Prediction of SINR Improvement with a Directional

Antenna or Antenna Array in a Cellular System

Karthik KS

Department of Electrical Engineering,

Indian Institute of Technology Madras,

Chennai, 600036, India

Email: kartks@tenet.res.in

Bhaskar Ramamurthi

Department of Electrical Engineering,

Indian Institute of Technology Madras,

Chennai, 600036, India

Email: bhaskar@tenet.res.in

Abstract—We consider a reuse-1 cellular system and study theimprovement in SINR possible for a fixed/nomadic receiver, fromthe use of an optimally oriented directional patch antenna or aUniform Linear Array (ULA) with 2 or 4 antenna elements alongwith Minimum Mean Square Error (MMSE) combining. Weperform the studies with a ray-tracing propagation model as wellas an empirical statistical model that is based on measurementvalues, in an urban macro scenario. The results show that amean improvement of around 5 dB in SINR is possible usingeither the directional antenna or a 2-antenna ULA. In contrast,a 4-antenna ULA gives a mean improvement of around 11 dB.Interestingly, the results are similar with both channel models.

Index Terms—Ray-tracing, SINR, directional antenna, ULA,MMSE, relay.

I. INTRODUCTION

Comprehensive planning is essential for building a mobile

cellular network, especially for the major emerging standards

of the next-generation cellular networks that target high spec-

tral efficiency. Although there is no frequency planning due

to 1:1 spectrum reuse, the locations of base stations and their

configurations and specifications still need to be determined

and an accurate prediction of coverage and capacity is essen-

tial. There exist a number of prediction models which can be

used for this purpose.

One method of estimating the behavior of signals in a

mobile communication system is by the use of a statistical

propagation model. These models are empirically derived

estimates of attenuation and propagation of electromagnetic

waves within the geographical area of the cell. They make use

of various parameters such as building heights, transmitter and

receiver heights, transmitter-receiver distance and frequency.

Since these are empirical models, an accurate characterization

of the environment with precise building data is not taken

into consideration and the prediction for a receiver location

represents only a typical estimate. The cells are characterized

as urban, suburban and rural, and the model parameters are

varied accordingly.

Ray-tracing [1] is a technique that provides a deterministic

estimate of the mobile radio channel at a particular location.

A model of the actual 3-D environment is created and the

physical wave propagation process is modeled. The radiation

emitted by the transmitter is subjected to suitable formulations

of propagation phenomena such as reflection, refraction and

scattering until several multi-path components reach the re-

ceiver. This ray-tracing technique is used, for example, in the

Radio Propagation Simulator1 (RPS) tool in a deterministic

manner using Geometrical Optics and Uniform Theory of

Diffraction.

The emerging wireless cellular networks are likely to re-

use spectrum in every sector (1:1 reuse) in order to maximize

the system spectrum efficiency. This in turn can lead to

a situation where the receivers near the cell edge experi-

ence a poor SINR (Signal-to-Interference-plus-Noise-Ratio)

due to significant Co-Channel Interference (CCI) from the

adjacent cells. One of the ways to increase the SINR for

fixed/nomadic users is to use a directional antenna at the

receiver in order to suppress the CCI from the adjacent cells.

Employing multiple antennas at the receiver and using some

well-known receiver-based techniques such as MinimumMean

Square Error (MMSE) combining also results in interference

suppression [2].

Using ray-tracing technique in a 3-D model of Dresden city,

we find that the number of strong interferers is mostly limited

to 3 or less in a reuse-1 cellular system. Hence significant

improvement in SINR is possible using either a directional

antenna, or a uniform linear array with MMSE combining at

the receiver. The results are compared with the urban macro-

cell scenario of the WINNER (Wireless World Initiative New

Radio) II generic channel model [3].

The emerging cellular networks are expected to have relays

and pico base stations in large numbers [4]. Relays can be

used to address the problem of poor SINR at cell edges.

In this paper, we attempt to obtain insights regarding the

SINR improvement in cellular networks due to the large-

scale deployment of wireless relays using well-known SINR

improvement techniques, with two different channel models.

Both the models are seen to predict similar improvements,

and hence either of the two models can be used to study

deployment-related issues on wireless relays.

The paper is organized as follows. The ray tracing simula-

tion using RPS is introduced in Section II, followed by the

comparison with WINNER model in Section III. The simula-

1Product of Actix GmbH

tion results are discussed in Section IV, before concluding in

Section V.

II. RAY TRACING SIMULATION

The RPS ray tracing simulation algorithms are based on

geometrical optics. The simulator determines the propagation

paths that can contribute to the signal at a given receiver

position. Besides the geometrical calculation, the propagation

loss is determined for each ray separately.

