Location Classification in Fractional Frequency Reuse (FFR)-based Systems

A Logistic Regression Approach to LocationClassification in OFDMA-based FFR Systems

Ajay Thampi

University of Bristol

[email protected]

June 7, 2013

Ajay Thampi (University of Bristol) Location Classification in FFR Systems June 7, 2013 1 / 33

Thanks to...

Co-Authors/Supervisors

Dr. Simon Armour, University of BristolDr. Zhong Fan, Toshiba Research Europe Ltd.Dr. Dritan Kaleshi, University of Bristol

Also, thanks to U.K. Research Council and Toshiba for jointly funding myPhD under the Dorothy Hodgkin Postgraduate Awards.


Overview

Focus is on the problem of location classification in Fractional FrequencyReuse (FFR) systems. Topics covered include:

Background on Interference

Overview of FFR

Importance of User Location Classification

Two Approaches1 One-Dimensional Threshold (SINR)2 Logistic Regression (Received Power and SINR)


Background

Interference is one of the major performance limiting factors incellular networks

Intra-Cell Interference1 Orthogonal Frequency-Division Multiple Access (OFDMA)

Inter-Cell Interference (ICI)1 Interference Regeneration and Cancellation2 Interference Coordination (ICIC)

Popular ICIC Techniques:1 Power Control2 Fractional Frequency Reuse (FFR)3 Network or Cooperative MIMO4 Interference Alignment5 Network Coding6 ...


Fractional Frequency Reuse (FFR)

The basic idea is to partition the bandwidth of the cell so thatcell-edge users have a higher reuse factor than cell-centre users

Usually, cell-centre users enjoy a reuse factor of 1

Optimal reuse factor for cell-edge users is 3 [1]

In order to further improve the SINR and throughput for cell-edgeusers, power control is done on the downlink (DL)

Pm =

{P0 if m is a cell-centre userP1 if m is a cell-edge user

, (1)

where P0 < P1.


FFR Strategies

There are two broad classes of FFR schemes:

1 Static: Resource partitioning and sub-carrier allocation is donestatically

2 Adaptive: Semi-static Radio Resource Management (RRM) andDynamic RRM

The focus is on FFR schemes with static resource partitioning, where agreater portion of the sub-bands are reserved for cell-centre users.


FFR Schemes

1 Strict-FFR (FFR-A)

2 Soft Frequency Reuse (FFR-B)


Static Resource Partitioning

Ri is one of the most important design parameters in FFR systems.For FFR-A and FFR-B,

Nc =

⌈Nband

(Ri

R

)2⌉

(2)

For FFR-A,

Ne =

⌊Nband − Nc

3

⌋(3)

For FFR-B,

Ne = min

(⌈Nband

3

⌉,Nband − Nc

)(4)

Equations (2), (3) and (4) obtained from [2].


Resource Allocation Comparison

For the optimum RiR ratio of 0.63 [1], FFR-A utilises only 60% of the total

sub-bands as opposed to about 73% for FFR-B.


User Location Classification

FFR schemes with static resource partitioning require knowledge ofthe user location - centre or edge

In [3] and [4], a graph-based approach was used for resourceallocation in both static and adaptive FFR schemes

I Interference graph that requires knowledge of the user location isconstructed

I Assumption is that accurate user location is available

Common technique is to use a one-dimensional threshold such asSINR or f-factor

Alluded to in 3GPP TSG-RAN R1-050738 that in the presence ofshadowing, some users within Ri were misclassified as edge users

Focus is on the implications of this classification mix-up on the overallsystem performance (DL)


Classification based on a One-Dimensional Threshold


Location Classification

One-dimensional threshold denoted as SINRth

Location of MS m is then given by,

ym =

{0 if SINRm ≥ SINRth

1 if SINRm < SINRth, (5)

where 0 → cell-centre and 1 → cell-edge.


