4.1 Single room AP number
4.1.1 Conventional scenario
In the single room scenario, the article has investigated the maximum downlink user QoS achieved by at least 95% of the users and the average user data rate. This was done by the simulation only. A total number of 50 users are distributed randomly and uniformly across the whole indoor room whose area is 20 m × 16 m. Only one single floor building without light internal walls (e.g. plaster board) is considered. Due to the omnidirectional radiation pattern of the AP, its deployment was conducted to minimise the mean distance from users to AP. Therefore, there is always one AP deployed in the middle of the room except for the case of two APs, in which case they are placed at the foci of the ellipse layout. For the remaining deployments, all other APs excluding the middle one are placed evenly around the circumference of the ellipse as shown in Figure 3.
Investigation of optimal FAP placement and interference management will be described in the next subsection. It is shown that 1 FAP can achieve the highest user QoS and average user data rate of just over 1 Mbit/s with SISO deployment owing to the absence of any interference. It is worth mentioning that there is a 43% improvement in the spectral efficiency when using 1 FAP as compared to 1 802.11n AP as shown in Figure 4a. This gain is due to the different scheduler mechanism as well as the link level MCS between LTEfemtocell and 802.11n network. For the same bandwidth, LTEfemtocell employs a more spectral efficient adaptive MCS than 802.11n. 1 FAP offers 4.44% ERG against 1 baseline 802.11n AP with SISO deployment. This is shown in Figure 4d. It was found that for a single AP deployment, a single FAP is more spectral and energy efficient than a single 802.11n AP.
As the number of APs is increased, the 802.11n deployment is always more spectrally and energy efficient due to the increased operating bandwidth of 60 MHz with frequency reuse pattern 3, compared to the LTE bandwidth of 20 MHz with frequency reuse pattern 1. As the number of 802.11n APs increases to beyond 3, the interference that arises between the APs will cause a degradation of overall downlink user QoS and average user data rate performance. For the number of APs greater than 2, 802.11 APs provides 2.61 to 21.80% ERG over the FAP deployment. The results are shown in Figure 4b,d.
Therefore, for a single AP deployment, an LTE FAP is more spectrally and energy efficient than an 802.11n AP. This is true both with and without a fully loaded microcell interference source. In order to achieve a higher user QoS performance, deploying more 802.11n APs is the more spectrally and energy efficient. No more than 3 802.11n APs should be deployed in the same room; any more causes mutual interference and degrades the aggregate QoS received by the users.
4.1.2 Alternative scenario
The alternative scenario is defined in the body of investigation, in which both FAPs and 802.11n APs have a total bandwidth of 20 MHz with different frequency reuse pattern 1 and 3, respectively. The result of 1 FAP and 1 802.11n AP for both conventional and alternative scenarios are identical as shown in Figure 4a. Figure 4c,d, average user data rate and ERG performance for 1 FAP and 3 FAPs in both conventional and alternative scenario with a baseline 802.11n network. In the alternative scenario, FAP outperforms 802.11 AP when the number of APs is 3. The average user data rate for three FAPs is 1.12 Mbit/s while this value for 3 802.11APs is 0.22 Mbit/s. This is because 802.11 AP suffers server interference from other APs in the alternative scenario and its PHY adopts convolution codes which is less efficient than turbo codes used in LTEfemtocell. Figure 4d indicates three FAPs provides an ERG of 20.08% in alternative scenario while 3 802.11n APs offers an ERG of 21.80% in conventional scenario. Hence FAP investigation is particular interest in the following sections.
4.1.3 Remarks
The results in Figure 4a covers the results of all four possible combinations of comparison between one FAP and one 802.11n AP in either conventional or alternative scenario while the results in Figure 4c contains the same number of combinations results for the case of 3 FAPs and 3 802.11n AP. These four possible combinations are conventional FAP versus alternative AP and conventional AP versus alternative FAP besides the other two which have already been covered in the above sections. It is worth mentioning that 3 FAPs in conventional scenario is more energy efficient than 3 APs in alternative scenario. This is due to the mutual impact from the the different scheduler mechanism and coding scheme applied in both systems.
