**3 WCDMA REPEATER**

**3.2 Repeater Equipments**

A repeater system consists of repeater unit, donor and service antennas, and feeder cables as shown in figure 3.4. The main tunable equipment of repeater is the gain. The donor antenna is likely to be directional since it points straight to a particular base station (Node B). It intercepts the base station signal (downlink) as well as transmits back the amplified signal from the user equipment to the base station (uplink).

Vice-versa, the service antenna transmits the downlink signal to as well as intercepts the uplink signal from the user equipment. Service antenna radiation pattern usually has wider beam width that depends on the intended coverage area.

Figure 3.4. A typical repeater installation in a building rooftop.

WCDMA repeater is similar to analog repeater. It does not regenerate data. This means that also noise and interference are amplified. It is the main issue that we are going to deal with. Repeater is also transparent to the surrounding network. Neither the parent cell nor the user recognizes whether a repeater is installed under its coverage area or not. Repeaters are „invisible‟ to both base station and users. More clearly repeater acts as a loud speaker, no one expects a repeater to show up somewhere. In the following chapter we will depict more characteristics of repeater transmission in WCDMA system. These properties help us to understand the behavior of repeater and also relate to the following works.

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**4. Radio network planning **

### 4.1. Radio network characteristics

Before going further, we make some assumptions about repeater first.

A. Repeaters have perfect isolation.

Both donor and service antennas are characterized amongst others by their gain and radiation pattern. The antenna radiation pattern shows the angular attenuation in horizontal or vertical plane. There exists some degree of coupling or feedback path between donor and server antennas used. This attenuation or loss in the feedback path is called the antenna isolation and in general must be at least 15 dB higher than the repeater gain to give sufficient margin against potential self-oscillation in the repeater system. An oscillating repeater will not function properly and may present a large interfering signal into the network. We assume perfect isolation of repeater which means the antenna isolation is large enough so that there will be no oscillation.

B. No feedback interference.

In real world, feedback interference can be reflected from buildings, mountains, hills, and moving vehicles around the repeater. Signals received by donor antenna including designated BS signal (input signal), feedback interference (direct feedback) and reflected interference (multipath feedback). Repeater simultaneously transmit and receive, so feedback interference from transmit antenna to receive antenna can be significantly larger than the desired signal when these two antennas are closely located. Interference cancellation system (ICS) is used to cancel unwanted signal by repeater itself. ICS is a technique which estimates the amplitude, phase and delay of the feedback signal buried in the input signal to the repeaterand cancels the feedback signal with the signal generated from the estimated amplitude, phase, and delay. Here we assume repeater can cancel unwanted signals by itself using ICS and neither feedback interference nor reflected interference is in consideration.

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The repeater functions considered in this thesis are shown in figure 4.1 which consist
*of a repeater gain unit and a maximum output power limitation unit. The input signal s *
*is multiplied by repeater gain G to form the output signal. If the output signal Gs *
exceeds the maximum output power restriction it is forced to lower down the output
power to maximum output power level at most.

Figure 4.1. Repeater functions.

In WCDMA system signals are differentiated by PN (pseudo-noise) codes of users.

Each user is assigned a unique code sequence that is used to spread the information signal on the common channel. At the receiving end each user exacts its own information by multiplying the received signal by the code. We can have the sense that in a repeater embedded system BS transmits signals to all the users and repeaters at the same time and users use their unique PN codes to differentiate signals from noise and interference. The same thing happens to the repeater.

BS knows which user is covered in the cell but it is not quite true for repeater. The size of repeater‟s coverage area depends on the repeater output power. The larger the output power is the more users it covers. The number of users served by a repeater is not constant. The relationship between repeater and user is not as close as in BS and user. It is conformed to the role repeater plays: an invisible loud speaker.

Repeater receives signal and re-transmits it without regenerate the data. Namely repeater does not decode signals it receives; it has no idea about the packet of what information it carries and whom it transmits to.

To summarize, due to the characteristics of repeater no power control over singer user is available. No matter the BS or repeater, every transmission carries all the signals of all users, rather than independent transmission. From the repeater‟s point of view it is not possible to do single user power allocation. In the contrast we need to consider the gain control of each repeater at every transmission.

