Shadow Chasing Enhancement in Resource Allocation For Heterogeneous Networks

Transcription

1 Shadow Chasing Enhancement in Resource Allocation For Heterogeneous Networs Ahmed R. Elsherif, Zhi Ding, Xin Liu, and Jyri Hämäläinen University of California, Davis, California Aalto University, Espoo, Finland Abstract In this paper 1, we propose an enhancement to a resource allocation scheme nown as shadow chasing for interference mitigation in heterogeneous networs composed of Macrocell User Equipments MUEs and Home User Equipments HUEs. In shadow chasing, the Home enb HeNB uses Downlin Control Information DCI together with the overheard ACK/NAK feedbac and CQI reports to assign its HUEs the Physical Resource Blocs PRBs that are assigned to outdoor MUEs. Since the HeNB receives an outdated DCI due to bachaul delay, our solution is to derive a lielihood metric for each PRB being either empty or assigned to an outdoor MUE by using a MC model for the state of each PRB. By dynamically separating the MUE and HUE PRB assignments, enhanced shadow chasing can better constrain the downlin interference to the MUE. Our results show effective reduction of probability of PRB assignment collision and MUE interference compared to schemes that do not integrate the delay effect or exploit user feedbacs. I. INTRODUCTION Recent studies have shown that indoor usage maes up more than 50% of voice calls and more than 70% of wireless data traffic [1]. Instead of re-deploying cellular base stations wherever users may congregate, a femtocell indoor base station can be deployed as a plug-and-play user device to connect a registered group of indoor subscribers at a high speed and low power by reusing the same spectrum occupied by an existing cellular macrocell base station [2]. Using commercial Digital Subscriber Line DSL or cable modem as a bachaul channel, plug-and-play femtocells improve indoor signal quality and reduce co-channel interference by using very low power. The concept of heterogeneous networing, and femtocells in particular, has been already proposed in the standardization process for next generation communication systems such as LTE, LTE-A, and WiMAX [3]. The main challenge of femtocell-macrocell deployments is interference management due to spectrum sharing of timefrequency physical resource blocs PRBs between femtocells and macrocells. HetNet is a natural evolution from the rigid cell coverage to a more flexible and better radio coverage. Cooperative HetNet focuses on resource allocation and channel access of multiple networs simultaneously to achieve maximum throughput and high spectrum utility. It can be viewed as a special case and intelligent form of cognitive networing. The concept of 1 This material is based on wors supported by the National Science Foundation under Grants and The material was also supported in part by Academy of Finland under grant cognitive radio typically refers to radio units having the ability to sense the environment and to adapt its frequency, power, and transmission schemes. This subject has attracted much research interest e.g., see [4] for an overview. In cognitive radio framewor, the MUE may be viewed as the primary user PU that demands rate assurance, whereas the HUE acts as the secondary user SU. Many wors exist in this context, specifically for sensing-based dynamic access strategies. In [5] the PU is not aware of SU activity whereas the SU can access any available channel except the one occupied by the PU. In addition to sensing, several interesting wors utilize feedbac information to improve SU performance. For example, in [6], the SU uses ACK/NAK response from the PU receivers to estimate the PU status. Femtocell resource management also attracted noticeable recent interests. Several mechanisms have been considered, including downlin power control [7], MIMO beamforming through precode matrix index selection [8], and interference avoidance by overhearing MUE resource bloc allocation information [9]. Femtocell interference management can be considered as a special case of HetNet resource management. In [10], the authors proposed an adaptive power control technique to limit the transmission power of femtocells in order to maximize frame utilization. In [11], the authors considered probabilistic assignment of PRBs by the HeNB for uplin where the HUE is assigned a higher access probability to those PRBs occupied by outdoor MUEs. Such schemes require HeNBs to acquire MBS control signals in a timely manner. Furthermore, both HeNB and MBS need to correctly classify MUEs as indoor versus outdoor user equipments UEs. In this wor, we advance beyond the basic cognitive paradigm of sensing before transmitting, which relies purely on spectral channel sensing to avoid collision with primary transmissions. Our wor in HetNet is based on a more advanced framewor that facilitates HetNet cooperation by controlling secondary networs according to a variety of data lin control information from primary networs. Such feedbac mechanisms for lin adaptation are available in most recent cellular systems such as LTE and WiMAX. Exploiting feedbac information has some advantages over the more traditional techniques proposed for HetNet systems. It provides a direct indication for the cumulative interference at the MUE and thus allows the HUEs to exploit the extra capacity of the system. Using the feedbac in the femtocells context is practical as they are now within the same operator which

