- Email: [email protected]
Antenna temperature compensation: The example of the ENVISAT-1 SAR
Am AstronauricaVol. 39. No. 7. pp. 529-535, 1996 0 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain PII:SOO94-5765(%)00099-9 0094-5765/96 $15.00+0.00
ANTENNA TEMPERATURE COMPENSATION: EXAMPLE OF THE ENVISAT-1 SARt
THE
M. A. B. COHENS Matra Marconi Space, Portsmouth, Hampshire, U.K. (Received 7 June 1995) Abstract-The paper describes the development of a computational process which compensates for the variation in gain and phase of active phased array antenna transmit/receive modules with temperature. The process described has been developed for use on the European Space Agency’s ENVISAT-I Advanced Synthetic Aperture Radar instrument and will allow the performance of its antenna to be improved significantly. The technique exploits systematic behavioural characteristics of the transmit/receive modules to provide a solution which is accurate, compact and fast to implement. 0 1997 Elsevier Science Ltd
1. BACKGROUND
The broadening
scope of uses being identified for spaceborne SAR data following the highly successful ERS-1 mission is leading to increasing interest in greater instrument performance. An important factor in achieving this goal is the improvement of antenna flexibility, and so the use of an active array has been introduced. A number of different modes are implemented by the ASAR instrument, each designed to achieve a different balance of image resolution, coverage area and science data rate: Image mode provides 30 m spatial resolution along a single selectable swath 50-100 km wide, transmitting the high rate science data directly to a ground station. l Wide Swath mode provides 100 m resolution across an effective swath -400 km wide. This is achieved by dynamically steering the antenna beam in elevation across five adjacent swaths. The data are transmitted to a ground station as in Image mode. l Global Monitoring mode operates in a similar fashion to Wide Swath mode but provides images at 1 km resolution, allowing compressed science data to be stored on tape. This provides global coverage, even outside the range of ground stations. l Wave mode images with 30 m resolution over small
l
tPaper IAF-94-US.492 presented at the 45th International Astronautical Congress, Jerusalem, Israel, 9-14 October 1994. $B. Eng. (Hons) AMIEE. Spacecraft Systems Engineer, Directorate of Earth Observation. AA 39/7--C
l
areas of 5 km x 5 km, again storing science data on tape. Alternating Polarisation mode is similar to Image mode, but uses vertical and horizontal transmit/receive polarisation alternately from cycle to cycle within the processed azimuth beamwidth to form continuous images in each polarisation.
A large number of antenna radiation patterns are required by the modes described above. The ASAR instrument must be able to form and maintain the stability of these patterns. Its ability to do this under all operating conditions is fundamental to its success as a high resolution SAR. The most significant variations for the ASAR instrument will be due to the extreme temperature variations of a Low Earth Orbit and stabilisation of these variations is therefore essential. For each signal path (TxV, TxH, RxV and R x H) on each of the 320 TR modules on the ASAR antenna, a gain control and phase control facility is provided. These enable the required beamforming capability to be realised. Figure 1 shows this function diagrammatically. At any given gain/phase control setting combination, the achieved gain and phase shift vary significantly with temperature due to the thermal characteristics of the module components. The achieved gain and phase shift also vary to a lesser extent from module to module due to manufacturing tolerances. By compensating for these variations it is possible to improve the correlation between required and achieved gain/phase weightings, and hence improve significantly the antenna beam performance. This process is termed ‘Temperature Compensation’, but may provide compensation for any module to module variations as well as for temperature variations. 529
M. A.
530
WEIQHTING CONTROL
Fig. I. TR
B. Cohen
WEIGHTING CONTROL
module gain/phase
control
function
2. COMPENSATION TECHNIQUES
There are many possible techniques for implementing Temperature Compensation, but the main categories of approach are as follows.
(4 Inclusion
(b)
of additional hardware complexity in the TR modules themselves (such as ovens or active feedback loops) in order to minimise the gain and phase variation with temperature. Mathematical modelling of measured TR module behaviour and subsequent implementation of a real-time computational algorithm which determines the optimum control settings to use for any given gain/phase requirement.
