Worst Case Analysis with the impact of the mobile-to- mobile-to-mobile interferencemobile-to-mobile interference

In this subsection, we will evaluate the impact of the mobile-to-mobile co-channel interference and describe how the proposed power ratio adjustments can alleviate type 1 and type 4 interference between the heterogeneous systems. In some issues of the radio resource management in the TDD/CDMA systems, the mobile-to-mobile co-channel interference is considered to significantly degrade the system performance [13, 58]. To alleviate this kind of interference, we suggest employing a power ratio adjustment method in subsection 7.2.2. Here we will describe how to adjust the power level to alleviate the impact of type 4 interference.

At first, we analyze the impact of type 4 interference in a worst case to de-fine the required received signal quality for the mobiles. The worst case about the most serious interference is illustrated in (7.4). This condition will happen when the interfering source is approaching the cell boundary with the maximum transmit power. The interfering mobile a is at the right side cell boundary of the microcell µ

and served by the macrocell. With the usage of the MCL, the received co-channel interference from the interfering mobile to the different positions can denoted as

I_m→m = P_M^r

where MCLm→m is the minimum coupling loss between two mobiles, α^{(M )}a and α^b_a are the shadowing components between the interfering mobile a to the base-station of the macrocell M and target mobile b with standard deviation σa^{(M )} and σ_a^b, respectively.

The function ϕ(u, v) is used to indicate whether u ≤ v or not, i.e.,

ϕ(u, v) =





1, if u ≤ v .

0, otherwise . (7.29)

Then we can obtain the mean received mobile-to-mobile interference by taking average over α^{(M )}a and α^b_a, i.e.

Figure 5 illustrates the mean received mobile-to-mobile interference corre-sponding to the different locations in the microcell. The system parameters are outlined in Table 7.1, and we set R_µ/R_M = 0.1, d = 700 m, and α^{(M )}a = α^b_a = 5 dB. From the fig. 5, the mean received mobile-to-mobile co-channel interference from the interfering mobile only dominates around the cell boundary. The central position of the microcell (base station) only receive much less interference. In the

other words, the impact of the type 1 interference can be easily reduced by slightly increasing K1 of the PRA. While the mean received interference will be much serious around a circular-region of the interfering mobile, the mobiles in this region may be blocked easily. In this way, we should define a larger K2 to compensate the type 4 (mobile-to-mobile) interference.

To design a proper parameter K2 in (7.2), we evaluate the mean received power level for a mobile b in the microcell as follows

P_r^b = P_µ^t· G(r^(µ)_b , α^(µ)_b ) · ϕ(G(r^(µ)_b , α^(µ)_b ), (MCL_b→m))

+ P_µ^t· (MCL_b→m) · ϕ((MCL_b→m), G(r_b^(µ), α^(µ)_b )). (7.31) where MCL_b→m is minimum coupling loss between the base station and mobile, α^(µ)_b is the shadowing component with the standard deviation σ_b^(µ). Then we can obtain the mean received power level for the target mobile b as By taking average over α^(µ)_b , we can obtain

E[P_r^b] = P_µ^t· r_b^{(M )−4}· e^{12η2σb(µ)2} · Q(η²σ_b^(µ)2− k⁰ ησ_b^(µ) ) + P_µ^t· (MCL_b→m) · Q( k⁰

ησ_b^(µ)). (7.32)

where P_µ^t ∝ K2 in (7.2), and k⁰ = lnh

MCL_b→m· (r^(µ)_b )⁴i .

Figure 6 illustrates the ratio between the mean received mobile-to-mobile in-terference to the mean received signal quality corresponding to the different distance between the interfering mobile and the target mobile. We move the location of the target mobile along a direct line between the interfering mobile of the worst case to the base station of the microcell. With the increase of the K2 and the distance be-tween two mobiles, the received mobile-to-mobile interference decreases rapidly. The impact of mobile-to-mobile interference can be limited into a circular-region about 35

m around the interfering mobile when K2 is larger than 1500. While the mobiles are uniformly distributed, the probability for an approaching interfering mobile to cause heavy mobile-to-mobile interference will to much smaller.

7.4.2 Numerical Results

The outage probabilities in (7.18), (7.23) and (7.26) are evaluated by Monte Carlo simulation. In Fig. 7.7, we set L = 7, N_M = 36 (which is approximate 80% capacity of the homogenous macrocell without the embedded microcell), R_µ/R_M = 0.1, d = 700 m, K1 = 180 and K2 = 1800. One can see that, by jointly applying the AA and PRA, the uplink and downlink outage probabilities of the microcell are controlled to be below around 0.02 and 0.015, respectively. And the uplink outage probability of the macrocell increases slightly as N_µ increases. It is obvious that, the co-existence of such a heterogeneous system is feasible by using the proposed joint AA and PRA technique. Although not shown in the simulation, similar results can be obtained with different L, R_µ or d.

Figure 7.8 and Figure 7.9 show the the tradeoff between the outage proba-bilities of the macrocell and the microcell by adjusting the PRA constant K₁ and K₂. In Fig. 7.8, it is shown that when the K₁ increases, the uplink outage proba-bility of the microcell decreases and the uplink outage probaproba-bility of the macrocell increases slightly. Fig. 7.9 shows that the the uplink outage probability of the macro-cell is traded off against the downlink outage probability of the micromacro-cell with the increasing K₂.

Finally in Fig. 7.10, the worst one among the uplink outage probability of the macrocell, uplink outage probability of the microcell and downlink outage probability of the microcell is plotted with or without applying the AA and PRA. It is important to see that, only by jointly employing AA and PRA, we can obtain the full microcell

capacity without degrading the performance of the macrocells.

Table 7.1: System Parameters P G_M, P G_µ 128

γ_M^U, γ_µ^U, γ_µ^D 5 dB S_U, S_D 3

R_M 1000 m

K 6

σ 8 dB

v 3/8

m 4

Macro-cell

Mobile-to-mobile interference

Desired transmission direction

Mobile-to-mobile interference

ms-b ms-a Micro-cell

Figure 7.4: The worst case corresponding to the impact of mobile-to-mobile co-channel interference.

Figure 7.5: The mean received interference from the interfering mobile of the macro-cell to the different positions of micromacro-cell.

25 30 35 40 45 50

The distance between the target mobile and the interfering mobile (m) E[Im → m]/(PG ⋅ E[Prb])

Figure 7.6: The ratio between the mean received mobile-to-mobile interference to the mean received desired power level correaponds to the distance between two mobiles.

16 17 18 19 20 21 22 23 24

Number of mobiles per slot in the microcell

Outage Probability

FDD uplink TDD uplink TDD downlink

Figure 7.7: Outage probabilities as a function of N_µ for L = 7.

90 100 110 120 130 140 150 160 170 180 190 200

Figure 7.8: Outage probabilities as a function of K₁.

12000 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200

0.01

Figure 7.9: Outage probabilities as a function of K₂.

12 18 24 30 36 42 48 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

N_µ (number of mobiles in the microcell)

Outage Probability

No AA and PRA Only PRA Only AA Both AA and PRA

Figure 7.10: Comparison of the outage probabilities for (a) no AA and PRA; (b) only PRA; (c) only AA; and (d) joint AA and PRA are used.

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CHAPTER 8