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Average power control for RF EMF compliance


When cellular radio equipment is to be deployed, electromagnetic field (EMF) exposure regulations need to be accounted for. These regulations define limitations commonly referred to as radio frequency (RF) exposure limits, see 3 and 4 for details. These limits are typically based on the guidelines from the International Commission on Non-Ionizing Radiation Protection (ICNIRP) but may take different forms in some countries and regions. The aim of the RF exposure regulations is to ensure that the human exposure to RF EMF is kept below the prescribed limits. These limits have been set with wide safety margins.

When determining the RF EMF exclusion zones for deployments of multi-input-multi-output (MIMO) transmitting 4G or 5G radios with advanced antenna systems (AASs) capable of active beam steering, it is important to observe that the maximum beamforming gain and equivalent isotropic radiated power (EIRP) may be significantly increased as compared to traditional antennas. However, the time averaged gain and EIRP are similar since these antennas steer the beams in different directions to serve different users. This means that the traditionally used methods for calculating RF EMF exclusion zones based on maximum EIRP generate overly conservative results if used for AASs. The resulting RF EMF exclusion zones may then cause deployment challenges for the operator. Operators can benefit from using a more realistic exclusion zone calculation based on the time averaged EIRP instead and still strictly comply with RF exposure regulations.

Average power control

The potential deployment problem can be addressed by determining the exclusion zone using a selected threshold of the time averaged transmit power of the radio base station. The focus of the paper 3 is therefore on the feedback control functionality, which must provide a 100 % guarantee that the selected average power threshold is never exceeded. This feedback control problem is nonlinear, primarily due to the one-sided upper constraint in terms of the selected average power threshold. The problem is relatively hard, although there are controller design methods available. The most advanced methods use a state space formulation of the nonlinear dynamics together with the selected average power threshold as a constraint, when minimizing a selected criterion function, this approach is typically denoted model predictive control (MPC).
These methods are however all computationally intense and non-trivial to maintain in commercial systems.

The first contribution of the paper 3 proposes a low complexity average power feedback controller, based on a combination of proportional-differentiating (PD) control and a low complexity variant of MPC. The PD controller provides smooth average power regulation during normal operating conditions such as for regular traffic, while the MPC acts as a safety net that guarantees that the selected average power threshold cannot be exceeded at any given time for any traffic type. A block diagram of the average power feedback control loop appears in Fig. 1.


Figure 1. Block diagram of the average power feedback control loop for the alternatives with computed and measured momentary power.

The selected average power threshold associated with the exclusion zone is used to compute the average total power reference value of the control loop. The average power controller then forms the control error and a control signal is computed. In normal operation, PD control is used, based on a pole placement design described in 3. The control signal commands a rate of change to a dynamic actuator operating in the scheduler. The actuator consists of a momentary data resource limitation operating on the resource grid of the OFDMA air interface. The scheduler then creates the data stream that is further processed in the radio to generate the transmit power. In the feedback path, two architectural alternatives are shown. The first one is the one described in 3. This alternative performs a computation of the momentary total transmit power of the cell in base-band, after scheduling. The advantage to the alternative using the measurement of the total momentary power in the radio, is that the complete solution is in the base-band without radio impact, a fact that significantly simplifies testing. Finally, the latest momentary power sample is stored in a sliding window of duration T, and the oldest momentary power sample in the sliding window is shifted out. The average power is then computed for each sampling time instance of the feedback loop.

To design the algorithm needed to provide a 100 % guarantee against average power threshold overshoot, an analysis of a theoretical power profile is presented next. This power profile is depicted in Fig. 2, and it is a worst case in the sense that it represents the quickest possible reach of the average power threshold. It is first noted that it is not possible to limit the momentary power to zero. The reason is that PDCCH is untouched and that it is not desirable to regulate PDSCH all the way to zero schedulable PRBs. This situation is illustrated by Fig. 2. As can be seen, the momentary power window of duration T is first filled with zero power samples (yellow) during initialization, after which maximum momentary power is turned on. This leads to a linear increase of the average power (green). As illustrated by the lower diagram, the momentary power then needs to be reduced at some point in time. The lower diagram shows a predicted situation ahead in time (dashed), used for the analysis performed by the model predictive control (MPC) algorithm. In the example of Fig. 2, the average power precisely hits the selected average power threshold at the end of the predictive window. The figure thus illustrates a case where an overshoot of the selected average power threshold would occur when time increases further. This follows since when the averaging window is shifted to predict further ahead, samples with zero momentary power are shifted out of the averaging window and samples with non-zero momentary power are shifted into the averaging window, resulting in a net increase of the average power. This discussion puts the focus on the problem: how to decide when regulation to the minimum resource level needs to start, so that the average power always remains below the selected average power threshold (red)? This problem is solved by the algorithm of 3, and it operates as a safety net in case PD control would not be enough.


Figure 2. The situation in the power averaging window at current time (upper figure) and at a predicted time (lower figure), assuming control to minimum momentary power. Yellow is momentary power, green average power and red illustrates the selected average power threshold associated with the exclusion zone.

The average power controller is today successfully fielded worldwide. A simulated example of its operation appears in Fig. 3. and Fig. 4.


Figure 3. Momentary incoming traffic, transformed to power (blue), and the PRB limitation, also transformed to power (red).


