TECHNICAL FIELD

[0001] The present disclosure relates to the field of antenna orientation, and in particular to a method, antenna control device, computer program and computer program product for compensating for orientation discrepancy of a first antenna in relation to a second antenna, wherein the first antenna is used for reception of radio signals transmitted by the second antenna.

BACKGROUND

[0002] For cellular communication, various frequency bands are used. One such frequency band is called the E-band (71-76 and 81-86 GHz), and is available in many countries with light licenses, and is uncongested with narrow pencil beams. This allows dense re-use of the spectrum with no interference between links. The E-band provides high bandwidths comparable to 10-100 Gbps fibre connections with low latency, allowing high-speed data transmission over short distances (e.g. 2 km to 3 km). The E- Band can thus be used to deploy wireless backhaul links densely in congested cities. Since the communication is wireless, this avoids the need for trenches for cables and fibre optics (required for other types of backhaul links), which can be costly, slow, and highly disruptive. The narrow beams also make such backhaul links inherently secure.

[0003] High-gain antennas at both the transmit and receiver site of the backhaul link are applied to deliver acceptable levels of SNR (signal-to-noise ratio) to overcome the effects of rain attenuation and the significant free-space attenuation. Because of the high-gain antenna requirement, the radiation pattern has a very narrow beamwidth, often between about 0.7 and 1.2 degrees. Consequently, the antenna gain becomes extremely sensitive to any undesired movement of the antenna mast. Due to mast movement (as a result of wind-induced mast movement or solar-induced mast bending), the propagating wave will no longer be transmitted or received at the maximum of the radiation pattern of the antenna, resulting in additional attenuation. Excessive wind-induced sway and twist of the antenna mast will thus cause significant degradation of the communication link. The sways typically have frequencies between 0.4 Hz to 5 Hz and can change the orientation of the antenna by up to +/- 3 degrees depending on the type of structure that the antennas are attached to. In short, the mast movement should be compensated to provide wireless backhaul communication in E- band with good performance.

SUMMARY

[0004] One object is to provide a way to compensate for orientation discrepancy of an antenna.

[0005] According to a first aspect, it is provided a method for compensating for orientation discrepancy of a first antenna in relation to a second antenna. The first antenna is used for reception of radio signals transmitted by the second antenna. The method is performed by an antenna control device. The method comprises: obtaining an indication of received power; obtaining a presently applied orientation control value; determining a new orientation control value of the first antenna based on an extremum seeking control, ESC, algorithm to approach a maximum of the indication of received power, based on the indication of received power and the presently applied orientation control value for the first antenna; and providing the new orientation control value to an actuator to control the orientation of the first antenna.

[0006] The method may further comprise: obtaining an indication of antenna orientation of the first antenna; and computing an orientation of the first antenna towards the second antenna based on the indication of antenna orientation. In this case, the ESC algorithm is also based on the orientation of the first antenna.

[0007] The determining the new orientation control value may comprise calculating the new orientation control value based on a first control signal component and a second control signal component. The first control signal component is based on the ESC algorithm to approach a maximum of the indication of received power, and the second control signal component is based on a mapping function based on at least one the orientation of the first antenna towards the second antenna and the presently applied orientation control value. [0008] The method may further comprise: deriving the mapping function based on data points comprising values of the indication of received power, orientation of the first antenna towards the second antenna and the presently applied orientation control value.

[0009] The mapping function may be based on both the orientation of the first antenna towards the second antenna, and the presently applied orientation control value for the first antenna.

[0010] The new orientation control value may be calculated by adding the first control signal component and the second control signal component.

[0011] The method may be repeated at an operational frequency, in which case the method may further comprise: determining a frequency of sway of the first antenna; and determining the operational frequency based on the frequency of sway of the first antenna.

[0012] The method may further comprise: adjusting the new orientation control value based on a feedforward controller.

[0013] The obtaining an indication of antenna orientation of the first antenna may comprise obtaining the indication of antenna orientation of the first antenna based on a motion sensor mounted to the first antenna.

