## 4 Discussion
### Improvement by Angular Combining  
Because of the very high propagation losses at millimeter-wave frequencies, angular combining techniques, as far as they may help to enhance link quality, are quite relevant for 5G communications at 60 GHz. Using the measurement results presented in this paper, we could estimate the maximum improvement that could be reached by an ideal combining system. Signals received through each propagation path may be combined to improve the total received signal power. Two different combining methods have been studied in the literature: coherent combining and non-coherent combining [24; 36; 41]. For coherent combining, the total received power would be:  
\[P_{CC}=\left(\sum_{i=1}^{N_{r}}\sqrt{P_{i}}\right)^{2} \tag{1}\]  
where \(N_{r}\) is the number of beams used for combining, and \(P_{i}\) is the received power on each beam. For non-coherent combining:  
\[P_{NCC}=\sum_{i=1}^{N_{r}}P_{i} \tag{2}\]  
Without loss of generality, we can consider that \(P_{1}\) corresponds to the power received through the beam with maximum power and define the combining improvement for the coherent and non-coherent cases as:  
\[g_{CC}=\left(1+\sum_{i=2}^{N_{r}}\sqrt{\frac{P_{i}}{P_{1}}}\right)^{2} \tag{3}\]  
\[g_{NCC}=1+\sum_{i=2}^{N_{r}}\frac{P_{i}}{P_{1}} \tag{4}\]  
We give in Table 4 the mean, \(\mu\), and standard deviation, \(\sigma\), of the improvement (in dB) for coherent (GCC) and non-coherent (GNNCC) combining in the four environments considered. For the open environment, with a low number of lobes per location, the combining improvement was low. The combining improvement increased from open to suburban areas, from suburban to wooded areas, and from wooded to urban areas. GCC values up to 7 dB f were reached in the urban environment. We can also observe that the coherent combining values were larger than the non-coherent combining ones, which agrees with previous results in the literature. Te values for the urban environment were lower than the values given in reference [36] for 28 GHz, where the mean improvement of the combined signal relative to the best single signal ranged from 2.3 dB to 4.7 dB for non-coherent combining and from 5.1 dB to 10.6 dB for coherent combining. However, the higher attenuation at 60 GHz reduced the number of beams available for combining, and, consequently, the combining improvements were lower. The results in Table 4 agree with what could be expected a priori. If there is a dominant propagation path with much higher power, like under LOS conditions, or even just one propagation path, then:  
\[P_{i}\ll P_{1},\quad i=2,\ldots,\ N_{r} \tag{5}\]  
and  
\[g_{CC}\approx 1 \tag{6}\]  
\[g_{NCC}\approx 1 \tag{7}\]  
therefore, there will be no combining improvement. However, under NLOS conditions, if there is no dominant propagation path and:  
\[P_{i}=P_{1},\quad i=2,\ldots,\ N_{r} \tag{8}\]  
then the combining improvement will be maximum and equal to:  
\[g_{CC\ max}=N_{r}^{2} \tag{9}\]  
\[g_{NCC\ max}=N_{r} \tag{10}\]  
Equations (9) and (10) indicate that there is a maximum value for the combining improvement that depends exclusively on the number of combined beams. Results given in Table 4 and in reference [36] comply with these limits. These equations also explain why higher combining improvement can be achieved by coherent combining. As \(N_{r}\geq 1\), then:  
\[P_{NCC}=\sum_{i=1}^{N_{r}}P_{i} \tag{2}\]0  
It should also be noted that, when omnidirectional antennas are used at the mobile end, the existence of a dominant propagation path, i.e., under LOS conditions, will yield a fast fading with a Rice distribution [42] with a high K factor. On the other hand, if there is no dominant path, i.e., under NLOS conditions, the K factor will be lower, and eventually the fast fading distribution will be Rayleigh. Higher combining improvements could be expected under Rayleigh fading conditions (NLOS) than under Rice fading ones (LOS). This makes angular combining techniques so interesting, as, usually, propagation losses are higher under NLOS conditions.