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Applications of Blind Interference Alignment in Cellular Networks with Short Coherence Times

Applications of Blind Interference Alignment in Cellular Networks with Short Coherence Times. Ramin Bakhshi. Supervisor: Prof. Dr. Erhan A. İ nce. Eastern Mediterranean University. Outline. Problem Statement Definitions Interference Alignment (IA) Degree of Freedom (DoF)

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Applications of Blind Interference Alignment in Cellular Networks with Short Coherence Times

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  1. Applications of Blind Interference Alignment inCellular Networks with Short Coherence Times Ramin Bakhshi Supervisor: Prof. Dr. Erhan A. İnce Eastern Mediterranean University

  2. Outline • Problem Statement • Definitions • Interference Alignment (IA) • Degree of Freedom (DoF) • Standard Blind Inference Alignment (s-BIA) • State-of-the-art • BIA schemes for Homogenous Cellular Networks • Synchronized BIA (sync-BIA) • Extended BIA (ext-BIA) • Topological BIA (top-BIA) • Network BIA (n-BIA) • Hierarchical BIA (h-BIA) • BIA schemes for Heterogenous Cellular Networks • Cognitive BIA (cog-BIA) • Contributions • Proposed Hybrid BIA scheme for Homogenous cellular networks • Proposed BIA schemes for two-tier Heterogenous Cellular Networks • Scheme#1 : Cross-tier Interference Alignment • Scheme#2: DoF maximization under limited coherence time • Summary & Conclusions • Future Work

  3. Problem Statement • The ever-increasing demand for faster and higher capacity internet connections and multimedia services has made it a necessity for communication engineers to propose new solutions • One suggested solution is to make use of homogeneous cellular networks with smaller cell sizes (densification) • An alternative solution would be to deploy picocells or femtocells under the coverage area of macrocells (heterogeneous networks). It is expected that this will provide the required capacity and in-building penetration and at the same time reduce the load on macrocells.

  4. Dense Homogenous Cellular Network Over the next decade, the wireless traffic volume is expected to greatly increase To meet this demand the use of dense cellular networks by deploying small cells has been suggested. BS3 BS1 BS2 U[1,2] U[2,1] U[2,3] U[1,1] U[2,2] U[1,3] U[4,3] Intra-cell interference Desired signals Densification: reduces the coverage area of cells, allows spatial reuse of spectrum through cell splitting and results in high throughput and cuts down on the energy consumption. Inter-cell interference U[3,3] Base Station (BS) U: th user in BS • Co-tier interference • interference between users of a single cell (intra-cell interference) • interference from neighboring cells (inter-cell interference).

  5. Heterogenous Cellular Networks Femtocell: • Small base stations, low cost, plug and play • Providing coverage to a small area (indoor 10-50m) • Reduces the load on the Macrocell (MC) network • Usually at the same band with the existing MC • Allocates the resources, truly to the mobile users • Can provide high data rates • Co-tier interference • Cross-tier interference (Macrocell to femtocell users) Deployment of femtocells under macrocell coverage Two-tier HetNet • Conventional solution : • Orthogonal access (TDMA/FDMA) • Zero Forcing • Full CSI required at transmitters • Fast and synchronize backhaul links • Number of transmit antennas = Number of desired signals • Interference alignment (IA) • Blind interference alignment (BIA) (requiresNO CSIT)

  6. Outline • Problem Statement • Definitions • Interference Alignment (IA) • Degree of Freedom (DoF) • Standard Blind Inference Alignment (s-BIA) • State-of-the-art • BIA schemes for Homogenous Cellular Networks • Synchronized BIA (sync-BIA) • Extended BIA (ext-BIA) • Topological BIA (top-BIA) • Network BIA (n-BIA) • Hierarchical BIA (h-BIA) • BIA schemes for Heterogenous Cellular Networks • Cognitive BIA (cog-BIA) • Contributions • Proposed Hybrid BIA scheme for Homogenous cellular networks • Proposed BIA schemes for two-tier Heterogenous Cellular Networks • Scheme#1 : Cross-tier Interference Alignment • Scheme#2: DoF maximization under limited coherence time • Summary & Conclusions • Future Work