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Also we have to note that when dealing with repeater, interference is the major issue.

Both BS and repeaters deliver the same signals in different power. The received signals of a user from different directions contain both wanted and unwanted information. Traditionally when talking about interference, there is only one node delivering useful information and the rest are regarded as interference sources. But repeater in WCDMA system is totally different. We cannot treat signals as pure useful information or interference. Instead we have to extract desired part of signal and regard the rest as interference.

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### 4.2. Problem formulation

Under the characteristics of repeater-embedded WCDMA system, the problems we want to solve are classified into two categories as follows:

A. Find out the impact of repeater to the whole system in different scenarios. It is done by increasing the repeater gains from 0 to 80 dB (effective output power range).

There are three situations:

i. Single cell. Without inter-cell interference.

ii. Multi cell with fixed inter-cell interference.

iii. Multi cell with changeable inter-cell interference.

Here the words „fixed‟ and „changeable‟ are comparative to the increasing repeater gains (from 0 to 80 dB). If the inter-cell interference is fixed during the center cell repeater gains increase it is defined as fixed inter-cell interference and vice versa.

First we want to figure out if repeaters can really benefit the system on capacity and coverage area. If yes, further question is how much and what‟s the behavior?

B. The most important part is to maximize the system capacity with the use of repeater gain control.

We expect there are maximum values in three different scenarios. If there are no such optimum points, then what is the behavior and in what situation can we find an optimum value? In the following chapter we will find out.

The methods to find the optimum value of capacity are done by applying the optimization algorithm and proposed algorithm which are introduced in the following chapters.

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### 4.3. Radio Network Performance indicators

Indicators are defined to give information about the UMTS network performance.

Some important indicators for the studies in this document are described shortly to understand the analysis performed in the following chapters in this document.

**Repeater deployment threshold **

This threshold which is based on user SINR is an indicator to determine which repeater should be turned on. Repeaters are built at fixed positions. The surrounding environment may change with time due to the buildings or constructions. Repeaters are adapted to the changing circumstances by turning on or off. This threshold gives a criterion of how worse the received SINR be should a repeater be turned on. The threshold also determines how many active repeaters are in a cell.

**Spectrum efficiency **

Spectrum efficiency refers to the information rate that can be transmitted over a given bandwidth. It is a measure of how efficiently a limited frequency spectrum is utilized by the physical layer protocol. Here we use Shannon capacity defined as follow:

*Spectrum efficiency = log*

*2*

*(1+SINR) (1) *

where SINR is the signal to noise and interference ratio of single user. It is sum up to all the cell users in the situations of without and with repeater embedded.

**Outage number **

Outage number is the number of users whose SINR are below a certain threshold. In the simulation we will set a threshold which can be a SINR value or the percentage of outage user number to all users.

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**5. Capacity analysis **

The user SINR is a very important indicator in this thesis. In this chapter we are going to demonstrate the user SINR and the associated Shannon capacity.

Figure 5.1. Transmission paths for a repeater installation.

Figure 5.1 shows the transmission paths from BS and repeater to user. Now we only
consider single cell. BS transmits signals to both repeaters and users; repeaters
amplify the signal and re-transmit to users. From the user‟s point of view the only
*possible paths it could receive are from BS and cell repeaters. P**BS** and P**REP* are
*transmitting power of BS and repeater. G**ij** is the path gain from j*^{th}* transmitter to i** ^{th}*
receiver. It can encompass path loss, shadowing, antenna gain, coding gain, and other
factors.

Assume each user is assigned different power. The total transmitted power (could be
*of BS or repeater) is P**total**. For i** ^{th}* user it is allotted

(2)
* is the power ratio of user i to total power which value is between 0 and 1. It is the *
weighting of how much power is allocated to a user. And . The rest of the
power _{ }

* is regarded as interference from transmitter to other users *

*except user i. The overhead channel power is*

_{ }.