L
The first approach is not only very difficult to achieve but also has major mass and power impacts, particularly on an antenna with many TR modules. The second approach, however, permits a relatively low complexity TR module to be used, but requires the inclusion of microprocessor-based units to implement the necessary compensation algorithm. Figure 2 summarises the computational technique. With the considerable number of TR modules on its antenna, this second approach was the more attractive option for the ASAR project. Having selected a general philosophy for solving the compensation problem, a suitable detailed solution needed to be developed. This solution was required to have the following features. l
l
l
Fig. 3. Measured phase
at
24°C.
3. DEVELOPMENT OF THE SOLUTION .Z.1.
Assessment
qf TR module behaviour
The first stage in the development process was to assess the measured behaviour of the ASAR TR modules. Data were available for the four signal paths of a number of development model TR modules, comprising measured phase and gain at all phase and gain control setting combinations, for seven temperatures spanning the operating range of -20 to +55”C. Figures 3 and 4 show example measurements at 24C. As the phase setting is varied, insertion loss variations affect the total gain achieved. Similarly, as the gain setting is varied, a variation in total phase shift occurs. These effects can clearly be seen in Figs 3 and 4. The shapes of these surfaces vary with temperature, most significantly the gain surface along the gain control axis. These temperature variations are shown in Figs 5 and 6 by means of plots showing
Good correlation between required and achieved gain and phase. Compact behavioural models (i.e. minimal storage required). Fast-implementing algorithm to ensure maintenance of good beam performance during periods of rapid temperature change (such as during eclipse).
Fig. 2. Algorithm-based
compensation
architecture.
Fig. 4. Measured
gain at 24 C.
Antenna temperature compensation
-90 -20
-10
I 0
I 10
20
30
40
50
60
TEMPERATURE PC Fig. 5. Variation
in phase with temperature.
Fig. 7. Optimum
the temperature variation of a number of selected points on the phase and gain surfaces, respectively. 3.2. Selection qf approach A possible approach to a solution is to model the measurement data, and then use the model in real-time to determine the optimum gain setting and phase setting for any required-gain/required-phase/ temperature combination. This approach requires an iterative algorithm since the models would give achieved gain and phase as a function of settings (and temperature). Such an algorithm would be quite complex and slow to implement. An alternative approach is to pre-process the measurement data to determine the optimum gains setting and phase setting for every possible requiredgain/required-phase combination, at each measurement temperature. This effectively reverses the axes of the measurement data to give a new data set, the ‘optimum setting data’. This gives the optimum gain setting and phase setting as a function of gain and
2oc
phase settings at 24’C.
phase required at each measurement temperature and so, when modelled, leads to an algorithm which is a ‘single-shot’ model evaluation. This is the adopted solution.
3.3. Generation of optimum settings Optimum gain and phase settings are derived for each required-gain/required-phase combination, at each measurement temperature, by scanning all the measured data. At each temperature the settings which give the smallest r.s.s. gain/phase error from the required values are determined. Figures 7 and 8 show the optimum phase and gain setting data, respectively, as generated from the measurement data in Figs 3 and 4, at a single temperature. In order to create a monotonic, and hence easily modelled surface for the optimum phase setting data in Fig. I, values outside the range &63 are used. This accommodates the O-360” wrap-around nature of the phase control. The true optimum phase settings are the MODULO 64 equivalents of those plotted. 128 112
-501 -20
, -10
0
10
20
30
40
50
60
TEMPERATURE I”C Fig. 6. Variation
in gain with temperature.
Fig. 8. Optimum
gain settings at 24’C.
M. A. B. Cohen
532
where
t is temperature in ‘C g is required gain in dB 4 is required phase in degrees.