4.2 Single room AP placement
Previously, the optimal number of APs to deploy in a single room has been considered. The conclusion was that for a low QoS target, 1 FAP is the most energy efficient deployment. For higher user QoS targets, 23 802.11n APs should be deployed. Next, simulation is used to determine where to place the 1 FAP given that there is an outdoor interference source from a microcell, and where to place 26 cofrequency FAPs that interfere with each other. Furthermore, result of 1 FAP with a theoretical background has been reinforced, which can be found in the Appendix of this article.
4.2.1 1 FAP
The optimal placement of 1 FAP is judged according to the strength of the outdoor microcell source. Another baseline FAP deployment has been considered for comparison. In this baseline scenario, FAP is placed at the corner of the room where the power socket is typically located.
The expression of the mean capacity of the femtocell network with respect to the position of the FAP b can be expressed as:
{\stackrel{\u0304}{C}}^{b}=\left\{\begin{array}{cc}\hfill {P}_{1}+{Q}_{1}+{R}_{1}\frac{\alpha}{Y}\left({T}_{1}{U}_{1}\right),\hfill & \hfill 0<b\le {b}_{1}\hfill \\ \hfill {P}_{2}+{Q}_{2}+{R}_{1}+{R}_{2}\frac{\alpha}{Y}\left({T}_{1}+{T}_{2}{U}_{1}{U}_{2}\right),\hfill & \hfill {b}_{1}<b\le {b}_{2}\hfill \\ \hfill {P}_{3}+{Q}_{3}+{R}_{2}\frac{\alpha}{Y}\left({T}_{2}{U}_{2}\right),\hfill & \hfill {b}_{2}<b<Y\hfill \end{array}\right.
(9)
where {P}_{1}=\frac{\left(b+{d}_{bp2}\right){C}_{\text{s}}}{Y}, {Q}_{1}=\frac{\left(Yb{d}_{bp2}\right){\text{log}}_{2}{K}_{\gamma}}{Y}, {R}_{1}=\frac{\beta {\text{log}}_{2}10}{2Y}\left[{Y}^{2}{\left(b+{d}_{bp2}\right)}^{2}\right], α=1.87 and Y is the length of the room. T_{1} = Y log_{2}(Y −b)−(b+d_{bp 2}) log_{2}d_{bp 2}, {U}_{1}=\left(\frac{Yb{d}_{bp2}}{\text{ln}2}+b{\text{log}}_{2}\frac{Yb}{{d}_{bp2}}\right). C_{s} in P_{1} equals {\text{log}}_{2}\left(1+1{0}^{\frac{\gamma s}{10}}\right) bit/s/Hz where γ_{
s
}is the saturation SNR threshold. {P}_{2}=\frac{\left({d}_{bp1}+{d}_{bp2}\right){C}_{\text{s}}}{Y}, {Q}_{2}=\frac{\left(Y{d}_{bp1}{d}_{bp2}\right){\text{log}}_{2}{K}_{\gamma}}{Y}, {R}_{2}=\frac{\beta {\text{log}}_{2}10}{2Y}{\left(b{d}_{bp1}\right)}^{2}, T_{2}=(bd_{bp 1})log_{2}d_{bp 1}and {U}_{2}=\frac{b{d}_{bp1}}{\text{ln}2}+b{\text{log}}_{2}\frac{{d}_{bp1}}{b}. K_{
γ
}in Q_{2} is \frac{{P}_{\text{FAP}}{D}^{3.67}\times {{10}^{\left(22.7+\text{P}{\text{L}}_{\text{wall}}\right)}}^{/10}\times \phantom{\rule{0.3em}{0ex}}{\left(\frac{f}{5}\right)}^{2.6}}{{P}_{\text{micro}}{\u1e20}_{\text{micro}}\times {10}^{46.8/10}\times {\left(\frac{f}{5}\right)}^{2}}, where P_{FAP} and P_{micro} are the transmitting power of FAP and microcell station, respectively. {\u1e20}_{\text{micro}} is the expected value of the antenna gain from the microcell BS. f is the operation frequency. d_{bp 1}= B exp [−W (F) and d_{bp 2}= B exp [−W (−F)] where B={10}^{{\scriptscriptstyle \frac{b}{20\alpha}}}{\left({\scriptscriptstyle \frac{K\gamma}{{10}^{\frac{{}_{\gamma s}}{10}}}}\right)}^{{\scriptscriptstyle \frac{1}{\alpha}}}, F=\frac{\text{ln}10}{20\alpha}B, W is Lambert W function. Finally, {P}_{3}=\frac{\left(Yb+{d}_{bp1}\right){C}_{\text{s}}}{Y}, {Q}_{3}=\frac{\left(b{d}_{bp1}\right){\text{log}}_{2}{K}_{\gamma}}{Y}, {b}_{1}=\sqrt[\alpha ]{\frac{{K}_{\gamma}}{{10}^{\frac{{\gamma}_{s}}{10}}}} and {b}_{2}=Y\sqrt[\alpha ]{\frac{{K}_{\gamma}{10}^{\beta Y}}{{10}^{\frac{{\gamma}_{s}}{10}}}}.