2 maes it easy to access the macrocell information. The rest of the paper is organized as follows: In Section II, we summarize the basic idea of the previously proposed shadow chasing method. The detailed derivation of the proposed method is presented in Section III. In Section IV, we provide numerical performance comparison of the proposed scheme, a random scheduling scheme, and a DCI Following scheme that does not integrate the delay effect nor the ACK/NAK feedbac. Finally, Section V concludes this wor. II. PRINCIPLE OF SHADOW CHASING If an HeNB nows that an MUE is far away as an outdoor MUE, and nows which PRBs are assigned to that MUE s downlin, then the HeNB can re-assign the same PRBs to its own HUEs with confidence of low downlin interference. The HeNB can classify MUEs as outdoor/indoor using the Downlin Control Information DCI together with the overheard ACK/NAK in MUEs uplin feedbac. From the DCI, the HeNB nows the PRB assignment pattern of different UEs. If the DCI shows that some PRBs are assigned to a certain MUE but neither ACKs nor NAKs are heard from that MUE, this means that this MUE is far enough such that we can fairly assume the MUE to be outdoor. On the other hand, if either ACKs or NAKs are received from an MUE, then it is liely to be close as the HeNB is already able to hear its feedbac signals. Moreover, the HeNB can learn from the DCI whether some empty PRBs not assigned to any UE. Based on the decision regarding which MUE is outdoor and whether there are empty PRBs or not, the HeNB can either use the same PRBs as those assigned to outdoor MUEs without causing considerable interference or use the empty PRBs. However, the main challenge is that DCI may only be acquired by the HeNB through bachaul connection or by overhearing the DCI from the MBS. Hence, the MUE PRB assignment information at the HeNB is outdated lie seeing a target s shadow. To tacle this problem, we propose that the HeNB estimates the lielihood that a certain PRB is empty or allocated to an outdoor MUE. Because the HeNB is trying to find and use the PRBs of an outdoor MUE, and because its DCI is delayed, we call this proposed algorithm Shadow Chasing. The original shadow chasing concept was presented in [12]. In [12], we presented a heuristic expression for the lielihood metric that accounts for the delayed DCI effect and exploits the ACK/NAK signals. In this wor, we derive an analytical expression for the lielihood using a Marov chain MC model. Furthermore, we present an enhancement through additionally exploiting the CQI reports. Our goal is to derive a metric for each PRB on its lielihood of not being used by an indoor MUE based on the incomplete and delayed observation of DCI, ACK/NAK signals, and CQI reports. By forming a lielihood table for each PRB, the HeNB then assigns its HUEs the PRBs with the largest lielihood metric. For HeNB assignment to cause little interference to neighboring MUEs, the HeNB should first use the PRBs that are most liely to be empty. Next it should use the most liely outdoor PRBs. The PRBs that are probably assigned to indoor MUEs would be the least favorable. To lower the possibility of using some PRBs already assigned to indoor MUEs, the HeNB can compare the lielihood metric with a pre-determined threshold such that if the lielihood is lower than that threshold for some PRBs, the HeNB does not assign those PRBs. In this case, the HeNB avoids causing much interference to indoor MUEs by lowering HUEs rates. We note that our scheduling and decision time units are in terms of Transmission Time Interval TTI which is one subframe duration in LTE. Before proceeding, we first introduce the following notations to be used throughout the paper: M i /M o : Index set of PRBs assigned to indoor/outdoor MUEs. M e : Index set of empty PRBs. R i /R o : Index set of PRBs to be exchanged for indoor/outdoor MUE. U i /U o : Index set of empty PRBs with good CQI quality for indoor/outdoor MUE. N i /N o : Number of PRBs assigned to indoor/outdoor MUEs. N e : Number of empty PRBs. N t : Total number of PRBs N t = N i +N o +N e. N f : Number of PRBs requested by HUE. D : Delay of the bachaul connection in TTI units. T m /T f : MBS/HeNB scheduling period in TTI units. A. Basic Idea III. SHADOW CHASING ALGORITHM The principle of shadow chasing hinges on the derivation of the lielihood metric for a given PRB to not being used by an indoor MUE. To calculate the lielihood metric, we use the outdated DCI together with ACK/NAK information and CQI reports. At each scheduling instant, indoor MUE reports to the serving MBS two sets of indices, namely R i and U i. Here R i refers to PRBs that admit poor channel quality while U i refers to empty PRBs that admit good channel quality. Similarly, outdoor MUE reports to the serving MBS the two sets R o and U o. We consider a sequential scheduling policy in which the MBS tries to fulfill the PRB requirement of a certain MUE indoor or outdoor before another MUE. The MBS may choose this order randomly or according to a certain policy, e.g. start with the MUE that is suffering from poor channel quality on most of its PRBs. The MBS feeds this order information to the FBS through the bachaul connection. This order information should not be varying rapidly and should be generally semi-persistent. If an MUE is assigned a PRB at time index n 1, it will stay assigned the same PRB at time n if at least one of the following is true : It has good channel quality on PRB at time n. It has a bad channel quality on PRB but there is no enough empty and good PRBs at time n, where the time index n is in terms of TTI in LTE.