User BS

Repeater

*P*_{BS}*P*_{REP}

*G*_{user_BS }*G**user_REP*

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The signal power may decay during transmission, but the ratio of every user‟s power stay unchanged even the signal goes through fading. It becomes

* * _{ } _{ }

* (3) *

When user receives signal the above part is the desired information and the other is
unwanted which has power
_{ } _{ } _{ } (4)

Assume there are users and repeaters with power in a cell and
signals from different paths can be processed by the user (upper bound). The SINR of
*user i is *

_{ } _{ } _{ } _{ }

_{ } _{ } _{ } _{ } _{ } _{ }

* is the orthogonality factor which ranges from 0 to 1. * is the thermal noise.

Both the numerator and denominator include signals from BS and repeaters.

Traditionally we do power allocation on each user according to its channel condition.

However in repeater embedded system, every user‟s power is determined by BS,
repeaters only amply signal. We can see from the above formula, * for j = 1,…, *
are the variables and they are affected by repeater gains. The power allocation is done
on repeaters not on users. Every transmission each repeater has to decide the gain
associated with each other.

Equation (5) is the single cell case. If we consider multi-cell, the only difference from equation (5) is the inter-cell interference. The formula becomes

_{ } _{ } _{ } _{ }

_{ } _{ } _{ } _{ } _{ } _{ } _{ }

* can come from other-cell BS and/or repeaters. *

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The capacity of a user can be calculated as

(7)

And the cell capacity is

(8)

So far we have proposed the user SINR and cell capacity. These are the measurements of the repeater buried system performance. The next thing we want to know is how much improvement can repeaters increase? This is done by solving the following optimization problem:

subject to

_{ }

The objective function is the overall system throughput. It is optimized over the set of all feasible powers . The transmit power of every repeater has to be a positive value.

The second set of constrains gives a limit on repeater‟s output power. The last set of constraints is the data rates demanded by existing system users.

We use cvx which is a modeling system for disciplined convex programming developed by Michael Grant and Stephen Boyd to solve this problem. However since the mapping from repeater transmitting power to SINR function is not convex, it is impossible to directly deal with it via cvx. Alternatively we take the approach to approximate the non-convex Shannon capacity equation into piecewise linear functions, which can be managed by cvx.

To do so, we first look at the characteristic of Shannon capacity:

= _{ } _{ } _{ } _{ } _{ } _{ } _{ }
_{ } _{ } _{ } _{ } _{ } _{ } _{ } * *

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As seen above, Shannon capacity is decomposed into and – functions, which takes the sum of linear variables as the input. Therefore, if we can approximate the and – into linear functions, Shannon capacity is also approximated into linear functions. Fortunately is a concave function, which can be easily approximated as the sum of piecewise affine functions:

(9)

*where n is an index variable and * is a positive value. Specifically, the parameters of
each line and the number of lines can be adjusted according to the required precision.

By using this approximation technique, we can represent part of Shannon functions; and are approximation parameters.

While can be directly approximated through simple intersection, –
cannot be done in such way, but can be approximated by getting the union region. To
*do so, we need to select a proper affine function depending on domain x. More *
specifically we will add the virtual infinite value to the other affine functions except
the proper affine function to safely ignore them. We take the selection technique again,
*and hence, an indicator variable v**in* is introduced to choose the proper affine function,
which gives the biggest value for a given input. Finally we obtain the inequality
*A constrain for v**in* is also required:

_{ } * *

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Finally we can define the optimization problem as follows:

re-write it more clearly, it would be like this:

*For k = 1,…,N *

18 performance is close to the optimization result.

With the knowledge of repeater the most apparent factors one might think of affecting repeater gains are the distance and user distribution. The former means the distance from repeater to users or repeater to the cell edge. With the existence of multi-cell interference the critical thing is to avoid repeater transmits severer interference which might damage the surrounding users and when the repeater is close to the cell edge the gain should be low for the same reason. The latter means to tune the repeater gains according to the user distribution.

We try to verify the above assumptions by observing the optimization result. The conclusion however does not conform the assumptions, namely it is not directly related to the distance and user distribution. The most critical factor is the SINR ratio of repeater to its posterior users. If the posterior users of a repeater are all good users (whose SINR are greater than their anterior repeater) the repeater should turn diminish its gain to avoid interfering the covered users. On the other hand if there are many bad users (whose SINR are smaller than their anterior repeater) the repeater should raise its gain in order to enhance the signal qualities of covered users.