[0014] According to a second aspect, it is provided an antenna control device for compensating for orientation discrepancy of a first antenna in relation to a second antenna. The first antenna is configured to be used for reception of radio signals transmitted by the second antenna. The antenna control device comprises: a processor; and a memory storing instructions that, when executed by the processor, cause the antenna control device to: obtain an indication of received power; obtain a presently applied orientation control value; determine a new orientation control value of the first antenna based on an extremum seeking control, ESC, algorithm to approach a maximum of the indication of received power, based on the indication of received power and the presently applied orientation control value for the first antenna; and provide the new orientation control value to an actuator to control the orientation of the first antenna.

[0015] The antenna control device may further comprise instructions that, when executed by the processor, cause the antenna control device to: obtain an indication of antenna orientation of the first antenna; and compute an orientation of the first antenna towards the second antenna based on the indication of antenna orientation; and wherein the ESC algorithm is also based on the orientation of the first antenna.

[0016] The instructions to determine the new orientation control value may comprise instructions that, when executed by the processor, cause the antenna control device to calculate the new orientation control value based on a first signal component and a second signal component. The first signal component is based on the ESC algorithm to approach a maximum of the indication of received power, and the second signal component is based on a mapping function based on at least one the orientation of the first antenna towards the second antenna and the presently applied orientation control value.

[0017] The antenna control device may further comprise instructions that, when executed by the processor, cause the antenna control device to: derive the mapping function based on data points comprising values of the indication of received power, orientation of the first antenna towards the second antenna and the presently applied orientation control value.

[0018] The mapping function may be based on both the orientation of the first antenna towards the second antenna, and the presently applied orientation control value for the first antenna.

[0019] The new orientation control value may be calculated by adding the first signal component and the second signal component.

[0020] The antenna control device may further comprise instructions that, when executed by the processor, cause the antenna control device to: determine a frequency of sway of the first antenna; and determine an operational frequency based on the frequency of sway of the first antenna. The instructions are then repeated at an operational frequency.

[0021] The antenna control device may further comprise instructions that, when executed by the processor, cause the antenna control device to adjust the new orientation control value based on a feedforward controller.

[0022] The instructions to obtain an indication of antenna orientation of the first antenna may comprise instructions that, when executed by the processor, cause the antenna control device to obtain the indication of antenna orientation of the first antenna based on a motion sensor mounted to the first antenna.

[0023] According to a third aspect, it is provided a computer program for compensating for orientation discrepancy of a first antenna in relation to a second antenna, the first antenna being used for reception of radio signals transmitted by the second antenna. The computer program comprises computer program code which, when executed on an antenna control device causes the antenna control device to: obtain an indication of received power; obtain a presently applied orientation control value; determine a new orientation control value of the first antenna based on an extremum seeking control, ESC, algorithm to approach a maximum of the indication of received power, based on the indication of received power and the presently applied orientation control value for the first antenna; and provide the new orientation control value to an actuator to control the orientation of the first antenna.

[0024] According to a fourth aspect, it is provided a computer program product comprising a computer program according to the third aspect and a computer readable means comprising non-transitory memory in which the computer program is stored.

[0025] Generally, all terms used in the claims are to be interpreted according to their ordinary meaning in the technical field, unless explicitly defined otherwise herein. All references to "a/an/the element, apparatus, component, means, step, etc." are to be interpreted openly as referring to at least one instance of the element, apparatus, component, means, step, etc., unless explicitly stated otherwise. The steps of any method disclosed herein do not have to be performed in the exact order disclosed, unless explicitly stated.

BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Aspects and embodiments are now described, by way of example, with reference to the accompanying drawings, in which:

[0027] Fig 1 is a schematic diagram illustrating an environment in which embodiments presented herein can be applied;

[0028] Figs 2A-B are schematic diagrams illustrating the consequence of sway of the first antenna of Fig 1;

[0029] Fig 3 is a schematic diagram illustrating a motion sensor and an antenna control device for the first antenna 5a of Fig 1;

[0030] Fig 4 is a schematic diagram illustrating components of the antenna control device of Fig 1 and surrounding devices according to one embodiment;

[0031] Fig 5 is a schematic diagram illustrating components of the antenna control device and the actuator of Fig 4 in more detail according to one embodiment;

[0032] Fig 6 is a schematic diagram illustrating components of the extremum seeking control module of Fig 5 in more detail according to one embodiment;

[0033] Figs 7A-B are flow charts illustrating embodiments of methods for compensating for orientation discrepancy of a first antenna in relation to a second antenna;

[0034] Fig 8 is a schematic diagram illustrating components of the antenna control device of Fig 1 according to one embodiment;

[0035] Fig 9 is a schematic diagram showing functional modules of the antenna control device of Fig 1 according to one embodiment; and

[0036] Fig 10 shows one example of a computer program product comprising computer readable means. DETAILED DESCRIPTION

[0037] The aspects of the present disclosure will now be described more fully hereinafter with reference to the accompanying drawings, in which certain embodiments of the invention are shown. These aspects may, however, be embodied in many different forms and should not be construed as limiting; rather, these embodiments are provided by way of example so that this disclosure will be thorough and complete, and to fully convey the scope of all aspects of invention to those skilled in the art. Like numbers refer to like elements throughout the description.

[0038] Embodiments presented herein compensate for orientation discrepancies in a first antenna, e.g. due to sway of a mast to which the first antenna is mounted. The compensation of the mast movement provides stable wireless backhaul communication, e.g. in the E-band where beamwidth is small, between a first and a second antenna. This is achieved by embodiments that compensate for sway movements with high precision. The method takes as inputs the received power, a current orientation control value and optionally the orientation of the first antenna (in relation to the second antenna), where the orientation of the first antenna can e.g. be measured by a motion sensor attached to the mast or other structure of the first antenna. A first control signal component can be computed without the need to know the orientation of the first antenna, where the received power and a current orientation control value (that is provided to an actuator for compensation) are the main input parameters for a calculation based on Extremum Seeking Control (ESC).

[0039] A second control signal component is optionally computed when the orientation of the first antenna is known, based on a known relationship between all the input variables. The second control signal component controls the feed to be within a small region around the maximum received power, while the first control signal component enables the continuous tracking of the maximum received power value. Due to its design, the first control signal component maintains high tracking performance even if the orientation of the first antenna is incorrectly measured, e.g. due to sensor drift, or when there are dynamically changing weather conditions and or sways affecting the second antenna. [0040] Fig 1 is a schematic diagram illustrating an environment in which embodiments presented herein can be applied.

[0041] A first antenna 5a and a second antenna 5b are provided to implement a communication link 3, such as a backhaul link. In this example, the second antenna 5b transmits a signal on the communication link 3, that is received by the first antenna 5a. In other words, the first antenna 5a here operates as a reception antenna and the second antenna 5b operates as a transmission antenna. It is to be noted though, that the antennas 5a, 5b can optionally switch their roles. The first antenna 5a and the second antenna 5b can be implemented as any suitable antenna type, e.g. a reflector antenna for implementing a wireless backhaul link, e.g. in the E-band (71-76 and 81-86 GHz).

[0042] Figs 2A-B are schematic diagrams illustrating the consequence of sway of the first antenna 5a of Fig 1, and parameters relating to the sway. The first antenna 5a sways and/or twists, e.g. due to wind or solar-induced mast bending. The scenario is the same in Fig 2A and Fig 2B; the parameters are split between two Figures for reasons of clarity. First, Fig 2A will be described. It is to be noted that, for all embodiments presented herein, an orientation of any antenna can be defined by an orientation of a reflector of the antenna or other boresight indicator.

[0043] θ s (t) is used to denote the sway of the antenna mast in local coordinates. This is an angular value of the sway in relation to a centre (non-sway) position.