The transmitters and the receivers are placed as points

in a 3-D topographical database. The RPS accesses the 3-

D database and launches a finite number of rays from each

transmitter position into all directions with 1 deg resolution

in the three-dimensional space. When a ray encounters an

obstacle, the radio propagation effects of reflection, diffraction

and scattering are applied by the RPS simulation algorithms

as per the material properties of the obstacles, which are read

from the material property database. Each ray is traced until a

given maximum path loss is exceeded. A part of the Dresden

3-D environment model along with the rays is as shown in

Fig. 1.

Fig. 1. Dresden 3-D model snapshot

The algorithm calculates the properties of the electromag-

netic field, the complex channel gains, Angle of Departure

(AoD), Angle of Arrival (AoA), and Time Delay of Arrival

(TDoA) for every ray of every transmitter-receiver combi-

nation. The effects of the beam patterns of the transmit

and receiver antennas are taken into account by the ray

tracing algorithm during simulation. The result of the ray

tracing algorithm is a time-invariant (single sample point)

complex impulse response of a Single-Input-Single-Output

(SISO) radio channel between a particular pair of transmitter

and receiver, which can be written as:

hSISO =∑

n

βn (1)

where,

βn = αnexp

(

−j2πdn

λ

)

(2)

for a flat-fading channel [5]. Here, n denotes the path index

between transmitter-receiver pair, αn is the attenuation co-

efficient corresponding to the nthpath/ray, dn is the distance

between the transmitter and the receiver on path n, λ is

the carrier wavelength. RPS tool provides the values of βn

for every ray received in every receiver from each of the

transmitters.

The channel impulse response of a Multiple-Input-Multiple-

Output (MIMO) channel is in the form of a matrix and depends

on the antenna configuration that is used in transmitter and the

receiver as described in [6]. Separate placement of individual

antenna elements in the 3-D database, for an antenna array

with elements few centimeters apart from each other as in the

case of ULAs at a receiver, is not feasible since the resolution

is insufficient. Hence, the channel impulse response matrix is

constructed from the SISO channel impulse response (1) using

the plane wave model and the procedure explained in [6]. In

our simulations, we have considered the inter-element distance

of the ULA to be equal to δ = 0.5λ. The channel impulse

response matrix of a receiver with ULA having Nr antenna

elements can be constructed as a vector of length 1xNr as:

h =∑

n

αnexp

(

−j2πdn

λ

)

1

e−j2π∆ cos φn

...

e−j2π∆(Nr−1) cos φn

(3)

where, ∆ is the spacing between the antenna elements

within the ULA normalized w.r.t λ and φ is the angle of the

incoming ray w.r.t the ULA.

Ray tracing simulation using the RPS tool was carried out

for 100 receiver locations in the Dresden environment. The

entire geographical area was covered by 7 base-stations, each

having three sectors each. The sector antennas were oriented

at 120 degrees from each other and were located well above

(about 25 m) the average height of buildings. The sector

antennas used had a 3 dB bandwidth of 70 deg and a gain of

17 dBi, and a down tilt of 12 degrees. The transmitter power

in each sector of the base-station was fixed at 40 dBm. An

inter-site distance of at least 600 m or more was maintained.

The receivers were placed very close to the buildings, in

a random manner with heights varying from 1.5 m to 6.5

m, to simulate placement near windows. The simulation was

performed at 2 GHz center frequency with the channel band-

width set to 180 kHz, with the assumption that the channel is

approximately flat within 180 kHz bandwidth. The bandwidth

of a single Resource Block in the 3GPP LTE standard [7]

is 180 kHz. Rays were launched from every transmitter and

each ray was traced until a maximum path loss of −155 dBm

was reached. After the completion of ray-tracing simulation,

channel impulse responses were calculated as per (1) and the

SINR was calculated as follows for each transmitter-receiver

pair:

SINRik SISO =|hSISOik|

2

∑K

j=1,j 6=k |hSISOij |2 + σ2

(4)

where, SINRik SISO denotes the SINR at the ith receiver

due to kth transmitter, K is the total number of transmitters

which in our simulation is equal to 21 sectors. σ2 denotes

the thermal noise power corresponding to 180 kHz. We had

set the thermal noise level at −174 dBm/Hz. The transmitter

corresponding to the maximum SINR for a particular receiver

is considered as its best serving transmitter/cell.