Fig. 9. Optimum
gain settings at 24 C (rearranged)
Optimum gain setting data retain the stepped features of measured gain data. These features create a potential problem for the modelling of the data. In this case, eight regions (or segments) may be identified with the step discontinuities as their boundaries. Variations in gain as the phase setting is changed cause these step discontinuities to be non-parallel to the gain axis. In addition, the steps drift along the required phase axis as the temperature varies. This presents a complex modelling problem. However, by re-arranging the optimum gain setting data to be a function of the gain required and the corresponding phase setting, the steps become parallel to the gain required axis and fixed with respect to temperature. Figure 9 shows the data rearranged in this way. The boundaries of the eight segments of these revised optimum gain setting data are now easily defined (the segments lie in the Phase Setting regions O-7, 8-15, 1623, 2431, 32-39, 40-47, 48-55 and 5663) and a relatively simple approach to modelling of the data is now possible. 3.4. Modelling
the optimum
setting dutu
Optimum phase setting data may be modelled using a single polynomial in required-gain, requiredphase and temperature. In the trade-off between model accuracy and complexity, the following order in each of the variables was selected. Optimum
phase setting
model:
1
Order in required-phase Order in required-gain Order in temperature The polynomial
therefore
2 3. takes the form:
C” + c,g + c2g2 + c,ql + c,g+ + Cl&Y + Cag2t + C& + C,zt? + C,,gt’
+ Gg’4
+ Clog&
+ Gt
+ c, ,gyt
+ C14gY + c,v#u2 + c,ogqw
Optimum gain setting data, as illustrated in Fig. 9, could be modelled using eight polynomials (one for each segment), each a function of required gain, phase setting and temperature. In fact, the nature of the data in this case is such that it may be modelled in a more compact way by using a single polynomial, to model the average of the eight segments, in conjunction with eight fixed offset values. In order to take the average of the eight segments, the phase setting coordinates must first be folded into the range O-7 by applying a MODULO 8 function. In the trade-off between model accuracy and complexity, the following order in each of the variables was selected. Optimum
gain setting model (average
segment):
Order in phase setting Order in required-gain Order in temperature The polynomial
therefore
I 3 3. takes the form:
K,) + K,g + Kzg’ + KJg’ + K44 + KS& + Keg’+ + K,g’$
+ Kst + Ksgt + K,og’t + K,,g’t
+ K&t
+ K,ig&
+ K,,gt2 + K&t’ + Kz&%t’
+ K,,g’& + K,sgY
+ K,,g’&
+ Kz,,$t’ + K>,g&’
+ K23g’cjt’ + K&
+ K?,g’t’ f K&t’
+ K,ht’
+ Kzsgt’+ Klag?’
+ Kzqg&’
+ Ku,g+bF + Kug’$t’,
where
t is temperature in C g is required-gain in dB 4 is the phase setting MODULO
8.
Applying polynomial best-fit techniques to the data leads to the generation of the coefficients Co to Cl2 and K,, to RI. Subsequent processing leads to the generation of the corresponding offset values (Off, to Offs) for the eight gain setting segments. 3.5. Definition
of the algorithm
Having defined the model polynomials and determined their coefficients, an algorithm needs to be defined which uses the models to generate a gain setting and phase setting for any required gain/required phase/ temperature combination. The algorithm which meets this requirement is shown as a flow diagram in Fig. IO.
Antenna temperature compensation Evaluation of the optimum phase setting model is first performed to give the desired phase setting. This value is then available for input to the optimum gain setting model (average segment) and for the selection of the offset which is subsequently added. This simple single-shot algorithm is fast to implement, particularly if the model polynomials are factorised to minimise the number of addition and multiplication operations required. Figures 11 and 12 show the phase settings and gain settings respectively as evaluated by the algorithm in Fig. 10. These may be compared visually with the original optimum setting data in Figs 7 and 8. In order to assess the performance of the method a full performance analysis was quantitatively, carried out. The results of this analysis are presented in the next section. 4. PERFORMANCE ANALYSIS
Fig. 1I. Evaluated phase settings at 24°C.