[0044] θ t (t) is used to denote the orientation of the first antenna 5a towards the second antenna 5b. This is an angular value defining the angle towards the second antenna 5b, seen from the first antenna 5a, in the local coordinates. This can be defined according to θt (t)= θ _t - θ _S (t), where = θ _t is the angular position of the second antenna 5b in global coordinates, which can be obtained during an antenna setup phase and corresponds to the angular position of the target for which the antennas are aligned.

[0045] Looking now to Fig 2B, θf (t) is used to denote an orientation control value, which is an angular value for controlling the orientation of a structure on which the first antenna 5a is mounted or the orientation of the antenna structure itself. When the antenna is a reflector antenna, the orientation control value can be considered to control the feed of the reflector antenna, which is a rigid structure of a such an antenna. The orientation control value is implemented using an actuator (see below). The actuator controls the orientation of any movable part of the antenna which helps improving the signal quality between the two antennas as described for embodiments presented herein.

[0046] Fig 3 is a schematic diagram illustrating a motion sensor and an antenna control device for the first antenna 5a of Fig 1. A motion sensor 8 is here attached to, or integrated in, the first antenna 5a. The motion sensor 8 can be used to measure the orientationθ t (t) of the first antenna 5a towards the second antenna 5b. For example, the motion sensor may be an inclinometer, which estimates θ _S (t), that can be used to derive θt (t) according to the above. In another example, the motion sensor can be based on an Inertial Measurement Unit (IMU), typically composed of an accelerometer, gyroscope and magnetometer, which compute the antenna acceleration, angular velocity and magnetic field, which can be used to estimate the orientation of the antenna θ _S (t) using inertial odometry estimation methods in the art.

[0047] An antenna control device 1 is provided to compensate for orientation discrepancy of the first antenna 5a, in relation to the second antenna 5b, as described in more detail below. An actuator 6 is provided to control an angular position of the first antenna 5a based on control signals from the antenna control device 1.

[0048] Fig 4 is a schematic diagram illustrating components of the antenna control device 1 of Fig 1 and surrounding devices according to one embodiment. The first antenna 5a is affected by the sway θ _S and the orientation control value θf, which is determined to compensate for the sway θ _S as described below.

[0049] The sway θ _S also affects the motion sensor 8. A motion sensor orientation controller 9 take as input a motion sensor 1 ^st antenna orientation θt ^MS from the motion sensor, and determines a motion sensor orientation control value θf ^MS , e.g. based on the calculations mentioned below for the determine new orientation control value step 46 of Fig 7 A. [0050] The motion sensor orientation controller 9 can also be considered to form part of the following component, an extremum seeking control (ESC) module 12 of the antenna control module 1. The ESC module 12 also takes an indication of power p (e.g. Received Signal Strength Indicator (RSSI), or another power indicator) as an input, measured at the first antenna 5a. The antenna control module 1 also comprises a controller 11. The ESC module 12 determines, based on the indication p of received power and the motion sensor 1 ^st antenna orientation θt ^MS , an ESC orientation control value θf ^ESC , that is combined with the motion sensor orientation control value θf ^MS , yielding a target orientation control value θf that is provided to the controller 11. The controller subsequently provides a corresponding signal to the actuator, to thereby apply the orientation control value θf at the first antenna 5a.

[0051] Fig 5 is a schematic diagram illustrating components of the antenna control device and the actuator of Fig 4 in more detail according to one embodiment.

[0052] The controller 11 is shown comprising a feedback controller 13 and a feedforward controller 14. Outputs from the feedback controller 13 and the optional feedforward controller 14 are combined, yielding a controller output to the actuator 6.

[0053] The actuator comprises an actuator module 16 comprising one or more motors or other kinematic devices capable of adjusting the orientation of the structure on which first antenna 6a is mounted. A feed position module 17 obtains the current orientation control value θf and provides this to the ESC module 12 and to an adder, for adding the current orientation control value θf to the target orientation control value θy, to provide the result to the feedback controller 13. Furthermore, the target orientation control value θf is provided to the feedforward controller 14.

