Skip to main content
SpringerLink
Log in

Inter-cell interference in multi-tier heterogeneous cellular networks: modeling and constraints

  • Published:
Telecommunication Systems Aims and scope Submit manuscript

Abstract

Interference is the main source of capacity limitation in wireless networks. In some medium access technologies in cellular networks, such as OFDMA, the allocation of frequency subbands is such that interference between cells occurs. This article focuses on preventing harmful interference by properly allocating cells and wireless resources such as subbands to users. In this way, at any time, a set of connections is established that there is no harmful interference between them. In this study, we model inter-cell interference using the protocol interference model and describe interference graph. The proposed model is also applicable to heterogeneous cellular networks. This study provides several types of constraints for the feasibility of a set of connections; each uses a specific component in the network. All constraints are linear; thus, including them in the optimization programs does not increase their structural complexity. A network utility maximization program with joint cell association and interference management is presented, and the effect of applying such interference constraints on simplifying and linearizing the problem structure is described. The presented constraints are discussed in terms of necessary and sufficient conditions for the feasibility of connection, as well as the possibility of distributed construction and verification in cellular network. Two network scenarios are considered, and by using the proposed interference model and appropriate interference constraint, the problem of subband and cell allocation is formulated and solved. The simulation results strongly confirm the performance of the proposed model in practice.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Availability of data and material

Not applicable.

References

  1. Sarlak, A., & Darmani, Y. (2021). An Approach to improve the quality of service in DTN and Non-DTN based VANET. Journal of Information Systems and Telecommunication (JIST), 8(32), 240–248. https://doi.org/10.29252/jist.8.32.240

    Article  Google Scholar 

  2. Son, K., Chong, S., & Veciana, G. (2009). Dynamic association for load balancing and interference avoidance in multi-cell networks. IEEE Transactions on Wireless Communications, 8(7), 3566–3576. https://doi.org/10.1109/TWC.2009.071140

    Article  Google Scholar 

  3. Andrews, J. G. (2005). Modulation, coding and signal processing for wireless communications - Interference cancellation for cellular systems: a contemporary overview. IEEE Wireless Communications, 12(2), 19–29. https://doi.org/10.1109/MWC.2005.1421925

    Article  Google Scholar 

  4. Faizan Qamar, M. H. D., Hindia, N., Dimyati, K., Noordin, K. A., & Amiri, I. S. (2019). Interference management issues for the future 5G network: a review. Telecommunication Systems, 71(4), 627–643. https://doi.org/10.1007/s11235-019-00578-4

    Article  Google Scholar 

  5. Xiaodong, X., Zhang, H., & Wang, Q. (2011). Inter-cell interference mitigation for mobile communication system. In M. Almeida (Ed.), Advances in Vehicular Networking Technologies. InTech. https://doi.org/10.5772/15550

    Chapter  Google Scholar 

  6. Aljohani, S. L., & Alenazi, M. J. F. (2021). MPResiSDN: multipath resilient routing scheme for SDN-enabled smart cities networks. Applied Sciences, 11(4), 1900. https://doi.org/10.3390/app11041900

    Article  Google Scholar 

  7. Damnjanovic, A., Montojo, J., Wei, Y., Ji, T., Luo, T., Vajapeyam, M., Yoo, T., Song, O., & Malladi, D. (2011). A survey on 3GPP heterogeneous networks. IEEE Wireless Communications, 18(3), 10–21. https://doi.org/10.1109/MWC.2011.5876496

    Article  Google Scholar 

  8. Zahir, T., Arshad, K., Nakata, A., & Moessner, K. (2013). Interference management in femtocells. IEEE Communications Surveys & Tutorials, 15(1), 293–311. https://doi.org/10.1109/SURV.2012.020212.00101

    Article  Google Scholar 

  9. Chinipardaz, M., & Noorhosseini, M. (2017). A study on cell association in heterogeneous networks with joint load balancing and interference management. Telecommunication Systems, 66(1), 55–74. https://doi.org/10.1007/s11235-016-0272-1

    Article  Google Scholar 

  10. Denedo, D. O., Vien, Q.-T., & Phan, C. V. (2021). Time-based resource allocation for downlink in heterogeneous wireless cellular networks. Telecommunication Systems, 78(3), 463–475. https://doi.org/10.1007/s11235-021-00829-3