There are three types of situations: 1). . All of the posterior users get improvements on SINR and hence the capacity. The repeater gain can be as large as possible to increase the user qualities without any damage. 2). . It is the most common situation in which the repeater is beneficial to some users but harmful to the others. High quality users are sacrificed to increase the SINR of low quality users. 3). . It is the worst case that the repeater installation has no benefit to the posterior users. In this case the repeater gain should be as small as possible or just turned off.

The concept of the proposed algorithm is based on the above criteria and progressively converge the repeater gains.

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Figure 6.1. Flow chart of proposed algorithm.

Figure 6.1 is the flow chart of proposed algorithm. First we calculate the SINR of repeaters and users based on BS transmit power only and give initial values of repeater gains. The following steps are a repeated process to adjust repeater gains.

After the initial gain setting the users receive signals from both BS and repeaters which makes a change on user SINRs and we can calculate the updated SINR values.

Next we calculate the „quantities‟, which are the amount of gains that repeaters will
*alter in next iteration. There is a relation on quantities: quantities**i*

* = quantities*

*i-1*

*/ 2, *

*and quantities*

*0*depends on the initial repeater gains. The values of quantities are set to ensure that no matter the initial gain values of repeaters are they have the possibility to be in any gain levels by adding or subtracting the quantities in the following iterations. If the quantities are smaller than the threshold it means the repeater gains are converged to a set of values and the simulation terminated. If the quantities are greater than the threshold we then decide the repeater gains are going to add or subtract the quantities. A repeater with no posterior users adds the quantity in every iteration. For repeater with posterior users we calculate the ratio of bad users to good users. Quantity is added to repeater gain if it exceeds the ratio and subtracted if it is below the ratio. The above process progresses until the terminated condition achieved.

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**Parameters ** **values **

Repeater serving area 0~150 m
Quantities

*quantities*

*i*

* = quantities*

*i-1*

*/ 2 *

*quantities*

*0*

* = initial_repeater_gain / * *2 or (80- initial_repeater_gain) / 2 *

Threshold Smaller is more accurate
Bad user to good user ratio < 1

Table 6.1. Parameter settings.

Table 6.1 lists the parameters used in the proposed algorithm. There are no specific values because they change from times to times. However these values give a possible range to simulate with.

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**7. SIMULATION RESULTS **

### 7.1. Simulation environment

This chapter gives detailed information concerning the system level computer simulations performed for studying the effects of repeaters in 3G systems. Different elements of the radio network are modeled to provide as realistic network operation as possible. For example: propagation models for different radio propagation environments, digital maps for accurate terrain modeling, and antenna models for realistic coverage calculation. In the simulation we refer to the UMTS specification of 3GPP as a basis. Table 7.1 lists the parameter values used in simulation.

**Parameter ** **Value **

Log normal fading margin 10 dB

User distribution Random and uniform across the network

User number 60

Common channel Orthogonal

Maximum transmitting power 43 dBm macro 33 dBm micro Common channel power 30 dBm macro

BS transmit power 37 dBm

Orthogonality factor 0.1

BS antenna gain 11 dB

Repeater donor antenna gain 11 dB Repeater service antenna gain 11 dB Repeater noise figure 5 dB

MS antenna gain 0 dB

Noise power -99 dBm

MS power ratio 1/user number

Table 7.1. Summary of simulation parameters.

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### 7.2. Repeater performance understanding

In the following sections, performance with repeater-embedded system is presented in different scenarios, i.e. single cell, multi cell with fixed inter-cell interference and multi cell with changeable inter-cell interference. There are distinct behaviors in addition to the common parts. Among these scenarios optimization is applied on necessary ones to show the difference and enhancement.

**7.2.1. Single-cell **

Before performing the improvement of system capacity, we first take a look on the variation of received power after installing repeaters.

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Figure 7.3. Received power with repeaters.

Figure 7.4. Difference of received power before and after repeater.

Figure 7.1 is the received signal strength with only one BS. To construct the realistic

Figure 7.1 is the received signal strength with only one BS. To construct the realistic