Figure 4. The selected average power control threshold associated with the exclusion zone (red), the average power control reference value (yellow), together with unregulated average power (blue) and regulated average power (green).

Sometimes, e.g. in laboratory testing, the operation of the MPC can lead to oscillation. To understand why and to find a modification that avoids this, the paper 1 studies optimal average power control. The papers study a general constrained optimal control problem, where state and control signal constraints are handled by barrier functions. The use of logarithmic barrier functions for the control constraints, allows an analytical computation of the optimal state feedback control. The paper obtains a very general Hamilton-Jacobi-Bellman equation, suitable for numerical solution using Hamilton's method of characteristics. The method is then applied to the average power control problem for computation of state feedback surfaces depicted in Fig. 5 and Fig. 6. As can be seen the feedback controller exhibits a switching character both for large (Fig. 5) and small (Fig. 6) control signal constraints. Since the control signal is the rate of change of a power threshold, it follows from Fig. 6 that ramping control is close to optimal, which then follows as a recommended modification of the safety net.


Figure 5. Optimal control of 1 as a function of the measured state, with large

control signal limitations.


Figure 6. Optimal control of 1 as a function of the measured state, with small

control signal limitations.


As stated above, the 4G and 5G deployment of massive MIMO capable radios increases peak EIRPs, which in turn increase the sizes of the RF EMF exclusion zones applied for the general public and workers, sometimes to dimensions exceeding 20 meters. The deployment becomes even more challenging when multiple massive MIMO transmitters are co-sited with overlapping antenna ranges. In such situations it's often the case that radio transmitters experience very different loads that also vary over time. Therefore, it is suboptimal to allocate a fix EIRP budget for each radio transmitter, for the exclusion zone determined for the site. The paper 2 therefore proposes an algorithm for joint control of the time averaged EIRP produced by all co-sited radio transmitters with overlapping antenna disgrams at a site. The advantage of joint average EIRP control follows since trunking gains result when radio transmitters are jointly controlled.


Figure 7. An example of average EIRP control in case of dynamic spectrum sharing between LTE and NR, using a shared antenna array.

The average EIRP control algorithm of 2 is a so called cascade controller, shown in Fig. 7. The use case shown is a dynamic spectrum sharing one, where one carrier and OFDM resource grid is dynamically shared between 4G LTE and 5G NR traffic. In the present example, an antenna array and radio amplifier is shared. The cascade control paradigm, means that there is an outer controller, here performing a repeated computation of average power reference values that minimize the total throughput degradation of the coordinated radio transmitters. A new constrained optimal control problem based on a novel MIMO throughput degradation model forms the basis for the cascade controller. The unique analytical solution to the problem is computed in 2, the result being a negligible computational complexity when implemented.

The outer controller receives samples of the long term average traffic (or power), from each single controller. The resulting average power control reference values are signaled back to the single average power controllers that each control a power average of duration T. The outer controller operates with a longer averaging time than T, and with a longer sampling period.

The average EIRP controller was evaluated with live traffic profiles, using a sampling period of 0.6 s, and with a duration of 24 h. The single average power controller parameters appear in 2. The additional parameters appear in Table 1 of 2. The time evolution of the controlled average power of each radio transmitter, together with the sum of the powers of the two transmitters, appear in Fig. 8. It can be seen that balancing occurs. When the traffic of one radio transmitter is high, the average EIRP controller increases the reference value and slaved average power threshold of the corresponding single controller - if this is possible due to low traffic through the other radio transmitter. The balancing also leads to equalization of the clipped power (denied traffic), between the radio transmitters as shown by Fig. 9. It can also be seen that the controlled average powers (green) stay below the average power limits (red) at all times. This is not the case without average EIRP control (blue). Finally note that the sum of the average power thresholds stays constant as it should, as shown in the lower plot of Fig. 8.


Figure 8. Illustration of the average EIRP controller operation. Controlled average powers are shown green, reference values are shown yellow and the slaved average power limits relating to the exclusion zone are shown red. The average powers that would result without control are shown blue.


Figure 9. Clipped power without (top) and with (bottom) average EIRP control, for LTE (left) and NR (right).


1. T. Wigren and D. Yamalova, "Constrained optimal average power control for wireless transmission", IEEE Contr. Systems Letters, vol.6, pp. 1922-1927, 2022. DOI: 10.1109/LCSYS.2021.3133632

2. T. Wigren and C. Törnevik, "Coordinated average EIRP control of radio transmitters for EMF exclusion zone computation", IEEE Wireless Comm. Letters, vol. 10, no. 9, pp. 2075-2079, 2021. DOI: 10.1109/LWC.2021.3092190.

3. C. Törnevik, T. Wigren, S. Guo and K. Huisman, "Time averaged power control of a 4G or a 5G radio base station for RF EMF compliance", IEEE Access, vol. 8, pp. 211937 - 211950, Nov. 19, 2020. DOI: 10.1109/ACCESS.2020.3039365. Available: .

4. T. Wigren, D. Colombi, B. Thors and J.-E. Berg, "Implications of RF EMF exposure limitations on 5G data rates above 6 GHz", Proc. VTC 2015 Fall, Boston, Ma, Sep. 6-9, 2015.

Updated  2024-02-29 14:17:51 by Torbjörn Wigren.