    Article  Google Scholar 

  11. Huan, S., Linling, K., & Jianhua, L. (2009). Interference avoidance in OFDMA-based femtocell network. 2009 IEEE Youth Conference on Information, Computing and Telecommunication. https://doi.org/10.1109/YCICT.2009.5382410

    Article  Google Scholar 

  12. Wu, Y, Zhang, D., Jiang, H., & Wu, Y. (2009). A novel spectrum arrangement scheme for femto cell deployment in LTE macro cells. 2009 IEEE 20th International Symposium on Personal, Indoor and Mobile Radio Communications. https://doi.org/10.1109/PIMRC.2009.5450296

  13. Lee, P., Lee, T., Jeong, J., & Shin, J. (2010). Interference management in LTE femtocell systems using fractional frequency reuse. 2010 The 12th International Conference on Advanced Communication Technology (ICACT).

  14. Li, Y-Y. (2009). Cognitive interference management in 3G femtocells. 2009 IEEE 20th International Symposium on Personal, Indoor and Mobile Radio Communications. https://doi.org/10.1109/PIMRC.2009.5450030

  15. Liu, H., Pu, X., Chen, Y., Yang, J., & Chen, J. (2020). User-centric access scheme based on interference management for indoor VLC-WIFI heterogeneous networks. IEEE Photonics Journal, 12(4), 1–12. https://doi.org/10.1109/JPHOT.2020.3002246

    Article  Google Scholar 

  16. Yoon, J., Lee, J., & Lee, H. S. (2009). Multi-hop based network synchronization scheme for femtocell systems. 2009 IEEE 20th International Symposium on Personal, Indoor and Mobile Radio Communications. https://doi.org/10.1109/PIMRC.2009.5449937

  17. Park, S., & Bahk, S. (2011). Dynamic inter-cell interference avoidance in self-organizing femtocell networks. 2011 IEEE International Conference on Communications (ICC). https://doi.org/10.1109/icc.2011.5962707

  18. Zahir, T., Arshad, K., Ko, Y., & Moessner, K. (2011). A downlink power control scheme for interference avoidance in femtocells. Wireless Communications and Mobile Computing Conference (IWCMC), 2011 7th International. https://doi.org/10.1109/IWCMC.2011.5982714

  19. Chandrasekhar, V., Andrews, J. G., Shen, Z., Muharemovict, T., & Gatherer, A. (2009). Distributed power control in femtocell-underlay cellular networks. Global Telecommunications Conference, 2009. GLOBECOM 2009. IEEE. https://doi.org/10.1109/GLOCOM.2009.5425923

  20. Arulselvan, N., Ramachandran, V., Kalyanasundaram, S., & Han, G. (2009). Distributed power control mechanisms for HSDPA femtocells. VTC Spring 2009. IEEE 69th Vehicular Technology Conference. https://doi.org/10.1109/VETECS.2009.5073506

  21. Akbudak, T., & Czylwik, A. (2010). Distributed power control and scheduling for decentralized OFDMA networks. 2010 International ITG Workshop on Smart Antennas (WSA). https://doi.org/10.1109/WSA.2010.5456376

  22. Su, Q., Huang, A., Wu, Z., Yu, G., Zhang, Z., Xu, K., & Yang, J. (2009). A distributed dynamic spectrum access and power allocation algorithm for Femtocell networks. WCSP 2009. International Conference on Wireless Communications & Signal Processing https://doi.org/10.1109/WCSP.2009.5371629

  23. Tang, Y., Yang, P., Wu, W., Mark, J. W., & Shen, X. (2019). Interference mitigation via cross-tier cooperation in heterogeneous cloud radio access networks. IEEE Transactions on Cognitive Communications and Networking, 6(1), 201–213. https://doi.org/10.1109/TCCN.2019.2957457

    Article  Google Scholar 

  24. Tayyaba, S. K., Khattak, H. A., Almogren, A., Shah, M. A., Din, I. U., Alkhalifa, I., & Guizani, M. (2020). 5G vehicular network resource management for improving radio access through machine learning. IEEE Access, 8, 6792–6800. https://doi.org/10.1109/ACCESS.2020.2964697