We first considered omni-directional antennas at the re-

ceivers and performed the ray-tracing simulation. Next the

antennas were changed to directional patch antennas having

a gain of 5.5 dBi. Since the paths of the rays have been traced

already, it is not necessary to repeat the entire simulation

again. Instead, the channel gain co-efficients are re-calculated

taking the receivers’ antenna beam pattern and orientation into

consideration. The SINR was then calculated for each receiver-

transmitter pair using equation (4) by changing the horizontal

orientation of the receiver (i.e, the directional antenna) in

steps of 1 degree. The maximum SINR was taken to be the

SINR for that particular receiver from its serving cell, and

the corresponding angle taken as the best orientation angle. It

should be noted that the best angle is not necessarily in the

direction of the base-station with the strongest signal.

We then calculated the channel impulse response matrix

for a receiver with multiple antenna elements using (3), for

1x2 and 1x4 cases. Using these channel matrices, MMSE

combining was performed at each receiver and post-processing

SINR was calculated.

The tap weights of the MMSE combining receiver are

calculated as given in [2]:

wik = R−1ik hik (5)

where, Rik denotes the co-variance matrix (2x2 or 4x4 accord-

ingly) of the CCI signals at the receiver i with kth transmitter

considered as the serving cell. Rik is given by

Rik =

K∑

j=1,j 6=k

hijhHij + σ2

I. (6)

MMSE post-processing SINR is calculated for each receiver-

transmitter pair using the following formula:

SINRik M = hHikR

−1ik hik (7)

The transmitter corresponding to the maximum SINR for a

particular receiver is considered as its best serving transmit-

ter/cell, which need not be the same as the one found for the

receiver with a single omni-directional antenna.

III. COMPARISON WITH WINNER GENERIC CHANNEL

MODEL

For validating these results, we took the WINNER II generic

channel model with urban macro cell scenario. WINNER II

generic channel model is a geometry-based stochastic model

whose modeling approach is recommended by International

Telecommunication Union (ITU) for the evaluation of Interna-

tional Mobile Communications-Advanced (IMT-A) candidate

radio interface technologies [8]. In this model, the channel

parameters for the individual snapshots are determined in

a stochastic manner, based on the statistical distributions

extracted from several channel sounding measurement cam-

paigns. The distributions are defined for the large-scale param-

eters such as the delay spread, angle spread, shadow fading

etc., and these are drawn randomly from the tabulated distribu-

tions. The small-scale parameters and the channel realizations

are then generated using these values as control parameters.

In the urban macro cell scenario, 100 receivers were

“dropped” at locations having same x-y co-ordinates as was

done for ray-tracing. The base-stations were placed at the same

locations with the same orientation for the sector antennas. The

generic channel model was built as per the steps enumerated

in [3] for four different cases: single omnidirectional antenna

at all the receivers, single directional patch antenna at all

the receivers, and 1x2 and 1x4 ULA MIMO configurations

respectively. For the directional patch antenna, the same an-

tenna pattern was used as in ray-tracing and the orientation

was varied from 0 deg to 359 deg in steps of 1 deg in the

horizontal direction. After obtaining the channel co-efficients,

the best serving-cell SINR was calculated for each receiver-

transmitter pair.

IV. DISCUSSION OF SIMULATION RESULTS

The cdf of SINR of all the receivers with different an-

tenna configurations obtained with both ray-tracing as well

as generic channel model are shown in Fig. 2 and Fig. 3. It

is seen that the ray-tracing and statistical models give very

similar results.

−10 0 10 20 300

0.2

0.4

0.6

0.8

1

SINR in dB

cdf of SINR

Pro

bability[S

INR

≤ a

bscis

sa]

Omnidirectional (RT)

Directional antenna (RT)

Directional antenna (GCM)

Omnidirectional (GCM)

Fig. 2. CDF of SINR of receivers with Ray-Tracing (RT) and WINNERGeneric Channel Model (GCM)

−10 0 10 20 30 40 500

0.2

0.4

0.6

0.8

1

SINR in dB

cdf of SINRP

robability[S

INR

≤ a

bscis

sa]

1x2 ULA + MMSE (RT)

1x4 ULA + MMSE (RT)

1x2 ULA + MMSE (GCM)

1x4 ULA + MMSE (GCM)

Fig. 3. CDF of SINR of receivers with Ray-Tracing (RT) and WINNERGeneric Channel Model (GCM)

The mean improvement in SINR is around 5 dB for the

directional patch antenna as well as the 1x2 ULA configura-

tion with MMSE combining at the receiver, while the mean

improvement with 1x4 ULA configuration is around 11 dB.

We found that the mean improvement in SINR is similar

in the results obtained from both the ray-tracing technique as

well as WINNER generic channel model. Hence, either of the

two models can be used to study the SINR profiles in reuse-1

cellular system. The cdf of SINR improvement is plotted in

Fig. 4.