3 B. Marov Chain Description We consider a scenario with one indoor MUE and one neighboring outdoor MUE that are assigned N i and N o PRBs, respectively. We consider a MC model with three states for each PRB as shown in Fig. 1. The states of the MC model are defined as follows : State 0 : PRB is empty unoccupied. State 1 : PRB is assigned to the outdoor MUE M 1. State 2 : PRB is assigned to the indoor MUE M 2. We assume the states of different PRBs to be independent such that we have N t independent MC models. Fig. 1: Marov Chain model for lielihood. To calculate the transition probabilities in Fig. 1, we first assume that an MUE has a good channel quality on a PRB if its CQI is greater than or equal to a quality threshold γ. Thus, p g1,n = PrCQI 1,n γ. We also assume that all PRBs have the same probability of having good or bad CQI reports. This is reasonable if the channel is slowly varying or when CQI is reported with a low rate. In this case, p g1,n represents an average value for the probability that M 1 has a good channel quality on a PRB at time n. Thus, p g1,n = p g1 = Pr Pm H 1,n 2 N 01 +P f I f,n γ, 1 where H 1,n is the complex channel response of M 1 at PRB and time n with magnitude of H 1,n. Channels are assumed to be CN0,1. P m and P f are the transmission powers of the MBS and HeNB, respectively, and N 01 is the noise power at M 1. The indicator function I f,n is equal to 1 if HUE is assigned PRB at time n and 0 otherwise. Conditioning on the two outcomes of I f,n, we get Pm H 1,n 2 p g1 = Pr γ PrI f,n = 1 N 01 +P f Pm H 1,n 2 +Pr γ PrI f,n = 0. 2 N 01 In fact, I f,n depends on HeNB decision at time index n 1 which, in turn, depends on the values of CQI of both M 1 and M 2 for different PRBs at n 1 as well as on N f. Finding the exact expressions of PrI f,n = 1 and PrI f,n = 0 can be difficult. Thus, we assume that each PRB is equi-probably assigned to the HeNB. We then have for a single antenna transmission: p g1 = N f N t Pr H 1,n 2 γn 01 +P f +1 N f N t Pr P m H 1,n 2 γn 01 P m = N f exp γn 01 +P f +1 N f exp γn 01. N t N t P m P m Note that H 1,n 2 is exponentially distributed with mean 1. Similarly, the expression for p g2 can be obtained similarly by considering CQI 2 and the distribution for H 2,n 2. C. Scheduling Analysis of Marov Chain Model Without loss of generality, we analyze the case when the MBS decides to schedule the indoor MUE, M 2, first since it suffers more interference than the outdoor MUE, M 1. We define q 02 as the probability that PRB is assigned to M 2 at time n given that it was empty at time n 1. We use the notation M 2 to denote that is assigned to M 2. Thus, q 02 = Pr M n n 1 4 = Pr M 2, R i = r, U i = u M e N i N e = Pr M 2 R i = r, U i = u, M e Pr R i = r U i = u, M e Pr U i = u M e, where X refers to cardinality of a set X. Because the event R i = r is independent of both the events U i = u and M e, Pr R i = r U i = u, M e = Pr R i = r. The probability Pr R i = r is the probability that M 2 has r PRBs with poor channel quality out of the N i PRBs, thus Ni Pr R i = r = 1 p g2 r pg Ni r r 2. 5 Furthermore, we find that Pr M 2 R i = r, U i = u, M e 6 = Pr M 2 R i = r, U i = u, M e, U i Pr U i R i = r, U i = u, M e. The condition R i = r in the second term in the right side can be removed since the event that M 2 has good CQI on is independent of the event that there are r PRBs with poor CQI values for M 2. This can be further simplified to Pr M 2 R i = r, U i = u, M e 7 where = Pr M 2 R i = r, U i = u, U i Pr U i = u U i Pr U i Pr U i = u M e Pr M e, Pr M 2 R i = r, U i = u, U i = min{ r u,1}, 8 3