    Article  Google Scholar 

  25. Li, S., Guo, L., Liu, J., Huang, T., Cui, X., & Zhang, Y. (2020). Partial interference alignment scheme for three-tier downlink heterogeneous networks. IEEE Access, 8, 155602–155610. https://doi.org/10.1109/ACCESS.2020.3015779

    Article  Google Scholar 

  26. Madan, R., Borran, J., Sampath, A., Bhushan, N., Khandekar, A., & Ji, T. (2010). Cell association and interference coordination in heterogeneous LTE-A cellular networks. IEEE Journal on Selected Areas in Communications, 28(9), 1479–1489. https://doi.org/10.1109/JSAC.2010.101209

    Article  Google Scholar 

  27. Bejerano, Y., & Han, S.-J. (2009). Cell breathing techniques for load balancing in wireless LANs. IEEE Transactions on Mobile Computing, 8(6), 735–749. https://doi.org/10.1109/TMC.2009.50

    Article  Google Scholar 

  28. Hassan, N., & Fernando, X. (2020). An optimum user association algorithm in heterogeneous 5G networks using standard deviation of the load. Electronics, 9(9), 1495. https://doi.org/10.3390/electronics9091495

    Article  Google Scholar 

  29. Akyildiz, I. F., Gutierrez-Estevez, D. M., & Reyes, E. C. (2010). The evolution to 4G cellular systems: LTE-Advanced. Physical Communication, 3(4), 217–244. https://doi.org/10.1016/j.phycom.2010.08.001

    Article  Google Scholar 

  30. Boostanimehr, H., & Bhargava, V. K. (2015). Unified and distributed QoS-driven cell association algorithms in heterogeneous networks. IEEE Transactions on Wireless Communications, 14(3), 1650–1662. https://doi.org/10.1109/TWC.2014.2371465

    Article  Google Scholar 

  31. Khandekar, A., Bhushan, N., Tingfang, J., & Vanghi, V. (2010). LTE-advanced: Heterogeneous networks. 2010 European Wireless Conference (EW). https://doi.org/10.1109/EW.2010.5483516

  32. Hossain, E., Rasti, M., Tabassum, H., & Abdelnasser, A. (2014). Evolution towards 5G multi-tier cellular wireless networks: an interference management perspective. IEEE Wireless Communications, 21(3), 118–127. https://doi.org/10.1109/MWC.2014.6845056

    Article  Google Scholar 

  33. Mihovska, A. (2020). Small cell deployment challenges in ultradense networks: Architecture and resource management. 2020 12th International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP), https://doi.org/10.1109/CSNDSP49049.2020.9249560

  34. Khan, H. Z., Ali, M., Naeem, M., Rashid, I., Siddiqui, A. M., Imran, M., & Mumtaz, S. (2020). Joint admission control, cell association, power allocation and throughput maximization in decoupled 5G heterogeneous networks. Telecommunication Systems, 76(1), 115–128. https://doi.org/10.1007/s11235-020-00707-4

    Article  Google Scholar 

  35. Iyer, A., Rosenberg, C., & Karnik, A. (2009). What is the right model for wireless channel interference? IEEE Transactions on Wireless Communications, 8(5), 2662–2671. https://doi.org/10.1109/TWC.2009.080720

    Article  Google Scholar 

  36. Wang, Y., Wei, G., & Xiang, W. (2013). Inter-cell interference modeling for cellular networks. Telecommunication Systems, 53(1), 99–105. https://doi.org/10.1007/s11235-013-9682-5

    Article  Google Scholar 

  37. Gupta, P., & Kumar, P. R. (2000). The capacity of wireless networks. IEEE Transactions on information theory, 46(2), 388–404. https://doi.org/10.1109/18.825799

    Article  Google Scholar 

  38. Bakhshi, B., Khorsandi, S., & Capone, A. (2011). On-line joint QoS routing and channel assignment in multi-channel multi-radio wireless mesh networks. Computer Communications, 34(11), 1342–1360. https://doi.org/10.1016/j.comcom.2011.02.001

    Article  Google Scholar 

  39. Gupta, R., Musacchio, J., & Walrand, J. (2007). Sufficient rate constraints for QoS flows in ad-hoc networks. Ad Hoc Networks, 5(4), 429–443. https://doi.org/10.1016/j.adhoc.2006.01.003