It can be shown that the function is convex and that according to the first rule of finding the maximum value of a function, stationary points can be determined by differentiating Equation (9) \left(\text{Note}:\frac{\partial {d}_{bp1}}{\partial b}=\frac{B\text{exp}\left[W\left(F\right)\right]\text{ln}10}{20\alpha \left[1+W\left(F\right)\right]}\text{and}\frac{\partial {d}_{bp2}}{\partial b}=\frac{B\text{exp}\left[W\left(F\right)\right]\text{ln}10}{20\alpha \left[1+W\left(F\right)\right]}\right)and then solving the differentiated function for zeros. The resulting expression is a closed form expression, but is unfortunately too long for the scope of this article. All the stationary points are tested in order to verify the type of the stationary points (max) by checking if the corresponding value in the secondorder differential function of Equation (9) is negative. Finally, the mean capacity value(s) corresponding to all the stationary points are compared with all endpoints of the interval of each subfunction in Equation (9) and the global maximum value is selected as the maximum of mean capacity. The solution b_{opt} is the optimal coordinate for FAP placement. Detailed derivations of Equation (9) can be found in the Appendix.
The result of the mean capacity difference between the optimal and the conventional is illustrated in the subplots of Figure 5a. The theoretical results are shown in lines and are compared with the simulation results shown as symbols. The parameters used in the investigation are as follows: office size (10 m × 20 m), system bandwidth (20 MHz), carrier frequency (2,130 MHz), total number of users (10), subcarriers per Physical Resource Block (12), FAP transmitting power (0.1 W), microcell transmitting power (20 W), FAP RH efficiency (6.67%), FAP OH power (5.2 W), microcell distance away from the room (150450 m), and Wall loss (10 dB).
Figure 5b shows the OP ERG performance. The result in line is calculated based on the throughput from the theory while the result in symbols is obtained based on the throughput from the simulation. They were both obtained from the Equation (8). The results in Figure 5 show that 1 FAP should be located between the middle of the room to the wall closest to the outdoor interference source. As the strength of the microcell interference decreases due to it being either further away, stronger wall loss, or lower transmitting power, the FAP should be moved closer to the wall. This is because most of the room is in capacity saturation, and the FAP should be moved to compensate for regions which are not. It is important to consider capacity saturation, without which the FAP's optimal location is always likely to be in centre of the room.