4.1. Error performance Clearly, using the optimum settings themselves (rather than modelled settings) would give the best possible error performance at the measurement temperatures. Using modelled optimum settings will
degrade this error performance. The best way, therefore, to assess the error performance of any compensation technique is to compare its performance with that achieved using the optimum settings. Error performance is determined by computing the r.m.s. error between required and achieved gain and phase at each measurement temperature. This approach to the analysis of error performance has been applied for the technique described and the following results from an R x V signal path are given as an example. Using the optimum settings, the minimum achievable r.m.s. phase and gain errors (over all required-gain/required-phase/measurement temperature combinations) are: RMS Phase Error : 1.747degrees RMS Gain Error : 0.100 dB The distribution of these phase and gain errors is as shown in Figs 13 and 14.
Fig. 10. Compensation algorithm.
Fig. 12. Evaluated gain settings at 24‘C.
M. A. B. Cohen
------I Total of
600
6 500 E 400 n 9
samples
16384
t
1
J
! 200
4
--__-_I
100 1
01 -25
-15
-5
5
15
25
-25
PHASE ERROR /Degrees Fig. 13. r.m.s.
phase error distribution settings.
using optimum
: 2.029 degrees : 0.115 dB.
Fig.
15. r.m.s.
usmg lookup settings.
15
5
ERROR
phase error distribution settings.
tables
to model
25
/Degrees
using modelled
the optimum
control
4.3. Speed of implementation
The distribution of these gain and phase errors was as shown in Figs 15 and 16. By comparison of the r.m.s. errors and the error distributions shown above. it can be seen that by modelling the optimum settings in the way described, only a small increase in error is incurred. 4.2. Storugc
-5 PHASE
Using the modelled sc/ting.s, as shown in Figs I1 and 12. the r.m.s. phase and gain errors are: RMS Phase Error RMA Gain Error
-15
16384 samples
I
300
w”
Total of
I
600
r~~quiremunts
Sixty-four coefficients (C,, to c’,,. K,, to K,, and Off, to OK) must be stored for each of the four signal paths on each TR Module in order to implement the technique described. This requires 64 x 4 x 2 = 512. l6-bit words per TR module, assuming two words of storage per floating-point number. This storage requirement is relatively low compared with that required if. for example. a solution were implemented
Implementation speed of the described method will be significantly higher than that achievable using an iterative method, which must re-evaluate models on each iteration. Hence, replacing an iterative method which uses ten iterations to reach a solution with the single-shot method will reduce the time taken for a compensation by a factor of about IO. Exact speeds clearly depend on processor choice and program coding efficiency, but as a guide, it is expected that for ASAR the algorithm will compensate a single required gain/required phase input in approx. 375 ps.
5. CONCLUSIONS
Despite the variations of TR Module behaviour with temperature and from module to module, the
700
“““.
”
I”“).
”
Total of 600 -
16384 samples
t+ c 500 z 5
400
-
cl g
300 -
z UJ 200 -
loo-
too-
,:
0: -1.0
-0.5
0.0
0.5
-1.0
1.0
-0.5
GAIN ERROR /dB Fig. 14. r.m.s.
gain
error distribution settings.
0.0
1.. 0.5
1.0
GAIN ERROR /clB usmg
optimum
Fig.
16. r.m.s.
gain
error distribution settings.
using
modelled
535
Antenna temperature compensation technique described maintains a close correlation between required and achieved gains and phase shifts over all operating temperatures and for all TR Modules. The achieved antenna beam performance is consequently comparable with that of an antenna using TR Modules which are all stable with temperature and all identical in behaviour. Such ‘ideal’ TR Modules are not a practical option, but the technique described provides a practical alternative. The improvement in antenna performance has been achieved by making use of a priori knowledge of TR Module behaviour. Since the modelling of optimum control setting data incurs only a small degradation in error, the performance of the technique is close to optimal. The pre-processing of the measurement data to yield optimum control setting data permits a fast, single-shot solution algorithm to be utilised, whilst requiring only a relatively small amount of data to be stored. Thus, the potential responsiveness of the compensation process to rapid temperature change is also improved. The compensation method described has been ‘fine tuned’ for a specific application, but the principles used in the development of the technique are
potentially very valuable. The fundamental requirement to control imperfect devices with accuracy and speed in varying conditions is common to many engineering systems. The ability to exploit the apriori knowledge of device characteristics in the modelling process provides a powerful means by which to ‘squeeze’ the maximum amount of performance from the minimum of device complexity. Acknowledgements-This work has been carried out under contract to the European Space Agency (ESA). The author would like to thank colleagues in the Systems Group at Matra Marconi Space, and at Dornier and the European Space Technology Centre (ESTEC) for their support and encouragement. The author would also like to thank Alcatel Espace for providing the TR Module characterisation data.