  7. Degree of Freedom (spatial multiplexing gain) [1] The number of interference free dimensions are referred to as the degree of freedom (DoF) + Channel ,, Channel Point-to-point channel (1Tx , 1Rx) bits/channel-use Capacity: (For large ) • bits/channel-use DoF = Pre-log of capacity = 1 (Point to point channel ) A Channel has “D” Degrees-of-freedom per channel-use iff • bits/channel-use

  8. Interference channel : 1 transmitter with transmit antennas, symbols to send (one symbol from each antenna) 1 receive antenna, times repetition Interference Alignment (IA) [1] observations (equation), Channel precoding (beamforming) vectors Can all the symbols be recovered form the observations available? No Under what condition, can symbol be recovered? Possible ways of achieving interference alignment include: can be recovered iff Span () • Shaping information (manipulating via precoding) • Shaping the channel (manipulating )

  9. Interference Alignment via Manipulation of Beamforming Vectors ( V[i] )[1] Goal : Align unintended signals in one dimensional space other than desired signal space. Interference Alignment at Rx-1 : channel matrix between ith receiver and jth transmitter . ≡ ≡ : beamforming vector of transmitter f. Interference channel (IC) with Under the assumption that full-CSI is available, each receiver solves two equations with 3 unknowns and extracts one desired interference-free signal. Interference Alignment 3 DoF Orthogonalization (TDMA FDMA) 2 DoF per channel use

  10. Standard Blind Interference Alignment (Manipulating )[2] Channel shaping over 3 channel uses Does not require any channel state information at transmitter (CSIT) 2-User 21 MISO BC DoF = Time =1 Rx1 switches on odd time slots Rx2 switches on even time slots Rx1 Ant1 1 transmitter with 2 transmit antennas, 2 receivers each with a single reconfigurable antenna, 4 symbols in total (2 symbols for each receiver). Ant2 Rx2 Time =2 • + • + Reconfigurable antenna • + Time =3 { { User one (Rx1) K-User MISO BC M: number of antennas K: number of users User two (Rx2) Reconfigurable antenna { precoder matrix

  11. Number of alignment blocks of each user-k : • DoF of s-BIA BC and IC[3] • Each Alignment block provide DoF during the supersymbol length (SL) 2-Usres MISO BC • Supersymbol Length (SL) compromises of two blocks: • Interference block with length channel uses • Interference-free block with length equal to channel uses • = The sum-DoF Achievable DoF of user-k : Achievable DoF of all users Supersymbol Length (SL) U2 U1 DoF 2-Usres MISO IC Channel Modes U1 U2 DoF U1 U2 Interference block sum-DoF= Supersymbol length (SL) Interference-free block DoF Alignment block of U1 Alignment block of U2 DoF sum-DoF= Precoder matrix Channel use

  12. DoF of s-BIA BC Under Limited Coherence Time K-User Mx1 MISO BC configuration. : required number of channel uses of s-BIA BC with configuration. : number of transmitted interference-free symbols. : maximum available channel uses at the given coherence time. if if the number of subtractions would result in noise increment Achievable DoF of s-BIA at any given coherence time: if Cost Achievement

  13. S-BIA under different Power Allocation Strategies π is the ratio of power allocated to each symbol in Block1 versus the power assigned to each symbol in Block 2. U1 U2 MISO BC sum-rates for improved BIA vs. standard BIA Interference block (Block1) i terms Supersymbol length (SL) Uniform power allocation = Interference-free block (Block2) (improved) = =