    Article  Google Scholar 

  40. Jain, K., Padhye, J., Padmanabhan, V. N., & Qiu, L. (2005). Impact of interference on multi-hop wireless network performance. Wireless networks, 11(4), 471–487. https://doi.org/10.1007/s11276-005-1769-9

    Article  Google Scholar 

  41. Luo, H., Lu, S., & Bharghavan, V. (2000). A new model for packet scheduling in multihop wireless networks. In 6th annual international conference on Mobile computing and networking (pp. 76–86). ACM. https://doi.org/10.1145/345910.345923

  42. Halldórsson, M. M. (1998). Approximations of independent sets in graphs. International Workshop on Approximation Algorithms for Combinatorial Optimization. https://doi.org/10.1145/345910.345923

  43. Halldórsson, M. M., & Radhakrishnan, J. (1997). Greed is good: Approximating independent sets in sparse and bounded-degree graphs. Algorithmica, 18(1), 145–163. https://doi.org/10.1007/BF02523693

    Article  Google Scholar 

  44. Chinipardaz, M. (2018). Cell Association in Heterogeneous Networks with Load Balancing Perspective and Interference Management Amirkabir University of Technology.

  45. Chinipardaz, M., & Noorhosseini, M. (2018). Joint distributed cell association and interference management in OFDMA-based heterogeneous networks. Transactions on Emerging Telecommunications Technologies, 29(9), e3439. https://doi.org/10.1002/ett.3439

    Article  Google Scholar 

  46. Abdelnasser, A., Hossain, E., & Kim, D. I. (2015). Tier-aware resource allocation in OFDMA macrocell-small cell networks. IEEE Transactions on Communications, 63(3), 695–710. https://doi.org/10.1109/TCOMM.2015.2397888

    Article  Google Scholar 

  47. Boyd, S., & Vandenberghe, L. (2004). Convex optimization. Cambridge University Press.

    Book  Google Scholar 

  48. Grant, M., & Boyd, S. (2014). CVX: Matlab software for disciplined convex programming, version 2.1.

  49. Hassan, N., & Fernando, X. (2019). Interference mitigation and dynamic user association for load balancing in heterogeneous networks. IEEE Transactions on Vehicular Technology, 68(8), 7578–7592. https://doi.org/10.1109/TVT.2019.2919812

    Article  Google Scholar 

  50. Bai, L., Wang, J., Han, R., Li, D., Liu, J., & Choi, J. (2020). A precoding compensation scheme for heterogeneous communication networks with CSI feedback delay. IEEE Transactions on Network Science and Engineering, 7(4), 2506–2514. https://doi.org/10.1109/TNSE.2020.3007649

    Article  Google Scholar 

Download references

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Jundi-Shapur University of Technology, Dezful, Iran

    Maryam Chinipardaz

  2. Department of Computer Engineering and Information Technology, Amirkabir University of Technology, Tehran, Iran

    Seyed Majid Noorhosseini

  3. Department of Electrical and Computer Engineering, K. N. Toosi University of Technology, Tehran, Iran

    Ahmad Sarlak

Authors
  1. Maryam Chinipardaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seyed Majid Noorhosseini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ahmad Sarlak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maryam Chinipardaz.

Ethics declarations

Conflicts of interest

The authors declare that they have no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendices

Appendix A

To prove Theorem 1, the proof by contradiction is used. Suppose that relation (7) is met for a connection array but the array is not feasible. Regarding infeasibility of the array and according to the definition, at least two connections such as \(\left(a,c\right)\) and \(\left(b,d\right)\) in the connection set interfere and simultaneously transmit on a subband such as \(m,\) therefore, \({x}_{ac}^{m}=1\) and \({x}_{bd}^{m}=1.\) Due to the interference between these two links, at least one of the following conditions has occurred: \(b\in {BI}_{c}\) or \(a\in {BI}_{d}\). Considering the first condition, \(b\in {BI}_{c}\), the relation (7) for user c on the subband m is presented as

$$ \mathop \sum \limits_{{k \in BI_{c} }} \mathop \sum \limits_{z} x_{kz}^{m} = \ldots + x_{bd}^{m} + x_{ac}^{m} > 1 $$

The proposed condition in the hypothesis is violated. The second condition is proved the same way.

