Placement of access points in an ultra-dense 5G network with optimum power and bandwidth

We address the problem of optimally placing the access points in an ultra-dense 5G network to cover a given rectangular region so that every point in the region will be covered by at least one access point (AP) with minimal sum of total transmission power used by all APs. We analyze the wastage of transmission power for different types of placement of the APs with touching and intersecting circles for the full coverage of the rectangular region. We show that the minimum wastages in the inner bulk region with touching and intersecting circles are 81.4% and 20.77%, respectively. We then propose a systematic scheme to place the intersecting circles and show that for moderate size of the rectangle, the wastage due to the spill over of the circles at the boundary can be much higher that 20.77%, but when the side(s) of the rectangle is(are) very large compared to the radius r of the circles, the wastage asymptotically tends to around 20.86%. Also, we show that use of a few circles of smaller radius r' = 0.62r would significantly reduce the wastage even for a rectangle of small size and that would not require any additional bandwidth compared to the scheme for using all circles of the same radius r. The proposed placement scheme is very simple, elegant and effective in minimizing wastage of transmission power of APs as well as optimizing the bandwidth requirement through reuse of channels avoiding co-channel and adjacent channel interferences.