Can we increase the power received at a point in the mobile network without increasing the transmission power? This is the question we will answer in this video. If you are a bit tired, go and have a coffee or do some relaxation exercises so you can come back ready to focus on this video, which requires some explanations. Let's consider a transmitter of power p that sends a sign is a sinusoidal signal at a frequency of for example, 1800 MHz to an Omni directional antenna. The antenna will create an electromagnetic field in all directions. We suppose that at distance D, which is large compared to the wavelengths we receive an electric field of amplitude L. We reason on the electric field but we could reason in the same way on the magnetic field. If we take a picture at time T, We consider the situation in space. We see the electromagnetic wave appearing with the wavelength lambda, we can consider that it is a plane wave. We have a wave front. When we move from north to south we remain on the same wave front. Let us consider a small displacement of lambda divided by two towards the south. Along the wave front. We have at X_1 an electric field E_1 and at X_2. an electric field E_2. If we move the same distance, I mean lambda divided by two but towards the the east, The phase shift is Pi. Now, let's consider two transmission antennas. We have an identical power P. The power is divided : P over two on each antenna. If the power is divided by two, it means that the signal amplitude is divided by the square root of two. When we consider the situation at X. X receives an E_1 field identical to the previous case with the same phase and an E_2 field coming from the Antenna represented in blue. The situation of X with respect to the blue antenna is exactly the same at the previous situation of X_2 with respect to the single antenna we were considering. So, the electric field E_2 has the same phase as E_1. What we receive is the sum of the two electric fields. So, we have a signal of amplitude two times L divided by the square root of two, which means that the amplitude is equal to the square root of two times L. If we multiply the amplitude by the square of two, we multiply the power by two. At X, we get power multiplied by two. No, let's look at the case at point Y We consider point Y to be due north, and we move the same distance lambda over two in the same direction at this point. Since moving from Y_1 to Y_2 brings us lambda over two closer to the antenna, we will have a phase shift of pi. This means that E_1 and E_2 are in phase opposition. Let's reason as before and consider not one antenna but two antennas with power P over two at the input of each antenna. If we do that, we find at Y E_1 with a certain phase and E_2 with the opposite phase. So the resulting signal is zero but there is always a little noise so it's not strictly zero. The power received at Y is almost zero. Now, if I change the phase on one of the antennas, let's say I play a systematic phase shift of Pi at this point. The signal from the black antenna and the blue antenna are in phase opposition. At X, I will receive E_1 and E_2 in phase opposition. The resulting field has almost zero power. Now let's look at the situation at Y. I still apply my face shift of Pi. The phase shift of Pi will allow me to compensate for the difference in distance traveled, which also corresponds to a phase shift of pi. Finally, E_1 and E_2 will have the same phase. The resulting signal E_1 plus E_2 has an amplitude of two times L divided by the square root of two, like before. So we find a power in Y multiplied by two. We have taken 2 extreme cases, we can apply not a phase shift of zero or pi, but the phase shift of an angle between zero and pi. We call this phase Phi. We can arrange for the phase to be carefully chosen so that in the alpha direction the steering direction we find E_1 and E_2 to be systematically in phase. In this direction, the power is multiplied by two. We have seen this principle with two antennas, but it's quite easy to understand that it can be generalized. If we consider N antennas, if we always apply the same power P the global power, but the power on each antenna is divided by N, by controlling the phase applied to each antenna, we can maximize the total signal in a given direction. We can multiply the power by N. We have shown an example of what we can get. First look at an omnidirectional antenna here, we represent the amplitude of the electric field in the different directions. Omni directional antenna: we find the reference value imposed at one in all directions. If we consider two antennas at a distance of lambda over two, we can multiply the amplitude by a factor of 1.4, which is the square root of two. The power will indeed be multiplied by two. We no longer have north or south radiation. If we take four omni directional antennas, we will have a slightly narrower beam and an amplitude multiplied by two. So the power is multiplied by four. If we increase to 16 Antennas, we see that the beam is even narrower and that we will gain a ratio of 16 in power. We keep the example with 16 Antennas arranged along a north-south axis, but we no longer assume that the same phase is applied to all antennas. By playing with the pahse shifts, we can either maximize the power due east or maximize with an angle of 15°, 30° or 45°. We can freely choose the angle we want. This is possible with an omni directional antenna, but we could also start with an antenna with a radiation pattern in a particular direction. Adding more antennas allows us to focus the energy in one direction to form the beam. To summarize, we have seen beam-forming, which involves taking an antenna array, a set of antennas generally lambda over 2 distance apart. If we consider the frequency of 1800 MHz 8 antennas give us a total spacing of 67 centimeters. If we consider eight antennas at 20 GHz, We get only 4.6 centimeters. From a theological point of view. Beam-forming and antenna arrays are possible at any frequency range but the higher the frequency, the smaller the footprint, and the more interesting the technology. Beam-forming involves controlling the phase of the signal on each antenna. This can be done in analog, then you have the same beam for all sub carries when transmitting OFDM. You can do it with digital signal processing and then you can have different beams for different sub-carriers. This requires computing power. So that is an additional constraint. The advantage of the antenna array is that we will have a focused energy in the desired direction. We have less energy radiated in other directions, so we generate less interference. The disadvantage is that by adding antennas that we have to control, we need processing power, which induces energy consumption. Note that we have focused the explanation on the transmitting antenna array. We can very well have a receiving antenna array. This array can amplify the signal in the desired direction.