APPENDIX Abbreciations
SAR ASAR
Synthetic Aperture Radar Advanced SAR (instrument)
TR TxV TxH RxV RxH
Transmit/Receive Transmit Vertical Transmit Horizontal Receive Vertical Receive Horizontal
ANTENNA TEMPERATURE COMPENSATION: EXAMPLE OF THE ENVISAT-1 SARt
THE
M. A. B. COHENS Matra Marconi Space, Portsmouth, Hampshire, U.K. (Received 7 June 1995) Abstract-The paper describes the development of a computational process which compensates for the variation in gain and phase of active phased array antenna transmit/receive modules with temperature. The process described has been developed for use on the European Space Agency’s ENVISAT-I Advanced Synthetic Aperture Radar instrument and will allow the performance of its antenna to be improved significantly. The technique exploits systematic behavioural characteristics of the transmit/receive modules to provide a solution which is accurate, compact and fast to implement. 0 1997 Elsevier Science Ltd
1. BACKGROUND
The broadening
scope of uses being identified for spaceborne SAR data following the highly successful ERS-1 mission is leading to increasing interest in greater instrument performance. An important factor in achieving this goal is the improvement of antenna flexibility, and so the use of an active array has been introduced. A number of different modes are implemented by the ASAR instrument, each designed to achieve a different balance of image resolution, coverage area and science data rate: Image mode provides 30 m spatial resolution along a single selectable swath 50-100 km wide, transmitting the high rate science data directly to a ground station. l Wide Swath mode provides 100 m resolution across an effective swath -400 km wide. This is achieved by dynamically steering the antenna beam in elevation across five adjacent swaths. The data are transmitted to a ground station as in Image mode. l Global Monitoring mode operates in a similar fashion to Wide Swath mode but provides images at 1 km resolution, allowing compressed science data to be stored on tape. This provides global coverage, even outside the range of ground stations. l Wave mode images with 30 m resolution over small
l
tPaper IAF-94-US.492 presented at the 45th International Astronautical Congress, Jerusalem, Israel, 9-14 October 1994. $B. Eng. (Hons) AMIEE. Spacecraft Systems Engineer, Directorate of Earth Observation. AA 39/7--C
l
areas of 5 km x 5 km, again storing science data on tape. Alternating Polarisation mode is similar to Image mode, but uses vertical and horizontal transmit/receive polarisation alternately from cycle to cycle within the processed azimuth beamwidth to form continuous images in each polarisation.
A large number of antenna radiation patterns are required by the modes described above. The ASAR instrument must be able to form and maintain the stability of these patterns. Its ability to do this under all operating conditions is fundamental to its success as a high resolution SAR. The most significant variations for the ASAR instrument will be due to the extreme temperature variations of a Low Earth Orbit and stabilisation of these variations is therefore essential. For each signal path (TxV, TxH, RxV and R x H) on each of the 320 TR modules on the ASAR antenna, a gain control and phase control facility is provided. These enable the required beamforming capability to be realised. Figure 1 shows this function diagrammatically. At any given gain/phase control setting combination, the achieved gain and phase shift vary significantly with temperature due to the thermal characteristics of the module components. The achieved gain and phase shift also vary to a lesser extent from module to module due to manufacturing tolerances. By compensating for these variations it is possible to improve the correlation between required and achieved gain/phase weightings, and hence improve significantly the antenna beam performance. This process is termed ‘Temperature Compensation’, but may provide compensation for any module to module variations as well as for temperature variations. 529
M. A.
530
WEIQHTING CONTROL
Fig. I. TR
B. Cohen
WEIGHTING CONTROL
module gain/phase
control
function
2. COMPENSATION TECHNIQUES
There are many possible techniques for implementing Temperature Compensation, but the main categories of approach are as follows.