4 and, Pr U i = Pr M e p g2. 9 The probability that the indoor MUE M 2 has u empty PRBs with good channel qualities out of the N e PRBs given that PRB is one of them, is of the form Pr U i = u U i = Ne 1 u 1 p u 1 g 2 1 p g2 Ne u. By substituting 5, 7, and 10 into 4, we obtain min{r, u} Ni Ne q 02 = N e r u 10 p Ni r+u g 2 1 p g2 Ne u+r. 11 Similarly, we define q 01 as the probability that PRB is assigned to M 1 at n given that is not assigned to M 2 at n and it was empty at n 1. Thus, q 01 = Pr M n not M n & n Following a similar approach, we can find that N o min{r, u} No Ne q 01 = N e r u p No r+u g 1 1 p g1 Ne u+r. 13 Next, we define q 20 as the probability that PRB is empty at n given that was assigned to M 2 at n 1. Thus, q 20 = Pr n M n 1 14 = Pr R i, exchanged, R i = r, U i = u M i = Pr exchanged R i = r, U i = u, R i Pr R i = r R i Pr U i = upr R i M i. Noting that Pr R i M i = 1 p g2 and applying similar steps as used earlier, we can get min{r, u} Ni Ne q 20 = N i r u p Ni r+u g 2 1 p g2 Ne u+r. 15 Similarly, we define q 10 as the probability that PRB is empty at n given that was assigned to M 1 at n 1, which can be derived to be N o q 10 = min{r, u} N o No r Ne u p No r+u g 1 1 p g1 Ne u+r. 16 Given the expressions for q 01, q 02, q 10, and q 20, we can now find expressions for the MC transition probabilities in Fig. 1. Recall that we assumed that the indoor MUE, M 2, is scheduled first. Under this assumption, we see that transition from state 1 to state 2 is excluded, i.e. p 12 = 0. We also see that for an empty PRB to be assigned to M 1, it first has to be not assigned to M 2 then assigned to M 1, that is why p 01 = 1 q 02 q 01. Following similar reasoning, the transition probabilities at a certain PRB can be written as follows : p 00 = 1 q 02 1 q 01, p 01 = 1 q 02 q 01, p 02 = q 02, p 10 = q 10, p 11 = 1 q 10, p 12 = 0, p 20 = q 20 1 q 01, p 21 = q 20 q 01, p 22 = 1 q 20, 17 where we dropped the index for simplicity. We also note that p 11 is the probability that PRB remains assigned to M 1 at time n, which can be written as p 11 = Pr / R n 1 OR R n 1& not exchanged M n 1 18 = 1 q 10. Given all transition probabilities in hand, we define the transition probability matrix P as follows p 00 p 01 p 02 P = p 10 p 11 p p 20 p 21 p 22 At DCI update instances at the HeNB illustrated in Fig. 2, the initial states of the Marov chains of each PRB are initialized with the received DCI as follows : p 0 = [ ] [ ] [ ] if PRB is empty if PRB is assigned to M 1 if PRB is assigned to M 2, 20 where p 0 is the initial state of the MC of PRB. Note that, if we assume uncertainty in the received DCI message itself, the initial probabilities will not necessarily be zeros and ones. Fig. 2: Illustration of the Shadow Chasing algorithm.