Simulation Setup (1)

Cell ParametersNumber of Cells 19

Cell Radius (R) 750m

Cell Interior Radius (Ri ) 500m

Load (MSs/cell) 5, 10, 15, 25, 30

Load Distribution Symmetric

Antennas SISO and Omnidirectional

OFDMA ParametersTotal Bandwidth 30MHz

Number of Subchannels (Nband) 30


Simulation Setup (2)

Channel ModelCarrier Frequency 1.9GHz

Reference Distance (d0) 100m

Path Loss Exponent (n) 4 (Urban)

Shadowing Model Log-Normal

Shadowing Variance (σ2) 10dB

Power Control ParametersCell-Centre Power (P0) 40 dBm

Cell-Edge Power (P1) 46 dBm

Thermal Noise Density (N0) -174dBm/Hz

QoS ParametersMinimum serviceable SINR (SINRQ) -1dB


Accuracy and Thresholds

FullLoad (MSs/cell) 5 10 15 25 30Accuracy (%) 84 84 84 84 84SINRth (dB) 9 9 9 9 9

Reuse-3Load (MSs/cell) 5 10 15 25 30Accuracy (%) 83 83 83 83 82SINRth (dB) 21 21 21 21 21

FFR-ALoad (MSs/cell) 5 10 15 25 30Accuracy (%) 67 67 67 67 67SINRth (dB) 23 23 23 23 23

FFR-BLoad (MSs/cell) 5 10 15 25 30Accuracy (%) 66 67 67 67 67SINRth (dB) 18 18 18 18 18


Performance Comparison

There is therefore a need for better user location classification in FFRsystems with static resource partitioning.


Classification based on Logistic Regression


The Classification Process

For Logistic Regression (LR), the hypothesis function is typicallyrepresented as a sigmoid function.

f (x (i)θ) =1

1 + exp(−x (i)θ)(6)

Hypothesis functions of various degrees form the hypothesis set, H.Examples for two primary features x2 and x3,

Degree = 1

f (x (i)θ) = f (θ1 + θ2x(i)2 + θ3x

(i)3 )

Degree = 2

f (x (i)θ) = f (θ1 + θ2x(i)2 + θ3x

(i)3 + θ4(x

(i)2 )2 + θ5(x

(i)3 )2 + θ6x

(i)2 x

(i)3 )


Structure of the Training Set

Besides SINR, an additional input feature is added - Received Power

Matrix X contains all the training examples

size(X ) = m× n where m is the number of training examples and n isthe number of features

At a bare minimum, H must contain one function for a polynomialinput of degree 1

Structure of X for degree 1

X =

x1 x2 x3

(7)

where x1 = 1 corresponds to the null input, and x2 and x3 containthe received power and SINR values from all the training examples

θ = (θ1 θ2 θ3)T for degree 1


Location Classification

Location of MS i is classified as follows,

y (i) =

{0 if f(x (i)θ) < 0.5

1 if f(x (i)θ) ≥ 0.5, (8)

where 0 → cell-centre and 1 → cell-edge

Probability of successfully classifying the user locations in-sample isgiven by,

Pin =m∏i=1

P(y (i)| x (i)), (9)

where P(y (i)| x (i)) = y (i)f (x (i)θ) + (1− y (i))(1− f (x (i)θ))Assumption: All the training examples are collected independently


Optimum Parameters (1)

Objective function is,

Ein(θ; f ) =1

m

m∑i=1

{ln(1 + e−x(i)θ) + (1− y (i))x (i)θ

}(10)

obtained by taking the negative of the natural logarithm of Pin inequation (9)

Optimum parameters given by, θ∗ = arg minθEin(θ; f )


Optimum Parameters (2)

Gradient descent algorithm is used, where the gradient is given by,

∇θEin(θ; f ) =1

m

m∑i=1

x (i){f (x (i)θ)− y (i)

}(11)

For faster convergence, the features are normalised as follows,

x j =x j − µjσj

; 2 ≤ j ≤ n, (12)

where µj is the mean and σj is the standard deviation of feature j .