[0054] Fig 6 is a schematic diagram illustrating components of the ESC module 12 of Fig 5 in more detail according to one embodiment.

[0055] The ESC module 12 comprises an extended Kalman filter 20 that accepts the inputs to the ESC module 12. A gradient ascent module 21 is provided as a stable discrete-time integrator. The gradient ascent scheme can be configured with relatively small step size, integrating the gradient to find the time-varying maxima. [0056] A dither signal a is applied to assist in finding the maxima, where the amplitude a of the dither signal is a tuning parameter, and the dither signal is typically of a relatively small amplitude. The frequency of the dither signal should also be tuned according to the performance requirements. It has been found that the frequency should be about (i.e. +-20% of) IOX larger than the sway frequency.

[0057] The operation of the ESC module 12 is explained in more detail below.

[0058] Figs 7A-B are flow charts illustrating embodiments of methods for compensating for orientation discrepancy of a first antenna 5a in relation to a second antenna 5b. The first antenna 5a is used for reception of radio signals 3 transmitted by the second antenna 5b. The method being performed by an antenna control device 1. First, embodiments illustrated by Fig 7 A will be described.

[0059] In an obtain indication of received power step 40, the antenna control device

1 obtains an indication p of received power. The indication p of received power is obtained by reading the received power level for signals received at the first antenna 5a while communicating with the second antenna 5b. The indication of received power can be any suitable power measurement, such as RSSI or Received Signal Level (RSL).

[0060] In an obtain present orientation control value step 45, the antenna control device 1 obtains a presently applied (i.e. current) orientation control value θf. As explained above, the presently applied orientation control value θf can be obtained from one or more sensors placed in the feed actuator unit, as for example encoders which are part of the motor which controls the feed, such as the feed position module 17 mentioned above.

[0061] In a determine new orientation control value step 46, the antenna control device 1 determines a new orientation control value θf of the first antenna 5a based on an extremum seeking control, ESC, algorithm to approach a maximum of the indication of received power, based on the indication p of received power and the presently applied orientation control value θf for the first antenna 5a. How this can be achieved is explained in more detail below. [0062] In a provide new orientation control value step 48, the antenna control device 1 provides the new orientation control value θf to an actuator 6 to control the orientation of the first antenna 5a.

[0063] The method then returns to the obtain indication of received power step 40.

[0064] Now, embodiments illustrated by Fig 7B will be described. Only new or modified steps compared to Fig 7 A will be described.

[0065] In an optional conditional use 1 ^st antenna orientation step 41, the antenna control device 1 determines whether to use the indication of antenna orientation for determining the new orientation control value.

[0066] In one embodiment, if the frequency f of the sway affecting the first antenna is slow, i.e. f is lower than a defined threshold, then the compensation can be calculated without consideration of the first antenna orientation, since the dynamics are considered low. The inventors have found that a high tracking performance of the compensation without motion sensors can be obtained for low sway frequencies as for example f < 1 Hz. Hence, if the antennas are installed in an area with slow sways (slow winds and slowly varying thermal changes), the motion sensor is not required.

[0067] For accurate readings, a motion sensor can be calibrated during runtime operation. According to this embodiment, such calibration can be scheduled dynamically, depending on the sway conditions. For instance, when the sway frequency f is low (less than the threshold), the motion sensor might not be used. On the other hand, when the sway frequency is high (greater than the threshold) the motion sensor is used, and its online calibration can be triggered.

[0068] If it is determined to use the first antenna orientation, the method proceeds to an optional obtain indication of antenna orientation step 42. Otherwise, the method proceeds to the obtain present orientation control value step 42

[0069] In the optional obtain indication of antenna orientation step 42, the antenna control device 1 obtains an indication θt of antenna orientation of the first antenna 5a. The indication of antenna orientation of the first antenna 5a is optionally obtained based on a motion sensor 8 mounted to or forming part of the first antenna 5a.