5 D. Delayed DCI and ACK/NAK Consideration The delay D in Fig. 2 is the delay of the bachaul connection in TTI units. T m is the MBS scheduling period in TTI units and we assume that T m D. The larger the MUE scheduling period T m is relative to the bachaul delay D, the more confident the HeNB is in the outdated DCI information it receives. On the other hand, if T m is comparable to D, the actual MUE PRB assignment might be completely different from the received outdated DCI which leads to more incorrect HeNB assignment decisions. The HeNB can classify indoor versus outdoor MUEs using the ACK/NAK signal it overhears. The ACK/NAK signal is one bit indicating the success/failure of MUE pacet reception and decoding. Unlie DCI and CQI, ACK/NAK information is not given at the PRB level. However, using the DCI we can find the PRBs assigned to a certain MUE and, therefore, update PRB lielihood metric according to ACK/NAK for the entire bloc of corresponding PRBs. If the HeNB does not overhear the ACK/NAK signal from a specific MUE, it liely means that the MUE is outdoor. Thus, all assigned PRBs of that MUE should have higher lielihood metric. If the HeNB hears an ACK from an MUE, it means it is liely nearby and indoor albeit with good channel quality. If, instead, the HeNB hears a NAK, then the MUE is liely indoor and is already experiencing a poor channel condition. Assuming a homogeneous MC, the state probabilities at a time instant n can be obtained as p n = p 0 Pn. Consequently, we define the probability of PRB being empty, outdoor, or indoor at time n as p e,n = p n 0, p o,n = p n 1, or p i,n = p n 2, respectively. The delay D determines the time intervals in which the HeNB has outdated DCI information, i.e. [0,D], [T m,t m + D], etc., as highlighted in Fig. 2. The state of the MC model is updated, i.e. p n = p 0 Pn is evaluated, only in these designated intervals, whereas, in the complementary time intervals [D,T m ], [T m +D,2T m ], the HeNB is using the last MC state it had. Finally, the lielihood L can be written as a function of the probabilities p e,n, p o,n, and p i,n. Since p e,n+ p o,n+p i,n = 1, we define L as the two-dimensional vector below [ ] pi,n L,n = 21 p o,n The HeNB updates the lielihood table in each TTI at time n and maes the scheduling decision accordingly for every T f TTIs. The HeNB first sorts L,n based on a descending order of 1 p i,n to get a sorted lielihood vector ] [ pi,n L,n = 22 p o,n We define a decision metric M,n as follows : M,n = 1 p i,n or alternatively, 23 M,n = max{w e p e,n,w o p o,n,w i p i,n}, 24 where w e, w o, and w i are weights for the empty, outdoor, and indoor states, respectively, such that w e w o w i. The HeNB calculates the metricm,n for each PRB and assigns the PRBs that have largest metric for the HUE. IV. SIMULATION RESULTS We now present some numerical simulation test results of a HetNet that utilizes the enhanced Shadow Chasing algorithm e-sca. We consider a HetNet with two MUEs and one HeNB. Each MUE has a certain PRB requirement and the HeNB has a desired number of PRBs to satisfy the requirements of associated HUEs. To simulate an overloaded system, we set the total number of required PRBs for all MUEs and HUEs greater than the maximum number of available PRBs. MUE i is at a certain distance from its serving base station, denoted d m i, and at a certain distance from the HeNB, d h i. The distances d h i are chosen so that one MUE is outdoor i.e. d h i is large enough and the other is indoor. The simulation parameters are summarized in Table I. Parameter Value N o/n t N i /N t N f /N t MBS, HeNB Transmit Powers 47dBm, 20dBm MBS to MUE Path Loss log10d mi/1000 HeNB to HUE Path Loss log10d f /1000 d f : distance between HeNB & HUE in meters TABLE I: Simulation Parameters. As a performance metric, we examine the probability of PRB collision versus the MUE scheduling period T m, where the probability of PRB collision is defined as the probability that the HeNB uses a PRB assigned to an indoor MUE. As D 0 and ifn f is less than the number of PRBs requested by the outdoor MUE plus the number of empty PRBs i.e. N f N o +N e, our proposed scheme should have a zero probability of collision. However, because the bachaul connection delay D plus the reaction time by the HeNB is typically in the order of tens of TTIs assuming a DSL bachaul, the probability of collision can be substantial. For performance comparison, we also consider two additional and more naive methods of PRB assignment: random assignment scheme and DCI Following scheme. In random assignment, the HeNB blindly assigns PRBs without exploiting any DCI information about MUE scheduling. In fact, it does nothing special to avoid interference to near-by MUEs. The DCI following scheme is a smarter but naive scheme that merely uses the outdated DCI as if it gives the accurate PRB assignment without accounting for the bachaul delay. This scheme assigns PRB according to the DCI as: L,n = { aempty PRB is empty at time n; a used otherwise. 25 Note that a empty and a used are two constants with a empty a used. Moreover, the DCI following scheme does not exploit