0 10 20 30 400

0.2

0.4

0.6

0.8

1

SINR in dB

cdf of improvement in SINR

Pro

ba

bility[S

INR

≤ a

bscis

sa

]

1x2 ULA + MMSE (RT)

1x4 ULA + MMSE (RT)

Directional antenna (RT)

Directional antenna (GCM)

1x2 ULA + MMSE (GCM)

1x4 ULA + MMSE (GCM)

Fig. 4. CDF of improvement in SINR with Ray-Tracing(RT) and WINNERGeneric Channel Model

We see that, the 1x4 ULA followed by MMSE processing at

the receiver provides the best SINR gain in all the investigated

cases. This is not surprising, as it has been shown in [2] that

an N-antenna receiver with MMSE combining can completely

cancel interference if there are N-1 interferers or less(in the

absence of noise). Hence, the 1x4 ULA based receiver with

MMSE combining can cancel upto 3 strong interferers. In

contrast, a 2-element ULA with MMSE processing can cancel

only a single source of interference. The SINR cdf of receivers,

plotted by taking into consideration only the three strongest

interferers and neglecting the remaining interference, showed

that the number of strong interferers is mostly limited to 3 or

less, as seen in Fig. 5. Thus, 1x4 ULA receiver with MMSE

combining can cancel the three strongest interferers most of

the time, thereby giving a significant improvement in SINR.

−10 −5 0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

SINR in dB

Pro

ba

bility[S

INR

≤ a

bscis

sa

]

SINR CDF calculated with strong interferers − all with omnidirectional antennas

SINR with all interferers

SINR with 3 strong interferers

SINR with 1 strong interferer

Fig. 5. SINR CDF with ray-tracing with 1, 3 and all interferers respectivelywith omnidirectional antenna

We then plotted the cdf of SINR of receivers with SINR

less than 0 dB with omnidirectional antenna. Typically, one

can expect the cell-edge receivers to have a low SINR. There

is at least a mean improvement of 5 dB for low-SINR receivers

using either 1x2 ULA with MMSE combining or a directional

antenna oriented at the best angle. With 1x4 ULA, the mean

improvement is more than 10 dB. Fig. 6 shows the absolute

SINR cdf for receivers which had a SINRSISO less than 0

dB with an omni-directional antenna, while Fig. 7 shows the

cdf of improvement in SINR for these receivers, compared to

the case with omni-directional SISO receiver antenna.

V. CONCLUSION

Use of a 4-antenna ULA followed by MMSE combining

provides a significant improvement in SINR on the downlink

for fixed/nomadic terminals, while the patch antenna oriented

at the best angle also performs as well as a 2-element ULA

with MMSE combining at the receiver. The advantage of

−5 0 5 10 15 20 25 30 350

0.2

0.4

0.6

0.8

1

SINR in dB

cdf of SINR of receivers with SINRomnidirectional

< 0 dBP

rob

ab

ility[S

INR

≤ a

bscis

sa

]

1x2 ULA + MMSE

1x4 ULA + MMSE

Directional antenna

Fig. 6. CDF of low-SINR receivers

0 5 10 15 20 25 30 350

0.2

0.4

0.6

0.8

1

SINR in dB

cdf of SINR improvement of receivers with SINRomnidirectional

< 0 dB

Pro

ba

bility[S

INR

≤ a

bscis

sa

]

1x2 ULA + MMSE

1x4 ULA + MMSE

Directional antenna

Fig. 7. CDF of improvement in SINR for low-SINR receivers

multi-antenna element ULA with MMSE processing compared

to the patch antenna is that the need for orienting the receiver

at the best angle is eliminated, while the complexity of MMSE

processing is not very high. The results obtained using ray-

tracing simulator in a realistic urban scenario were compared

to those obtained using a statistical propagation model, and

found to be similar in all cases. 3-D models may not always

be available and ray tracing may be cumbersome. This work

establishes the validity of the statistical model for predicting

the performance of network element nodes with directional

antennas/antenna arrays. This is a useful feature for future

simulation studies.

These results can be used in several applications such as

the design of fixed terminals or indoor relays [9]. It may be

difficult to realize the gains from directional antennas or ULAs

with a mobile device, due to the physical limit on the number

of antennas and antenna spacing. Indoor relays in particular

are very promising as an alternative, particularly when femto

base-stations [10] are not feasible due to the lack of wireline

connectivity.

ACKNOWLEDGMENT

The authors thank Jens Voigt and Actix GmbH for providing

one of the authors an internship opportunity, and for providing

access to the professional version of the Radio Propagation

Simulator (RPS) tool for this research work.

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