  14. Outline • Problem Statement • Definitions • Interference Alignment (IA) • Degree of Freedom (DoF) • Standard Blind Inference Alignment (s-BIA) • State-of-the-art • BIA schemes for Homogenous Cellular Networks • Synchronized BIA (sync-BIA) • Extended BIA (ext-BIA) • Topological BIA (top-BIA) • Network BIA (n-BIA) • Hierarchical BIA (h-BIA) • BIA schemes for Heterogenous Cellular Networks • Cognitive BIA (cog-BIA) • Contributions • Proposed Hybrid BIA scheme for Homogenous cellular networks • Proposed BIA schemes for two-tier Heterogenous Cellular Networks • Scheme-A : Cross-tier Interference Alignment • Scheme-B: DoF maximization under limited coherence time • Summary & Conclusions • Future Work

  15. Synchronized BIA(sync-BIA)[3] Goal: align intra-cell interference while reducing the effect of inter-cell interference 5 Cell3 6 BS3 • All BSs have same configuration . • S-BIA is implemented at each cell independently. • Neighboring cells are considered as a source of inter-cell interference. • If s-BIA codes of neighboring cells are synchronized (sync-BIA) then source of inter-cell interference would be reduced to users of other Bs with same color index. 2 3 BS2 1 BS1 4 Cell2 Cell1 • No intra-cell interference • The effect of inter-cell interference would be reduced • Supersymbol length (SL) would be significantly reduced Three cell scenario () where, each cell has configuration. Base Station (BS) user DoF= ; Due to the inte-rcell interference from the same color index users of neighboring cells. time slots Precoder matrix

  16. Extended BIA(ext-BIA)[4] Cell3 6 • Goal: align both intra-and inter-cell interferences. • All BSs (F) have same configuration • Precoder matrix is constructed via s-BIA when the whole network is considered as one big cell with transmit antennas and users • Requires a long supersymbol length 5 BS3 4 2 BS2 1 BS1 3 Cell1 Cell2 Three cell scenario () where, each cell has configuration. One big cell with configuration. • Sum-DoF==. Supersymbol length: 7 time slots. • Precoder matrix

  17. Topological BIA (top-BIA)[4] Cell2 Cell3 • Goal: align both intra and inter-cell interferences. • Exploit the location information of the users and base stations in the network to group suitable users that can be served at the same time as a single user (. • The network would be considered as one big cell with transmit antennas and users. , . • Users belong to a user-group () have same precoder. • Each user will be served by its corresponding BS. • Reducing the supersymbol length. 6 4 BS2 BS3 3 5 1 BS1 2 Cell1 Define a group indicator matrix B which labels the suitable users for grouping. Uses long term SINR value as threshold . Examine the proper sub-matrices of B to group the users. Update threshold Precoder matrix would be formed using s-BIA with configuration. Precoder matrix Group indicator matrix B Calculate throughput of top-BIA and compare with aforementioned BIA schemes • sum-DoF= SL =4 time slots

  18. Partially Connected Cellular Network (topological information)[5] A mid-point between providing global CSIT and totally blind schemes is the knowledge of network topology. • PCCNs use the location information of the users and BSs in a network to enhance the performance of BIA schemes. Intra-cell interference Inter-cell interference Base Station (BS) Desired signals U: th user in BS • Partially connected network • cells overlap with each other, • Shared users: users that are trapped in the overlapped region between two or more cells. • Shared users are exposed to both intra and intercell inferences. • Private users : users close to their corresponding BS • Private users can treat intercell interference as noise since they are far from other BSs. • More DoF than fully-connected networks BS2 BS1 U[3,1] U[1,1] U[2,2] U[1,2] U[2,1]

  19. Network BIA (n-BIA)[5] Partially connected network Goal: align both intra and intercell interferences • Benefits from the partially connected network • Private users are served by their corresponding BS. • Shared users are served by all BSs in their vicinity. • Preset modes for each shared user would be : • Shared user switch between modes which is greater than their actual preset modes. • n-BIA can achieve maximum DoF under symmetric homogenous cellular networks, however this is impractical in real scenarios • Beamforming matrix will be constructed based on s-BIA. • Reduce the supersymbol length (SL) P2 Two cell scenario () where, each cell has one private user with one shared user in the system. Each transmitter has antennas ∀. P1 P2 S BS2 BS1 • Precoder matric constructs for 2 users and S. • Precoder of user is same as due to the property of partially connected network. S Actual preset modes: , , Used preset modes: , P1 DoF = time slots