(4 Inclusion
(b)
of additional hardware complexity in the TR modules themselves (such as ovens or active feedback loops) in order to minimise the gain and phase variation with temperature. Mathematical modelling of measured TR module behaviour and subsequent implementation of a real-time computational algorithm which determines the optimum control settings to use for any given gain/phase requirement.
L
The first approach is not only very difficult to achieve but also has major mass and power impacts, particularly on an antenna with many TR modules. The second approach, however, permits a relatively low complexity TR module to be used, but requires the inclusion of microprocessor-based units to implement the necessary compensation algorithm. Figure 2 summarises the computational technique. With the considerable number of TR modules on its antenna, this second approach was the more attractive option for the ASAR project. Having selected a general philosophy for solving the compensation problem, a suitable detailed solution needed to be developed. This solution was required to have the following features. l
l
l
Fig. 3. Measured phase
at
24°C.
3. DEVELOPMENT OF THE SOLUTION .Z.1.
Assessment
qf TR module behaviour
The first stage in the development process was to assess the measured behaviour of the ASAR TR modules. Data were available for the four signal paths of a number of development model TR modules, comprising measured phase and gain at all phase and gain control setting combinations, for seven temperatures spanning the operating range of -20 to +55”C. Figures 3 and 4 show example measurements at 24C. As the phase setting is varied, insertion loss variations affect the total gain achieved. Similarly, as the gain setting is varied, a variation in total phase shift occurs. These effects can clearly be seen in Figs 3 and 4. The shapes of these surfaces vary with temperature, most significantly the gain surface along the gain control axis. These temperature variations are shown in Figs 5 and 6 by means of plots showing
Good correlation between required and achieved gain and phase. Compact behavioural models (i.e. minimal storage required). Fast-implementing algorithm to ensure maintenance of good beam performance during periods of rapid temperature change (such as during eclipse).
Fig. 2. Algorithm-based
compensation
architecture.
Fig. 4. Measured
gain at 24 C.
Antenna temperature compensation
-90 -20
-10
I 0
I 10
20
30
40
50
60
TEMPERATURE PC Fig. 5. Variation
in phase with temperature.
Fig. 7. Optimum
the temperature variation of a number of selected points on the phase and gain surfaces, respectively. 3.2. Selection qf approach A possible approach to a solution is to model the measurement data, and then use the model in real-time to determine the optimum gain setting and phase setting for any required-gain/required-phase/ temperature combination. This approach requires an iterative algorithm since the models would give achieved gain and phase as a function of settings (and temperature). Such an algorithm would be quite complex and slow to implement. An alternative approach is to pre-process the measurement data to determine the optimum gains setting and phase setting for every possible requiredgain/required-phase combination, at each measurement temperature. This effectively reverses the axes of the measurement data to give a new data set, the ‘optimum setting data’. This gives the optimum gain setting and phase setting as a function of gain and
2oc
phase settings at 24’C.
phase required at each measurement temperature and so, when modelled, leads to an algorithm which is a ‘single-shot’ model evaluation. This is the adopted solution.
3.3. Generation of optimum settings Optimum gain and phase settings are derived for each required-gain/required-phase combination, at each measurement temperature, by scanning all the measured data. At each temperature the settings which give the smallest r.s.s. gain/phase error from the required values are determined. Figures 7 and 8 show the optimum phase and gain setting data, respectively, as generated from the measurement data in Figs 3 and 4, at a single temperature. In order to create a monotonic, and hence easily modelled surface for the optimum phase setting data in Fig. I, values outside the range &63 are used. This accommodates the O-360” wrap-around nature of the phase control. The true optimum phase settings are the MODULO 64 equivalents of those plotted. 128 112
-501 -20
, -10
0
10
20
30
40
50
60
TEMPERATURE I”C Fig. 6. Variation
in gain with temperature.