[0070] This measurement can thus be obtained by reading the orientation from a motion sensor attached to the mast or other structure of the antenna. For example, the motion sensor maybe an inclinometer, which outputs θ _S (t). In another example, an Inertial Measurement Unit (IMU) may be used together with an orientation estimator to determine θ _s (t).

[0071] In an optional compute orientation towards 2 ^nd antenna step 44, the antenna control device 1 computes an orientation θt of the first antenna 5a towards the second antenna 5b based on the indication of antenna orientation. When this step is performed, the ESC algorithm can be based also on the orientation θt of the first antenna 5a.

[0072] Based on the measurement of the orientation of the first antenna that moves/ oscillates due to the mast sway, the orientation θ _t (t) of the first antenna 5a towards the second antenna can be computed as θ _t (t) = θ _t - θ _s (t), where θ _t is the angular position of the target in the global coordinates which is obtained during the antenna setup phase and corresponds to the angular position of the target for which the antennas are aligned.

[0073] Optionally, when steps 42 and 44 are performed, the determining 46 the new orientation control value θf comprises calculating the new orientation control value θf based on a first control signal component and a second control signal component, wherein the first control signal component is based on the ESC algorithm to approach a maximum of the indication p of received power, and the second control signal component is based on a mapping function based on at least one the orientation θt of the first antenna 5a towards the second antenna 5b and the presently applied orientation control value θf. The new orientation control value θf can be calculated by adding the first control signal component and the second control signal component.

[0074] In an optional apply feedforward step 47, the antenna control device 1 adjusts the new orientation control value θf based on a feedforward controller 14. [0075] The feedforward controller inverts the antenna control system, comprising an orientation control value, a linear/ rotary motor, and a feedback controller 13, to follow the desired orientation control value position θ _f (t). The resulting feedforward controller, in general, is non-causal; therefore, it is based on future (predicted) values of the input signal. The input of the feedforward controller is θ _f (t + A), i.e., the future predictions of the desired feed position, whereas the output of the feedforward controller is θf (t), i.e., the reference input of the antenna control system. The future prediction (i.e., delta seconds ahead) of the desired feed position θ _f (t + A) can be computed via Recursive Least Square (RLS) algorithm. The algorithm can be written as

[0076] In one embodiment, a predictor is used to counteract dynamics in the entire motion controller, not only in the feedforward controller. The predicted value can be calculated using the RLS algorithm described above. The predicted quantity can be the desired orientation control value , the indication p of received power (e.g. RSSI) value , or some other quantity relevant to the performance of the ESC or motion controller. In this way, better tracking of the desired feed position is achieved.

[0077] In an optional derive mapping function step 50, the antenna control device derives the mapping function based on data points comprising values of the indication p of received power, orientation θt of the first antenna 5a towards the second antenna 5b and the presently applied orientation control value θf.

[0078] The mapping function can be based on both the orientation θt of the first antenna 5a towards the second antenna, and the presently applied orientation control value θf for the first antenna 5a.

[0079] During a maintenance period or when the traffic or traffic importance is low, the system can be used to perform a full scan to construct or update the mapping function. This would entail varying the orientation control value when the antenna is being affected by sway (if the sway is static, then only one full sway is needed, providing one “slice” of the mapping function where the sway is the static value which defines a fixed θ _t (t) value). To provide all slices in the mapping function for all, this scan should be performed when a sway spanning the full range occurs.

[0080] In an optional determine frequency of sway step 52, the antenna control device 1 determines a frequency f of sway of the first antenna 5a.

[0081] In an optional determine operational frequency step 54, the antenna control device 1 determines the operational frequency based on the frequency of sway of the first antenna 5a.