  20. BIA schemes for Homogenous/Heterogenous Cellular Networks Hierarchical BIA (h-BIA)[6] 4-User MISO BC • Goal: Align both intra-and inter-cell interferences • Full network connectivity is required • Shortens the required supper symbol length • Only uses the actual preset modes of each user • Users are served by their corresponding BS • Suffers from some DoF-loss U2 U4 U1 U3 BS1 G2 G1 [2,2] [1,2] I I [1,1] [2,1] • Total number of users () will be spllited into groups • each, with users , here . • th user in th group with preset mode of • would be divided by group-mode value as • Set of all form a group mod set as . 0 I 0 I • To align the inter group interface, pattern would be formed according to the group-mode set • To align the intra group interface, pattern for each group would be formed according to the group mode set of that group as

  21. Hierarchical BIA

  22. Reducing the number of symbol extensions of BIA scheme General ways to reduce the number of symbol extensions (SL) Reduce the number of served users () (fairness problem ) Reduce the number of preset modes used by each user ( to ), Utilizing orthogonalization approaches such as TDMA and FDMA (waisting the available spectrum) Apply hierarchical BIA scheme : the truly used preset modes of user-k : actual preset mode of user-k S-BIA Conventional Preset mode pattern Design CPD

  23. Hierarchical BIA under Limited Coherence Time Dynamic Supersymbol Design (DSD) max Reduce the number of preset modes used by each user ( to ) while applying h-BIA. s.t. The sum-DoF attained for CPD and DSD algorithms assume 4 users and preset mode set with values DSD also includes CPD when

  24. Outline • Problem Statement • Definitions • Interference Alignment (IA) • Degree of Freedom (DoF) • Standard Blind Inference Alignment (s-BIA) • State-of-the-art • BIA schemes for Homogenous Cellular Networks • Synchronized BIA (sync-BIA) • Extended BIA (ext-BIA) • Topological BIA (top-BIA) • Network BIA (n-BIA) • Hierarchical BIA (h-BIA) • BIA schemes for Heterogenous Cellular Networks • Cognitive BIA (cog-BIA) • Contributions • Proposed Hybrid BIA scheme for Homogenous cellular networks • Proposed BIA schemes for two-tier Heterogenous Cellular Networks • Scheme#1 : Cross-tier Interference Alignment • Scheme#2: DoF maximization under limited coherence time • Summary & Conclusions • Future Work

  25. Cognitive BIA (cog-BIA)[7] Aligns both co and cross-tier interferences • The lower tier achieves non-zero DoF while the upper tier obtains the same optimal DoF as when the lower tier is not available. • MBS causes interference on femtocell users (FUs). • FBSs do not cause any interference on MUs. • BIA is adopted in both tiers. Channel Modes MU1 MU2 FU FU MU1 MU2 MU1 FB Desired signal • sum-DoF=. MC with configuration. FU1 Interference block MBS undesired signal Supersymbol length (SL) FC with configuration. FU MUs Interference-free block MU2 SL: 3 time slots. The beamforming vectors of MUs are designed based on s-BIA in absence of FUs. The FU dosn’t change its channel mode during the length of alignment block.