Fig. 8. Optimum
gain settings at 24’C.
M. A. B. Cohen
532
where
t is temperature in ‘C g is required gain in dB 4 is required phase in degrees.
Fig. 9. Optimum
gain settings at 24 C (rearranged)
Optimum gain setting data retain the stepped features of measured gain data. These features create a potential problem for the modelling of the data. In this case, eight regions (or segments) may be identified with the step discontinuities as their boundaries. Variations in gain as the phase setting is changed cause these step discontinuities to be non-parallel to the gain axis. In addition, the steps drift along the required phase axis as the temperature varies. This presents a complex modelling problem. However, by re-arranging the optimum gain setting data to be a function of the gain required and the corresponding phase setting, the steps become parallel to the gain required axis and fixed with respect to temperature. Figure 9 shows the data rearranged in this way. The boundaries of the eight segments of these revised optimum gain setting data are now easily defined (the segments lie in the Phase Setting regions O-7, 8-15, 1623, 2431, 32-39, 40-47, 48-55 and 5663) and a relatively simple approach to modelling of the data is now possible. 3.4. Modelling
the optimum
setting dutu
Optimum phase setting data may be modelled using a single polynomial in required-gain, requiredphase and temperature. In the trade-off between model accuracy and complexity, the following order in each of the variables was selected. Optimum
phase setting
model:
1
Order in required-phase Order in required-gain Order in temperature The polynomial
therefore
2 3. takes the form:
C” + c,g + c2g2 + c,ql + c,g+ + Cl&Y + Cag2t + C& + C,zt? + C,,gt’
+ Gg’4
+ Clog&
+ Gt
+ c, ,gyt
+ C14gY + c,v#u2 + c,ogqw
Optimum gain setting data, as illustrated in Fig. 9, could be modelled using eight polynomials (one for each segment), each a function of required gain, phase setting and temperature. In fact, the nature of the data in this case is such that it may be modelled in a more compact way by using a single polynomial, to model the average of the eight segments, in conjunction with eight fixed offset values. In order to take the average of the eight segments, the phase setting coordinates must first be folded into the range O-7 by applying a MODULO 8 function. In the trade-off between model accuracy and complexity, the following order in each of the variables was selected. Optimum
gain setting model (average
segment):
Order in phase setting Order in required-gain Order in temperature The polynomial
therefore
I 3 3. takes the form:
K,) + K,g + Kzg’ + KJg’ + K44 + KS& + Keg’+ + K,g’$
+ Kst + Ksgt + K,og’t + K,,g’t
+ K&t
+ K,ig&
+ K,,gt2 + K&t’ + Kz&%t’
+ K,,g’& + K,sgY
+ K,,g’&
+ Kz,,$t’ + K>,g&’
+ K23g’cjt’ + K&
+ K?,g’t’ f K&t’
+ K,ht’
+ Kzsgt’+ Klag?’
+ Kzqg&’
+ Ku,g+bF + Kug’$t’,
where
t is temperature in C g is required-gain in dB 4 is the phase setting MODULO
8.
Applying polynomial best-fit techniques to the data leads to the generation of the coefficients Co to Cl2 and K,, to RI. Subsequent processing leads to the generation of the corresponding offset values (Off, to Offs) for the eight gain setting segments. 3.5. Definition
of the algorithm
Having defined the model polynomials and determined their coefficients, an algorithm needs to be defined which uses the models to generate a gain setting and phase setting for any required gain/required phase/ temperature combination. The algorithm which meets this requirement is shown as a flow diagram in Fig. IO.