[0082] In one embodiment, if the frequency f of sway affecting the first antenna is slow, defined by the frequency f of sway being lower than a defined threshold, the operational frequency f _ope ration can be decreased. This reduces power consumption of the antenna control unit. For example, if the sway frequency f > f _min , a high f _ope ration frequency is chosen (e.g., 500 Hz), while if the sway frequency f < f _min , a low f _ope ration frequency is chosen (e.g., 100 Hz). The inventors have experimentally verified that for slow sways, a lower operating frequency is acceptable to achieve high tracking performance, while for higher sway frequencies a high operating frequency provides better performance.

[0083] The operational frequency defines how often the method should be repeated.

[0084] Details of how the new orientation control value in step 46 is obtained in three sub-steps i), ii) and hi) is now presented.

[0085] Sub-step i) A first control signal component u _power (t) is determined based on the indicator p of power from step 40 and the orientation control value from step 42 as follows (see also Fig 6):

[0086] For example, the quantity u _power (t) = ESC(p(t), _f θ(t)) is obtained by applying an Extremum Seeking Controller known in the art per se, e.g. as described in Gregor Gelbert et al “Advanced algorithms for gradient estimation in one- and two-parameter extremum seeking controllers,” Journal of Process Control, Volume 22, Issue 4, Pages 700-709, April 2012, doi:10.1016/j.jprocont.2012.01.022. When such a procedure is applied, we apply a model-free method that automatically determines the new orientation control value that maximizes the received power level as [0087] Optionally, due to the potentially fast sway frequencies (up to 5 Hz) and the need to track a time-varying maximum (since the optimal power level p(t) varies with the antenna orientation ^^ _^^ and the orientation control value ), the inventors have observed that a non-standard ESC as proposed in Gelbert et al is valuable to be employed. Such an ESC is characterized by: [0088] A fast, model-free gradient estimator computes the gradient for example a discrete-time extended Kalman filter 16 as known in the art per se, see the entry for “Extended Kalman Filter” on Wikipedia.org. The state variable at time contains the gradient to be estimated. The gradient can therefore be estimated using data until time , which can be computed using the expressions from the Wikipedia entry, where the state and measurement are given by: [0089] Considering only the measurement of is a tunable delay parameter, w denoted process noise, v denotes measurement noise and where the gradient is given according to (where the numerical subscript indicates the element number of the vector x): [0090] Considering the measurement o , and n ₁ and n ₂ are tunable delay parameters and the gradient

[0091] A stable discrete-time integrator, such as a standard gradient ascent scheme with small step size, integrates the gradient to find the time-varying maxima.

[0092] A dither signal a sin(cot) is applied to help the algorithm find the maxima, as described above, where the amplitude of the dither signal is a tuning parameter, and the dither signal is typically of a small amplitude.

[0093] Sub-step ii) In this optional sub-step, a second control signal component is obtained based on the first antenna orientation measured via the motion sensor in step b) and a mapping function M(0 _t , θ _f ) that relates the antenna orientation, the orientation control value and the power level as p = M(0 _t , _f θ). a. For example, the quantity where θ _t is obtained in step 42. In one embodiment, a robust, simple solution is to approximate the maximum of the mapping M by a simpler function (e.g., lower order, linear), e.g. by multiplying with a scalar value according to where a is a suitably selected constant. As an example, a can be set to 3/ 2. b. The ideal mapping function M can be found offline in step 50, by using the properties of the first antenna, reflected in data points containing values of θ _f , θ _t and p. The mapping function M can also be derived using experiments by collecting the data points containing values of θ _f , θ _t and [0094] Sub-step iii) The desired first antenna feed angle θ _f (t) can be calculated as a combination of the two control signal components defined above u _power (t) and For example,

[0095] In one embodiment, the embodiments presented herein can be applied to a single angle dimension, such as elevation/pitch. Alternatively, the embodiments presented herein are applied to multiple orientation angles, for example both azimuth/yaw and elevation/pitch.

[0096] Compared to methods that are mainly based on motion sensors, embodiments presented herein are not impacted by sensor drift and does not require accurate pre-aligning of the antennas to maintain the same orientation. Moreover, since the embodiments are based on ESC, there is no need for repetitive calibration of the motion sensor (when provided).