  26. Outline • Problem Statement • Definitions • Interference Alignment (IA) • Degree of Freedom (DoF) • Standard Blind Inference Alignment (s-BIA) • State-of-the-art • BIA schemes for Homogenous Cellular Networks • Synchronized BIA (sync-BIA) • Extended BIA (ext-BIA) • Topological BIA (top-BIA) • Network BIA (n-BIA) • Hierarchical BIA (h-BIA) • BIA schemes for Heterogenous Cellular Networks • Cognitive BIA (cog-BIA) • Contributions • Proposed Hybrid BIA scheme for Homogenous cellular networks • Proposed BIA schemes for two-tier Heterogenous Cellular Networks • Scheme#1 : Cross-tier Interference Alignment • Scheme#2: DoF maximization under limited coherence time • Summary & Conclusions • Future Work

  27. Proposed Hybrid BIA scheme (hybrid-BIA) • Goals: • Align both intra and intercell interferences • Reduce the supersymbol length (SL) • Overcome the DoF-loss that h-BIA suffers from • Each user would be served by its corresponding BS. • No data sharing between BSs is required. • Each user only switches between its actual preset modes. P1 P3 Partially connected network Fully connected network Apply h-BIA Proposed hybrid-BIA Apply top-BIA P4 S1 BS1 BS2 P2 P5 Cell1 Cell2 Cell2 Cell1 User-group , formed by top-BIA :Private user :Shared user Reduce the number of users from to .

  28. DoF-loss due to incomplete grouping Hybrid BIA Under Limited Coherence Time Effect of number of user-groups on performance of hybrid BIA P1 P3 Apply top-BIA P4 S1 BS1 BS2 P2 P5 Cell1 Cell2 Cell2 Cell1 Two cell partially connected network () where, each cell has configuration. • Cell1 has 2 private users (P1,P2) and one shared users (S1). • Cell2 has 3 private users (P3,P4,P5). Possible range of user-groups (depends on number of shared users) condition to apply hybrid BIA Note: each user-group with a single member would correspond to h-BIA

  29. S-BIA vs h-BIA under uniform or constant power allocation Throughput comparison between s-BIA and h-BIA assuming a single cell. A single cell with [K,M] = [4,4] configuration and h-BIA parameters . • At high SNR regime the achievable DoF for h-BIA is also lower than that of s-BIA. • Sum-rate of h-BIA would be less than that of the s-BIA even in a single cell scenario over a wide range of SNR values for both uniform and constant power allocation strategies .

  30. Proposed Hybrid BIA vs state-of-the-art BIA schemes Cumulative distribution function (CDF) for the throughput of BIA schemes compared. Simulation parameters • Sum-rate of the hybrid-BIA is higher than that of h-BIA • (more users would use similar beamforming vectors). • Other methods require long supersymbol lengths and in most practical scenarios they can not be implemented.

  31. Simulation Results for Proposed Hybrid BIA scheme Sum-DoF and Supersymbol Length for different number of users per cell (a) sum-DoF vs number of users per cell • (b) Supersymbol length vs number of users per cell Two-cell scenario where the number of users in each cell is varied from 3 to 14 (K) • Number of user-groups : • when , sum-DoF achieved is optimal for hybrid BIA , • when performance of hybrid-BIA will converge to h-BIA. • The supersymbol length required by top-BIA is much larger than the one for hybrid-BIA.

  32. Supersymbol length and sum-DoF ratios of h-BIA vs hybrid BIA • Each cell is assumed to haveconfiguration. • cells in the network. • Total of users in the network.

  33. Supersymbol length and sum-DoF ratios of h-BIA vs hybrid BIA (a) Effect of number of user-groups on DoF gain and supersymbol length ratio ] (b) Effect of number of transmit antennas (M) on the DoF gain ]

  34. Simulation Results for Proposed Hybrid BIA scheme Effect of number of small-cells (F) on DoF-gain and supersymbol length ratio (b) supersymbol length ratio between h-BIA and hybrid-BIA. (a) DoF gain of hybrid-BIA over h-BIA • Approximately a 3-fold increase in the DoF gain would be obtainedwhen F varies from 2 to 10 (