Appendix B

To prove that receiver conditional constraint is a sufficient condition for a connection set to be feasible, suppose that the relation (9) is stablished for a connection array, but the array is not feasible. Due to the infeasibility of the connection array, at least two connections, such as \(\left(a,c\right)\) and \(\left(b,d\right)\) in the connection set, interfere and transmit on a subband \(m\) simultaneously; therefore, \({x}_{ac}^{m}=1\) and\({x}_{bd}^{m}=1\). So at least one of these two cases is implied: \(b\in {BI}_{c}\) or\(a\in {BI}_{d}\). Considering the first situation,\({ }b \in BI_{c} ,\) the relation (9) for user \(c\) on the subband \(m\) is written as

$$ \mathop \sum \limits_{{k \in BI_{c} }} \mathop \sum \limits_{z} x_{kz}^{m} \le \left( {1 - \mathop \sum \limits_{mj} x_{jc}^{m} } \right)H + 1 $$
$$ x_{bd}^{m} + x_{ac}^{m} + \ldots \le \left( {1 - x_{ac}^{m} } \right)H + 1 $$
$$ 2 + \ldots \le 1 $$

which is not correct, therefore, in this situation, the relation (9) is not met and the proposed hypothesis is violated. The second situation is proved the same way.

For proving the necessary condition, suppose that a connection array is feasible, but the condition (9) is not met. Therefore, the following relation is applied for at least one receiver \(i\) on the subband \(m.\)

$$ \mathop \sum \limits_{{k \in BI_{i} }} \mathop \sum \limits_{z} x_{kz}^{m} > \left( {1 - \mathop \sum \limits_{j} x_{ji}^{m} } \right)H + 1 $$
(14)

In the following sections, all the cases which might lead to the relation (14) are examined.

Case 1 If \(\sum_{j}{x}_{ji}^{m}=0\), relation (14) is written as

$$ \mathop \sum \limits_{{k \in BI_{i} }} \mathop \sum \limits_{z} x_{kz}^{m} > H + 1 $$

Given that \(H \ge \left| B \right| - 1,\)

$$ \mathop \sum \limits_{{k \in BI_{i} }} \mathop \sum \limits_{z} x_{kz}^{m} > \left| B \right|. $$

The relation mentioned above implies that at least one of the BSs is connected to more than one user on the subband \(m.\) Therefore, those connections interfere with each other and this system is not feasible.

Case 2 If \(\mathop \sum \limits_{j} x_{ji}^{m} = 1\), there is a BS such as \(a\) and\(x_{ai}^{m} = 1\). By substituting the variable \(x_{ai}^{m}\), the relation (14) is re-written as

$$ 1 + \mathop \sum \limits_{{k \in BI_{i} }} \mathop \sum \limits_{{z - \left\{ i \right\}}} x_{kz}^{m} > 1 $$

Therefore,

$$ \mathop \sum \limits_{{k \in BI_{i} }} \mathop \sum \limits_{{z - \left\{ i \right\}}} x_{kz}^{m} > 0 $$

which means that there is a BS with a connection to a user other than \(i\) on the subband \(m.\) Since this BS is in the interference range of user \(i,\) the simultaneous transmission interferes with user \(i\) and this system is not feasible.

Case 3 If \(\sum_{j}{x}_{ji}^{m}>1\), there is more than one connection for user \(i\) on the subband \(m \) and this system is not feasible.

The result of investigating these three situations proves the necessity of condition (9). That is, the relation (9) is applicable for each connection vector.

Appendix C

For proving the sufficiency of connection constraint, suppose that the condition (10) is applicable to a connection array but this array is not feasible. Due to infeasibility of the connection array, at least two connections such as \(\left(a,c\right)\) and \(\left(b,d\right)\) interfere with each other in the connection set and transmit simultaneously on the subband \(m\); therefore, \({x}_{ac}^{m}=1\) and \({x}_{bd}^{m}=1\). So at least one of these two situations is implied:\(b\in {BI}_{c}\) or \(a\in {BI}_{d}\). Considering the first situation, \(b\in {BI}_{c}\), the relation (10) for \(i=c\), \(j=a\), and \(k=b\) is written as

$$ x_{ac}^{m} + \mathop \sum \limits_{z} x_{bz}^{m} = x_{ac}^{m} + x_{bd}^{m} + \ldots = 2 + \ldots \le 1. $$

which is not feasible. The second situation is proved the same way.

