institute 2009, 148.Google Scholar
 S Boyd: A tutorial on geometric programming. Optim. Eng 2007, 8: 67127. 10.1007/s1108100790017MathSciNetView ArticleMATHGoogle Scholar
 M Chiang: Power control by geometric programming. IEEE Trans. Wireless Commun 2007, 6(7):26402651.View ArticleGoogle Scholar
 S Boyd: Convex Optimization. Cambridge: Cambridge University Press; 2004.View ArticleGoogle Scholar
 M Grant: Matlab software for disciplined convex programming, v2.0 beta, Sep 2013. 2013.http://cvxr.com/cvx . Accessed 1 OctGoogle Scholar
 JF Sturm: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones Optimization Methods Softw. 11–12. 1999, 625653.http://sedumi.ie.lehigh.edu/Google Scholar
 P Viswanath: Opportunistic beamforming using dumb antennas. IEEE Trans. Inform. Theory 2002, 48(6):12771294. 10.1109/TIT.2002.1003822MathSciNetView ArticleMATHGoogle Scholar
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