  35. Outline • Problem Statement • Definitions • Interference Alignment (IA) • Degree of Freedom (DoF) • Standard Blind Inference Alignment (s-BIA) • State-of-the-art • BIA schemes for Homogenous Cellular Networks • Synchronized BIA (sync-BIA) • Extended BIA (ext-BIA) • Topological BIA (top-BIA) • Network BIA (n-BIA) • Hierarchical BIA (h-BIA) • BIA schemes for Heterogenous Cellular Networks • Cognitive BIA (cog-BIA) • Contributions • Proposed Hybrid BIA scheme for Homogenous cellular networks • Proposed BIA schemes for two-tier Heterogenous Cellular Networks • Scheme#1 : Cross-tier Interference Alignment • Scheme#2: DoF maximization under limited coherence time • Summary & Conclusions • Future Work

  36. Baseline Scheme (to which HetNet scheme #1 will be compared to) • All femtocells (FCs) operate at the same time while the macro base station (MBS) operates at a different time. • This implies that FCs and MBS are orthogonal. • (No cross-tier interference) Zero- forcing with water filling BIA • BIA is adopted at each FBS. • (No co-tier interference) • Zero-forcing with water filling has been adopted at MBS. • (one symbol for each Macro cell user (MU)) • (No co-tier interference) DoF 2 DoF 4/3 =10/6 (4/3)/2 DoF + + (2)/2 (2)/2 = 1 DoF 0 Co-tier Interference

  37. BIA schemes proposed for two-tier Heterogenous Cellular Networks HetNet Scheme #1 • Each femto base station (FBS) has been paired with a macrocell user (MU) and all pairs are operating in different time slots. • (Intercell interference from the macro base station (MBS)) • MBS causes interference on femtocell users (FUs). • FBSs do not cause any interference on MUs. • BIA is adopted in each FC. (Intracell Interference) BIA Channel state information (CSI) is known at MBS FU1 Goal: Find FBS FU2 MBS MU By taking the pseudo-inverse of the above equation can be recovered . 1-DoF Macrocell + 4/3 DoF Femtocell =7/3=14/6 DoF does not scale by increasing the number of pairs : Beamforming vector at time slot x

  38. Proposed HetNet Scheme #1 Simulation parameters and achievable sum-rates Achievable mean sum-rates for Proposed Scheme#1 vs. Baseline scheme Simulation parameters . Macro cells : COST231 channel model Femtocells : Non-Line-of-Sight (NLoS) Indoor Hotspot (InH) channel model Two MCs each with one MU and two FCs each with [K,M]=[2,2] configuration Baseline scheme: linear zero forcing with water filling

  39. Proposed HetNet Scheme #1 sum-rates of the proposed HetNet scheme#1 versus varying FBS and MBS transmit powers One MC with one MU and one FC with configuration Macro base station transmit power (dBw) Femto base station transmit power (dBw) MBS transmit power is fixed at 15 dBw and FBS transmit power varies from -20 to 0 dBw. FBS transmit power is fixed at -10 dBw while MBS transmit power varies from 4 to 20 dBw.

  40. Outline • Problem Statement • Definitions • Interference Alignment (IA) • Degree of Freedom (DoF) • Standard Blind Inference Alignment (s-BIA) • State-of-the-art • BIA schemes for Homogenous Cellular Networks • Synchronized BIA (sync-BIA) • Extended BIA (ext-BIA) • Topological BIA (top-BIA) • Network BIA (n-BIA) • Hierarchical BIA (h-BIA) • BIA schemes for Heterogenous Cellular Networks • Cognitive BIA (cog-BIA) • Contributions • Proposed Hybrid BIA scheme for Homogenous cellular networks • Proposed BIA schemes for two-tier Heterogenous Cellular Networks • Scheme#1 : Cross-tier Interference Alignment • Scheme#2: DoF maximization under limited coherence time • Conclusions • Future Work