For proving the necessity of connection constraint, suppose that the connection array is feasible but the condition (10) is not applicable. Therefore, for at least one case such as link \((j,i)\), subband \(m,\) and \(k\in {BI}_{i}\), the relation (10) is not applicable, so we have

$$ x_{ji}^{m} + \mathop \sum \limits_{z} x_{kz}^{m} > 1 $$

Two situations are taken into consideration.

Case 1 If \({x}_{ji}^{m}=0\), \(\sum_{z}{x}_{kz}^{m}>1\) which shows that BS \(k\) on the subband \(m\) connects to more than one user simultaneously, and therefore, there is an interference between connections and as the result the array is not feasible.

Case 2 If \({x}_{ji}^{m}=1\), \(\sum_{z}{x}_{kz}^{m}>0\); therefore, \(\sum_{z}{x}_{kz}^{m}\ge 1\) which shows that BS \(k\), in the interference range of user \(i,\) transmits to at least one of its users such as \(c\). As the result, both \((j,i)\) and \((k,c)\) are connected while they interfere with each other.

In both situations, the connection array is not feasible and the theorem is proved.

Appendix D

In order to prove the sufficiency of two-BS constraint, suppose that condition (13) is met for a connection array but this array is not feasible. Given the infeasibility of the connection array, at least two connections such as \(\left(a,c\right)\) and \(\left(b,d\right)\) in the connection set interfere with each other and transmit simultaneously on the subband \(m\); therefore, \({x}_{ac}^{m}=1\) and \({x}_{bd}^{m}=1\). In this case, at least one of the following cases is implied: \(c\in {UI}_{b}\) or \(d\in {UI}_{a}\). Considering the first case,\(c\in {UI}_{b}\), relation (13) for \(j=a\) and \(k=b\) is written as

$$ \mathop \sum \limits_{{i \in UI_{a} }} x_{ai}^{m} + \mathop \sum \limits_{{i \in UI_{a,b} }} x_{bi}^{m} = x_{ac}^{m} + x_{bd}^{m} + \ldots = 2 + \ldots \le 1 $$

As it is shown, this constraint is not met, and therefore, the sufficient condition is proved. The second case is proved the same way.

For proving the necessity of two-BS constraint, suppose that a connection array is feasible but the relation (13) is not met. Therefore, for at least one case such as \(j = a\) and \(k = b\), and the subband \(m\), condition (13) is no met as follows.

$$ \mathop \sum \limits_{{i \in UI_{a} }} x_{ai}^{m} + \mathop \sum \limits_{{i \in UI_{a,b} }} x_{bi}^{m} \ge 2 $$
(15)

Three different cases to examine the relation (15) is taken into consideration.

Case 1 If \(\sum_{i\in {UI}_{a}}{x}_{ai}^{m}\ge 1\) and \(\sum_{i\in {UI}_{a,b}}{x}_{bi}^{m}\ge 1\), it is assumed that users connected to BS \(a\) and BS \(c\) are called user \(b\) and \(d\), respectively. Given that \(d\in {UI}_{a}\), two links \(\left(a,c\right)\) and \(\left(b,d\right)\) interfere with each other, since they transmit simultaneously on the subband \(m\), So the connection array is not feasible.

Case 2 If \(\sum_{i\in {UI}_{a}}{x}_{ai}^{m}\ge 2\) and \(\sum_{i\in {UI}_{a,b}}{x}_{bi}^{m}=0\), BS \(a\) is connected to more than one user on the subband \(m\) simultaneously. Therefore, these connections interfere with each other and this connection array is not feasible.

Case 3 If \(\sum_{i\in {UI}_{a}}{x}_{ai}^{m}=0\) and \(\sum_{i\in {UI}_{a,b}}{x}_{bi}^{m}\ge 2,\) BS \(b\) is connected to more than one user on the subband \(m\) simultaneously. Therefore, these connections interfere with each other and this connection array is not feasible.

In all three cases, the connection array is not feasible, therefore, the necessary condition is proved.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chinipardaz, M., Noorhosseini, S.M. & Sarlak, A. Inter-cell interference in multi-tier heterogeneous cellular networks: modeling and constraints. Telecommun Syst 81, 67–81 (2022). https://doi.org/10.1007/s11235-022-00924-z

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11235-022-00924-z

Keywords

Search

Navigation