Optimum Hypothesis (1)

Out-of-sample error measure given by Eout(θ; f ), and computed thesame way as Ein(θ; f ) in equation (10)

Optimum hypothesis is one that minimises the generalisation errorgiven by Eout(θ; f )− Ein(θ; f )

Hypothesis with higher degree polynomial input is more likely toperform better in-sample than that with degree 1

If shadowing is extreme, this could lead to overfitting and highgeneralisation error

Overfitting can be countered by regularisation

Ein,r (θ; f ) = Ein(θ; f ) +λ

2m

n∑j=1

θ2j (13)


Optimum Hypothesis (2)

Optimum hypothesis is determined heuristically

Learning landscape for FFR-A under high load (25-30 MSs/cell)

Generalisation errors with regularisation for FFR-A under high load,where degree is 17 and m is 3650

λ 0 0.1 0.5 1 3 6

Error 7.95 7.93 6.01 8.02 8.10 8.18


Simulation Setup

Optimum LR Hypothesis

Degree of Polynomial, x (i)θ 1

Regularisation Parameter, λ 0

Gradient DescentStep Size, η 0.01


Accuracy and Parameters (1)

For FFR-A,

Load (MSs/cell) 5 10 15 25 30

Accuracy (%) 84 87 87 87 87

θ1 1.02 1.17 1.24 1.20 1.18

θ2 -59.09 -72.96 -76.28 -72.32 -72.00

θ3 51.14 64.23 68.66 72.21 65.54

µ2 (dBm) -67.82 -67.70 -67.98 -67.92 -68.01

σ2 (dBm) 63.96 64.62 68.61 64.69 65.33

µ3 (dB) 12.87 12.75 12.48 12.53 12.45

σ3 (dB) 65.12 64.91 70.20 73.24 67.59


Accuracy and Parameters (2)

For FFR-B,

Load (MSs/cell) 5 10 15 25 30

Accuracy (%) 84 83 82 83 83

θ1 1.12 0.92 1.04 0.97 1.01

θ2 -48.04 -55.15 -46.91 -46.77 -46.39

θ3 42.21 46.97 44.23 41.23 39.41

µ2 (dBm) -68.02 -68.10 -68.05 -67.95 -68.00

σ2 (dBm) 67.56 76.54 64.76 64.37 63.21

µ3 (dB) 7.26 6.70 6.78 6.84 6.76

σ3 (dB) 71.15 77.92 73.25 68.13 64.74


Performance Comparison


Practical Considerations

Huge training effort required for various loads and networkconfigurations

This effort can be ameliorated by the operators by employing MDTreports specified for LTE in 3GPP TS37.320 (Release 10)

The MDT report consists of:I Received Power (RSRP)I SINR (RSRQ)I Detailed Location Information


Conclusions

One-dimensional (SINR) threshold approach has serious shortcomingsI Location classification right only 67% of the timeI Under high load,

F 38% drop in cell throughput for FFR-A and 14% for FFR-BF 28% drop in service rate for FFR-A and 24% for FFR-B

Logistic Regression with two features (Received Power and SINR)does better

I Location classification right >80% of the timeI Compared to the SINR-threshold approach under high load,

F 52% improvement in cell throughput for FFR-A and 17% for FFR-BF 25% improvement in service rate for FFR-A and 20% for FFR-B


Possible Future Directions

Performance studies under asymmetric load distributions and forheterogeneous networks

Investigate other techniques such as Support Vector Machines andNeural Networks

Location classification could be circumvented if the resourcepartitioning is made dynamic

I Requires base station cooperation


Thank you for you attentionQuestions & Feedback


References

Assaad, Mohamad (2008)

Optimal FFR in multicellular OFDMA system

IEEE VTC Fall, pp. 1-5.

Novlan, Thomas; et al (2010)

Comparison of FFR approaches in the OFDMA cellular downlink

IEEE Globecom, pp. 1-5.

Chang, YJ; et al (2008)

A graph-based approach to multi-cell OFDMA downlink resource allocation

IEEE Globecom, pp. 1-6.

Chang, RY; et al (2009)

A graph approach to dynamic FFR in multi-cell OFDMA networks

IEEE ICC, pp. 1-6.


Engineering

Location Classification in Fractional Frequency Reuse (FFR)-based Systems