  41. BIA schemes proposed for two-tier Heterogenous Cellular Networks Proposed HetNet Scheme #2 • G MBSs. • Each MBS has only one MU. • Each MBS serves multiple FCs . • MBSs causes interference on FUs. • FBSs do not cause any interference on MUs. • FCs don’t cause any interference on each other (nointer-cell interference). • BIA is adopted in each FC ( nointra-cell Interference). BIA Channel state information (CSI) is known at MBSs Goal: Find FU1 MU FC1 FBS FU2 FC1 FC2 MBS +DoF Femtocells 1-DoF Macrocell FC2 MBS1 MU FC MBS2 MBS1 FC MU + DoF Femtocell 1-DoF Macrocell By taking the pseudo-inverse of the equation, can be recovered . MU : Beamforming vector at time slot : Number of FCs by config. DoF scales by number of MBSs and FCs configuration x

  42. Proposed HetNet Scheme #2 Maximum Possible DoF Under Limited Coherence Time • Goal • Maximizing the achievable DoF of FCs. • Minimizing the number of subtraction. • Serving Z-FUs at the given coherence time. The overall achievable DoF of the proposed scheme depends on number of MBSs plus the number of FCs of each configuration (. when is fixed and is varied. when is varied and is fixed. s.t. and Maximizing the achievable DoF of FCs. Minimizing the number of subtractions. (Indirectly minimizing values of K,M) reduce the noise increment Z-femto users are available. Coherence time condition. The main goal of IA is transmitting more interference free symbols per channel use. Find the best possible structures . Solution : Find Pareto optimal solution vectors (x), using epsilon constraint method.

  43. Proposed HetNet Scheme #2 Optimization Results Case when is fixed and is varied. • can change the number of Pareto optimal solution vectors () and the set of allowable configurations.

  44. Proposed HetNet Scheme #2 Casewhen is varied and is fixed. Optimization Results and . Lower bound on DoF andwith and Pareto optimal solution vectors follow predictable patterns with changing z, hence they can be formulated as: Upper bound on DoF andwith and

  45. Summary and Conclusions • Homogeneous Cellular Networks • A hybrid-BIA scheme was proposed to handle the inter and intracell interference in homogeneous cellular networks. The strong points of the proposed hybrid BIA include: • Has short supersymbol length (SL) hence can be applied under limited coherence time scenarios • Overcomes the DoF-loss of h-BIA scheme • Each user would be served by its corresponding BS • No data sharing between BSs is required • Each user only switches between its actual preset modes • Can be applied over both dense clustered and partially-connected cellular networks • Supersymbol length of Hybrid-BIA has been compared against the five state-of-the-art BIA schemes and it was shown that hybrid BIA has the shortest supersymbol length among all • Sum-rate formula for hybrid-BIA was driven and CDF versus throughput of five different BIA schemes at the center cluster of a cellular network was evaluated. It shown that the sum-rate for hybrid-BIA is higher than that of h-BIA. • Ratio of supersymbol lengths for h-BIA and hybrid-BIA and sum-DoF gain of hybrid-BIA over h-BIA were evaluated under 3 different scenarios • By varying number of user-groups: It was shown that when each user-group has a single member h-BIA constitutes a special case of hybrid-BIA and these two schemes converge in sum-rate and DoF and in other situations hybrid BIA achieves more DoF with fewer symbol extensions. • By varying number of small-cells: the DoF-gain and the supersymbol length ratio would scale up with the number of small-cells. It was noticed that a five-fold increase on the total number of users in the network would cause a three-fold increases in the DoF gain. • By varying number of transmit antennas: highest DoF gain would be achieved when and as the number of transmit antennas is increased the DoF gain gradually will reduce.

  46. Summary and Conclusions • Two-tier Heterogenous Cellular Networks MCs have access to the global CSIT and s-BIA was employed by each FC. • HetNet scheme#1 • Manage cross-tier interference in two-tier HetNets comprised of macrocell and femtocells. Aligning the interference from MBS on predetermined interference dimensions of FCs at each symbol extension. • Allows MCs and FCs working at the same time or frequency band. • Lower the load of the microcell. • Can be extended to a generalized scenario where each femtocell has different K-user, MISO BC configurations. • DoF and sum-rate were calculated, it was also shown that scheme#1 can achieve higher DoF than BIA schemes and conventional interference avoidance schemes such as TDMA and linear zero-forcing with water filling. • Sum-rate of HetNet scheme#1 was compared with that of the linear-zero forcing with water filling strategy (baseline scheme) by varying FBS and MBS transmit powers under a realistic channel model. It was shown that proposed scheme could achieve a higher sum-rate than the Baseline. • It was demonstrated that the sum-DoF of generalized version of proposed scheme#1 would scale up by increasing the number of FCs.