6 the ACK/NAK information, so it is not able to distinguish between PRBs assigned to indoor or outdoor MUEs. Performance evaluation of the three schemes is shown in Fig. 3 for various choices of T f recall that T f is the HeNB scheduling period in TTIs. In this simulation, the value of D is set to 50 TTI. Intuitively, as T m increases relative to the bachaul delay, D, the probability of collision decreases. When T m and D are comparable, the effect of D becomes more significant. On the other hand, the probability of collision rises if the HeNB scheduling period T f increases because the HeNB becomes less adaptive to MUE feedbac signals and scheduling updates. From Fig. 3, it is clear that random assignment leads to the highest probability of PRB collision. As expected, the performance of the random assignment scheme is independent of T m and T f. Moreover, the e-sca outperforms the DCI Following scheme for all values of T f since it uses lielihood information for scheduling decisions. Probability of PRB collision Random Assignment DCI Following D = 50 TTI Enhanced Shadow Chasing Tf = 1 Tf = 20 Tf = 40 Tf = 80 Tf = Tm [TTI] Fig. 3: PRB collision rate vs T m for different T f. Another performance metric we consider is the sum of MUEs rates. Fig. 4 compares the sum of MUEs rates for the three schemes. As seen from Fig. 3, as T m increases relative to D, the probability of HeNB interference to the indoor MUE decreases and, thus, the sum of MUEs rates improves as in Fig. 4. It is, however, worth noting that the rate attained by the HUE is independent of T m and T f, yet, it depends only on the relative value of the delay D compared to T m. V. CONCLUSION We proposed a novel enhancement to the shadow chasing technique for resource allocation in HetNet for interference mitigation. In this wor, the HeNB receives DCI from the MBS through bachaul and exploits its information jointly with its overheard ACK/NAK signal to classify neighboring MUEs into outdoor or indoor probabilistically. Using a lielihood metric for each PRB, the HeNB can assign its HUE the PRBs that are most probably empty or assigned to outdoor MUEs which correspond to the PRBs that are least liely to result in collision with HUE. If outdoor MUEs are far away, Sum of MUE rates [Mbps] D = 50 TTI Enhanced Shadow Chasing DCI Following Tf = 1 Tf = 20 Tf = 40 Tf = 80 Tf = 160 Random Assignment Tm [TTI] Fig. 4: Sum of MUEs rates comparison. they would experience less interference. As an enhancement to our previous wor, we presented analytical derivation for the probability of each PRB being empty, outdoor, or indoor through a MC model. Additionally, we exploited the CQI reports as well as the ACK/NAK feedbac. Furthermore, we provided numerical examples that illustrate the effective reduction of pacet collision and the spectrum efficiency as a result of applying the e-sca for resource allocation in HetNet. REFERENCES [1] Presentations by ABI Research, Picochip, Arivana, IP access, Gartner, Telefonica Espana, 2nd Int l Conf. Home Access Points and Femtocells. [2] V. Chandrasehar, J. Andrews, and A. Gatherer, Femtocell Networs: a Survey, IEEE Communications Magazine, 469:59 67, [3] J. Zhang and G. de la Roche, Femtocells : Technologies and Deployment, JohnWiley & Sons, New Yor, NY, USA, [4] I. F. Ayildiz, W.-Y. Lee, M. C. Vuran, and S. Mohanty, Next Generation/Dynamic Spectrum Access/Cognitive Radio Wireless Networs: a Survey, The International Journal of Computer and Telecommunications Networing, 5013: , [5] Y. Zhang, Dynamic Spectrum Access in Cognitive Radio Wireless Networs, in IEEE International Conference on Communications, Dec : [6] Q. Zhao, L. Tong, A. Swami and Y. Chen, Decentralized cognitive MAC for opportunistic spectrum access in ad hoc networs: A POMDP framewor, IEEE Journal on Selected Areas in Communications : [7] X. Li, L. Qian, and D. Kataria, Downlin Power Control in Co-channel Macrocell Femtocell Overlay, 43rd Conference on Information Sciences and Systems, pages , [8] C. Jiang, L. J. Cimini, and N. Himayat, MIMO Mode Adaptation in Femtocellular Systems, Computer Engineering, pages , [9] M. Sahin, I. Guvenc, M. Jeong, and H. Arslan, Handling CCI and ICI in OFDMA Femtocell Networs Through Frequency Scheduling, IEEE Trans. on Consumer Electronics, 554: , [10] P. Mach, Z. Becvar, Dynamic Power Control Mechanism for Femtocells Based on the Frame Utilization, in 6th International Conference Wireless and Mobile Communications, [11] Z. Zheng, J. Hämäläinen, and Y. Yang, On Uplin Power Control Optimization and Distributed Resource Allocation in Femtocell Networs, in VTC Spring 2011 BeFEMTO worshop, 15 May, Budapest, Hungary, [12] A. R. Elsherif, Z. Ding, X. Liu, J. Hämäläinen, and R. Wichman, Shadow Chasing : A Resource Allocation Scheme For Heterogeneous Networs, in 7th International Conference on Cognitive Radio Oriented Wireless Networs Crowncom 2012.