[0097] Embodiments presented herein have been found to effectively compensate for fast and varying sway movements with a frequency of up to 5 Hz with a precision which leads to less than a 3 dB degradation in the link power, in a way that is robust to the presence of drift and noise in the measurement of the first antenna structure orientation. Moreover the embodiments are robustness against dynamically changing weather conditions and any sway of the second antenna.

[0098] Fig 8 is a schematic diagram illustrating components of the antenna control device 1 of Fig 1 according to one embodiment. A processor 60 is provided using any combination of one or more of a suitable central processing unit (CPU), graphics processing unit (GPU), multiprocessor, microcontroller, digital signal processor (DSP), etc., capable of executing software instructions 67 stored in a memory 64, which can thus be a computer program product. The processor 60 could alternatively be implemented using an application specific integrated circuit (ASIC), field programmable gate array (FPGA), etc. The processor 60 can be configured to execute the method described with reference to Figs 7A-B above.

[0099] The memory 64 can be any combination of random-access memory (RAM) and/or read-only memory (ROM). The memory 64 also comprises non-transitory persistent storage, which, for example, can be any single one or combination of magnetic memory, optical memory, solid-state memory or even remotely mounted memory.

[0100] A data memory 66 is also provided for reading and/ or storing data during execution of software instructions in the processor 60. The data memory 66 can be any combination of RAM and/ or ROM.

[0101] The antenna control device 1 further comprises an I/O interface 62 for communicating with external and/or internal entities. Optionally, the I/O interface 62 also includes a user interface.

[0102] Other components of the antenna control device 1 are omitted in order not to obscure the concepts presented herein.

[0103] Fig 9 is a schematic diagram showing functional modules of the antenna control device of Fig 1 according to one embodiment. The modules are implemented using software instructions such as a computer program executing in the antenna control device 1. Alternatively or additionally, the modules are implemented using hardware, such as any one or more of an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or discrete logical circuits. The modules correspond to the steps in the methods illustrated in Figs 7A-B.

[0104] A power indication obtainer 70 corresponds to step 40. A 1 ^st antenna orientation use determiner 71 corresponds to step 41. An indication of antenna orientation obtainer 72 corresponds to step 42. An orientation computer 74 corresponds to step 44. A present orientation control value obtainer 75 corresponds to step 45. A new orientation control value determiner 76 corresponds to step 46. A feed forward applier 77 corresponds to step 47. A new orientation control value obtainer 78 corresponds to step 48. A mapping function deriver 80 corresponds to step 50. A sway frequency determiner 82 corresponds to step 52. An operational frequency determiner 84 corresponds to step 54.

[0105] Fig 10 shows one example of a computer program product 90 comprising computer readable means. On this computer readable means, a computer program 91 can be stored in a non-transitory memory. The computer program can cause a processor to execute a method according to embodiments described herein. In this example, the computer program product is in the form of a removable solid-state memory, e.g. a Universal Serial Bus (USB) drive. As explained above, the computer program product could also be embodied in a memory of a device, such as the computer program product 64 of Fig 8. While the computer program 91 is here schematically shown as a section of the removable solid-state memory, the computer program can be stored in any way which is suitable for the computer program product, such as another type of removable solid-state memory, or an optical disc, such as a CD (compact disc), a DVD (digital versatile disc) or a Blu-Ray disc.

[0106] The aspects of the present disclosure have mainly been described above with reference to a few embodiments. However, as is readily appreciated by a person skilled in the art, other embodiments than the ones disclosed above are equally possible within the scope of the invention, as defined by the appended patent claims. Thus, while various aspects and embodiments have been disclosed herein, other aspects and embodiments will be apparent to those skilled in the art. The various aspects and embodiments disclosed herein are for purposes of illustration and are not intended to be limiting, with the true scope and spirit being indicated by the following claims.