  47. Summary and Conclusions • Two-tier Heterogenous Cellular Networks MCs have access to the global CSIT and s-BIA was employed by each FC. • HetNet scheme#2 • Extension on HetNet scheme#1 by describing a framework in which maximum possible DoF can be achieved by FCs under limited coherence time • Manages cross-tier interference in two-tier HetNets comprised of macrocell and femtocells • Allows MCs and FCs to work at the same time or in the same frequency band • It was shown that DoF of HetNet scheme#2 is scalable with the number of FCs and their configurations. • Pareto-optimization to determine maximum DoF for minimum number of subtractions (control the noise power) at FCs under limited coherence time was derived. • Results of optimization shown that for fix number of FUs in the network as the values of coherence time is changed the number of Pareto optimal solutions would vary.

  48. Summary and Conclusions • Two-tier Heterogenous Cellular Networks • General framework for finding the upper and lower bounds of achievable DoF and the number of subtractions for a given coherence time and number of FUs has been derived. It was observed that the Pareto optimal solution vectors follow predictable patterns and they could be formulated. • Achievable DoF and sum-rate were calculated assuming both fixed and unlimited coherence times. • It was pointed out that with multiple Pareto optimal solutions, the network planner could flexibly choose a Pareto optimal solution based on available resources.

  49. Future work • Hierarchical BIA suffers from some DoF loss due to the following reasons : • Incomplete grouping problem • Indivisibility of users preset modes (by user-group preset modes () • e.g. DoF of would be same as • The theorical upper bound for DoF of K-user SISO IC using BIA has been evaluated in [9], however the achievability is still an open issue. • Develop user association for cellular network using BIA (investigate switching cells on/off etc.) • Hybrid-BIA can be applied in heterogeneous network. • Hybrid-BIA does not require any data sharing between BSs. Hence, independent of their tiers, users can be grouped together using top-BIA and be served by their corresponding BSs using h-BIA.

  50. Publications • Homogeneous Cellular Networks • [1] Bakhshi R., E. Ince , “Hybrid Blind Interference Alignment in Homogeneous Cellular Networks with Limited Coherence Time” • Int. J. of Commun. Syst., Nov 2018. (https://doi.org/10.1002/dac.3836) • Proposed hybrid-BIA scheme aligns the co-tier interferences in dense small-cell homogeneous cellular network with partial connectivity. The aim is to reduce the supersymbol length and overcome the DoF loss of the state-of-the-art hierarchical BIA (h-BIA) technique. • Heterogenous Cellular Networks • [2] Bahmani K, Bakhshi R, İnce E, Yetiş C, “Interference Management in Two-Tier Heterogeneous Networks Using Blind Interference Alignment” • In: IEEE 23nd Signal Process. and Commun. Appl. Conf., SIU 2015. • Proposed scheme#1: aligns the cross-tier interference in HetNet cellular networks. This method allow MBS and FBS to coexist and operate in the same frequency band and/or time slot. The knowledge of predetermined interference dimensions of the FUs set by BIA and CSIT at MBS are used to align the MBS interference on the FU’s. • [3] R. Bakhshi, E. A. Ince, and C. M. Yetis¸, “Dof maximization in heterogeneous networks using bia under limited coherence time,” • In: Signal Process. and Commun. Appl. Conf., SIU 2016, pp.1721–1724. • Proposed scheme#2: aligns the cross-tier interference in partially connected HetNet cellular networks where multiple FCs are deployed under the overlapping region of adjacent MCs . The paper describes a framework in which maximum possible DoF can be obtained by FC via structure optimization.

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