In this section, we introduce the interference model and give the notations used throughout the chapter.
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2.2.1 Network
We consider a cellular radio system withB base stations (BS) and U mobile stations (MS) and we focus on the downlink. Since we assume all the BS transmit power at the same frequency, we focus on CDMA systems. If a mobileu is attached to a base station b (or serving BS), we write b =ψ(u).
Soft handover (SHO) situations are not considered here. The position of mobile stationuis denotedx(u). Notice that “position” may include location and antenna pointing and gain. To simplify the presentation, position will just refer to a geographical location in a plane, x = (x1, x2) ∈ <2. The location of a base station is, as usual, called a site, and we assume omni-directionnal antennas, so that a base station covers a single cell.
2.2.2 Propagation
The propagation path gain gb,u designates the inverse of the pathloss L be-tween stations b and u, gb,u = 1/Lb,u. If a propagation path is considered between a BS and a particular location x, the corresponding path gain will also be denoted by gb,x. In this way, we assimilate gb,x(u) and gb,u, and more generally we will assimilate throughout the chapteru and x(u).
2.2.3 Power
The following power quantities are considered:
• Pb,u is the useful transmitted power from station b towards mobile u (for user’s traffic);
• Pb =PCCH + ΣuPb,u is the total power transmitted by stationb, PCCH represents the amount of power used to support broadcast and common control channels.
• pb,u is the power received at mobile u from station b;
we can writepb,u =Pb gb,u;
2.2. INTERFERENCE MODEL AND NOTATIONS 67
• Sb,u =Pb,u gb,u is the useful power received at mobile u from station b (for traffic data); since we do not consider SHO, we can write
• Su =Sψ(u),u=Sb,u.
2.2.4 Interferences
The total amount of power experienced by a mobile station u belonging to a cell b in a cellular system can be split up into several terms: useful signal (Sb,u), interference and noise (N0). Let the system power be the total power received by a mobile coming from all the base stations of the network. It is common to split the system power into two terms: pint,u+pext,u, wherepint,u
is the internal (or own-cell) received power and pext,u is the external power (or other-cell interference). Notice that we made the choice of including the useful signal Sb,u in pint,u, and, as a consequence, it has to be distinguished from the commonly considered own-cell interference.
With the above notations, we define the interference factor in u, as the ratio of total power received from other BS to the total power received from the serving BS b:
fu =pext,u/pint,u (2.1)
The quantities fu, pext,u, and pint,u are location dependent and can thus be defined in any location x as long as the serving BS is known.
We can express the interference factor as:
fu = 1
As a special case we notice that for a homogeneous network and traffic (uni-formly distributed), all the base stations transmit the same power. The interference factor can thus be expressed as
fu = 1
These expressions (2.2 and 2.3) show that, although very close to the common definition [HoT04] that considers a ratio of interferences, this new definition of f is interesting for the following reasons:
• Firstly, the total radio power received by a mobile pext,u +pint,u is a metric easy and simple to be measured by that mobile.
• Secondly, using this definition, the parameter f represents a charac-teristic of the network. It does not depend on any considered MS or service, but only on the number of base stations, their positions and transmitting power and the pathloss. This last one depends on the environment (urban, rural...): it can be considered characterizing a network zone. We moreover observe that in a case of an homogeneous network, the interference factor does not depend on the base station transmitting power.
• At last, that definition of f is still valid when the considered cellular system has no inner-cell interference. In this case, the denominator off is reduced to the useful power. So that definition of interference factor can be applied to other systems than CDMA, as for example OFDMA (WiMAX) or TDMA ones (GSM with frequency hopping), and can be extended to ad-hoc networks.
2.2.5 Transmitting channels orthogonality
In downlink, transmitting channels are orthogonal in a CDMA system. There is however a loss of orthogonality due to multipath. A coefficient α may be introduced to account for the lack of orthogonality between physical chan-nels in the own cell (see for example [NeM05]). Note that α, 0 ≤ α ≤ 1, a priori depends on the location, and should be notedαx. However this case is almost never considered. In the rest of our analysis, we follow the common assumption that α is not location dependent. An intra cell interference ex-pressed asα(pint,u−Sb,u) can appear due to the transmitting powers towards the other mobiles of the cell.
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2.2.6 Signal to Interference Ratio
The signal to interference plus noise ratio (SINR)is denoted :
• γu the SINR evaluated at station u;
• γu∗ the target SINR for the service requested by station u.
The signal to interference plus noise ratio will be used as the criteria of radio quality. Assuming mobiles use only one service, γu∗ is the target SINR for the service requested by MS u. This figure is a priori different from the SINR evaluated at mobile station u. However, we assume perfect power control, so γu =γu∗ for all users. In the UMTS case, we assume that perfect power control (PC) is performed for all users ([LaW01][HiB00]), the SINR γu experienced by a mobile has to be at least equal to the target value γu∗.
As a consequence of the perfect power control, at each moment the trans-mitting power Pb,u is adapted to the propagation conditions for the mobile to receive the power it needs. It means that Pb,u is not a constant. As a consequence the total transmitting power Pb of base stationb should not be constant, even in an homogeneous network. However we can assume that sta-tistically, when some mobiles need a lower power, others need a higher one.
And the total transmitting power is about constant. With the introduced notations, the SINR experimented by u can be derived (see e.g. [Lag05]):
γu = Su
α(pint,u −Su) +pext,u+N0 (2.4) where the term α(pint,u−Su) represents the intra cell interferences. For an OFDMA system, there is no internal interference, so we can consider that α(pint,u −Su) = 0.
For a UMTS System, as we assume perfect power control, we can write:
γu∗ = Su
α(pint,u −Su) +pext,u+N0 (2.5) From the expression (2.4), and introducing the parameter
βu = γu 1 +αγu
(2.6)
we can express Su as:
Su =βupint,u(α+pext,u/pint,u+N0/pint,u) (2.7)