5G Mobile Networks: A Systems Approach

Power amplifier behavioral modeling based on LaguerrePolar‐Volterraseries with independent truncations

“…In the structural comparison of the approaches, in terms of truncation, both models, in ( 5) and (11), have one truncation for amplitude polynomial order P 1 and another for phase polynomial order P 2 , while the model in ( 6) and ( 13) have four for amplitude polynomial order P 11 , P 12 , P 13 , and P 14 and a truncation for the phase polynomial order P 24 . The model in (5) has one truncation for the amplitude memory M and one truncation for the phase memory L, while the model in ( 6) has three truncations for the amplitude memory M 2 , M 3 and M 4 and two truncations for the phase memory L 3 and L 4 . The model in (11) has one truncation for the Laguerre basis functions φ L and one truncation for the phase memory J, while the model in (13) has three truncations for the Laguerre basis functions φ L 2 , φ L 3 , and φ L 4 , and two truncations for the phase memory J 3 and J 4 .…”

“…This difference is due to the additional time it takes the optimizer to reach each candidate's local minimum function. A strategy to reduce the simulation time of the model in (13) is to analyze the fourth sub-block of the models in (6) and in (13), which is still identical to the models in (5) and in (11), as a whole, hence, the contributions of this sub-block of the models in (6) and in ( 13) can be minimal. The strategy is to introduce, with little or no deterioration in the modeling accuracy of the fourth sub-block, only minimum values of the phase polynomial truncation, of the phase memory truncation and of the amplitude memory truncation, that is, making P 24 = 1, L 4 = J 4 = 0, and…”

“…In this work, to obtain the results of the simulations, the maximum values of the truncation factors of the models in (5) and in (11) are defined as P 1 = 4, P 2 = 1, M = φ L = 2, and L = J = 1, which corresponded to a total of 64 parameters when all the truncation values of the models in (5) and in (11) reach their maximum. For models in (6) and in (13), several instances are also implemented, where the values of the 10 truncations vary between their minimum and maximum, which are, in this case, equal to the minimum and maximum chosen in (5) and (11), that is, P 11 = P 12 = P 13 = 4,…”

“…In a first scenario of results, Tables 1 and 2 show the NMSEs relative to the direct and inverse modeling, respectively, for the models, PV in (5) and LPV in (11), characterized by having an equal number of coefficients in any combination of truncation factors. For example, for P 1 = 4, P 2 = 1, M = φ L = 2, and L = J = 1, the two models reach 64 coefficients each, however, as the difference between their NMSEs is not so significant for each of the P 1 variations, consequently, only one of the two models will be used in the second and third scenarios, for the purpose of comparison with the other models.…”

“…2,3 It is assumed there is no need for changes in the configuration of 4G transmitters 3 operating with the current orthogonal frequency-division multiplexing (OFDM) modulation technique, 4 since the third generation (3G) continues to set the standards for 4G and 5G. 5 In this case, the reuse of the existing 4G infrastructure through the installation of completely new hardware and the addition of compatible applications to the needs and software capable of adding value to the improvement of the transmitters, as a whole, are essential and can be done to meet the user's requirements 2,6 as well as new application areas. However, new challenges related to the performance of the 5G chain of transmitters are presented, mainly to the radio frequency power amplifier (RF PA).…”