4.2.2 26 FAPs
The results in Figure 6 shows that for more than one cofrequency AP is deployed in the same room, the mutual interference between them dominate. The meaning of dots in different colours in the plots is the association of users to different FAPs. Their location is a tradeoff between: being in the central area to reduce pathloss distance to the users, and being further away from each other to reduce mutual interference. The RAN throughput for both optimal and conventional scenario increases as more FAPs are deployed. It reaches saturation region when 6 FAPs are placed in optimal approach as shown in Figure 7a. Compared to the baseline elliptical deployment, there is an average 6% ERG obtained from the optimal deployment shown in Figure 7b.
4.3 Multiroom multifloor FAP placement
The article now considers a building with F floors R rooms per floor. The framework of this comparison is how much energy is saved when the location of FAP is optimised compared to an even distribution of FAPs across the building. This investigation is done for FAPs in the presence of an outdoor microcell interference source. A series of RAN QoS offered loads on the system is considered and what the minimum number of FAPs is required to meet this targeted load is examined. The parameters used in the investigation are as follows: number of floors (3), number of rooms per floor (9), room size (10 m × 20 m × 4 m), system bandwidth (20 MHz), carrier frequency (2130 MHz), total number of users per building (300), subcarriers per Physical Resource Block (12), FAP transmitting power (0.1 W), microcell transmitting power (20 W), FAP RH efficiency (6.67%), FAP OH power (5.2 W), microcell distance away from the room (200 m), and wall loss (10 dB). Figure 8 shows the optimal locations of FAPs for different number of FAPs required and the associated capacity and energy consumption improvements. The rooms on the top floor has been numbered as 19 followed by the rooms on the middle floor (1018) and the ones on the ground floor (1927). the microcell BS is located close to the side of room numbered (79, 1618 and 2527). FAP positions in yellow represent that the system performance will be almost same by deploying FAP on either of these positions. FAP positions in blue are the recommended optimal ones in each scenario.
The results in Figure 8a shows that at least 12 FAP(s) are always required near the wall that faces the outdoor interference source, and this should be on the floor with a similar height to the height of the interfering microcellsite. The other FAPs should be deployed on other floors at the far corners in alternating pattern to minimise the interference. The positions of the FAPs in blue have to be fixed while one of the FAPs in yellow can be selected as the last FAP position. A design principle can be summarised as follows:

(1)
In the presence of no strong outdoor interference, deploy a single FAP at centre of building. In the presence of outdoor microcell interference, deploy the FAP near the wall that is closest to the outdoor interference source. The floor level should be one that is closest to the height of the microcell.

(2)
Any single additional FAP should be deployed also near the aforementioned wall on the same floor, but not in the same room as the first FAP.

(3)
Any multiple additional FAPs should be deployed not on the same floor, and at the opposite side of the building in corner rooms. These FAPs should not be on the same floor as FAPs placed in Steps 1 and 2 and with each other in Step 3.

(4)
Any additional FAPs that do not satisfy rule 3. is likely to cause energy inefficiency.
Generally speaking, this rule can cover the optimisation of FAP placement for up to 6 FAPs, which can provide a sufficiently high QoS. The RAN QoS increases as the number of FAPs increases. This optimal deployment offers an average 12% ERG compared to the baseline even distributional deployment. This is shown in Figure 8b. Figure 8c illustrates that how much energy can be reduced while deploying the optimal FAPs in this building when comparing to the baseline scenario for a certain RAN QoS. As the number of FAPs needed for different targeted RAN QoS is not always same for optimal and baseline deployment, ERG threshold is waived is this comparison.
It can be noted that the solution of optimising the FAP location does not significantly degrade the outdoor network performance. By moving the FAP from centre to a point that is closer to the outdoor interference source, the interference from the FAP to the outside network is increased by up to 2.5 dB. Given that the outdoor interference is more dominated by outdoor interference from other microcells the total interference is not significantly increased. This is to say that the interference generated by the FAP to outdoor users is not significantly increased.