Antenna temperature compensation Evaluation of the optimum phase setting model is first performed to give the desired phase setting. This value is then available for input to the optimum gain setting model (average segment) and for the selection of the offset which is subsequently added. This simple single-shot algorithm is fast to implement, particularly if the model polynomials are factorised to minimise the number of addition and multiplication operations required. Figures 11 and 12 show the phase settings and gain settings respectively as evaluated by the algorithm in Fig. 10. These may be compared visually with the original optimum setting data in Figs 7 and 8. In order to assess the performance of the method a full performance analysis was quantitatively, carried out. The results of this analysis are presented in the next section. 4. PERFORMANCE ANALYSIS
Fig. 1I. Evaluated phase settings at 24°C.
4.1. Error performance Clearly, using the optimum settings themselves (rather than modelled settings) would give the best possible error performance at the measurement temperatures. Using modelled optimum settings will
degrade this error performance. The best way, therefore, to assess the error performance of any compensation technique is to compare its performance with that achieved using the optimum settings. Error performance is determined by computing the r.m.s. error between required and achieved gain and phase at each measurement temperature. This approach to the analysis of error performance has been applied for the technique described and the following results from an R x V signal path are given as an example. Using the optimum settings, the minimum achievable r.m.s. phase and gain errors (over all required-gain/required-phase/measurement temperature combinations) are: RMS Phase Error : 1.747degrees RMS Gain Error : 0.100 dB The distribution of these phase and gain errors is as shown in Figs 13 and 14.
Fig. 10. Compensation algorithm.
Fig. 12. Evaluated gain settings at 24‘C.
M. A. B. Cohen
------I Total of
600
6 500 E 400 n 9
samples
16384
t
1
J
! 200
4
--__-_I
100 1
01 -25
-15
-5
5
15
25
-25
PHASE ERROR /Degrees Fig. 13. r.m.s.
phase error distribution settings.
using optimum
: 2.029 degrees : 0.115 dB.
Fig.
15. r.m.s.
usmg lookup settings.
15
5
ERROR
phase error distribution settings.
tables
to model
25
/Degrees
using modelled
the optimum
control
4.3. Speed of implementation
The distribution of these gain and phase errors was as shown in Figs 15 and 16. By comparison of the r.m.s. errors and the error distributions shown above. it can be seen that by modelling the optimum settings in the way described, only a small increase in error is incurred. 4.2. Storugc
-5 PHASE
Using the modelled sc/ting.s, as shown in Figs I1 and 12. the r.m.s. phase and gain errors are: RMS Phase Error RMA Gain Error
-15
16384 samples
I
300
w”
Total of
I
600
r~~quiremunts
Sixty-four coefficients (C,, to c’,,. K,, to K,, and Off, to OK) must be stored for each of the four signal paths on each TR Module in order to implement the technique described. This requires 64 x 4 x 2 = 512. l6-bit words per TR module, assuming two words of storage per floating-point number. This storage requirement is relatively low compared with that required if. for example. a solution were implemented
Implementation speed of the described method will be significantly higher than that achievable using an iterative method, which must re-evaluate models on each iteration. Hence, replacing an iterative method which uses ten iterations to reach a solution with the single-shot method will reduce the time taken for a compensation by a factor of about IO. Exact speeds clearly depend on processor choice and program coding efficiency, but as a guide, it is expected that for ASAR the algorithm will compensate a single required gain/required phase input in approx. 375 ps.
5. CONCLUSIONS
Despite the variations of TR Module behaviour with temperature and from module to module, the
700
“““.
”
I”“).
”
Total of 600 -
16384 samples
t+ c 500 z 5
400
-
cl g
300 -
z UJ 200 -
loo-
too-
,:
0: -1.0
-0.5
0.0
0.5
-1.0
1.0
-0.5
GAIN ERROR /dB Fig. 14. r.m.s.
gain
error distribution settings.
0.0
1.. 0.5
1.0
GAIN ERROR /clB usmg
optimum
Fig.
16. r.m.s.
gain
error distribution settings.
using
modelled
535
Antenna temperature compensation technique described maintains a close correlation between required and achieved gains and phase shifts over all operating temperatures and for all TR Modules. The achieved antenna beam performance is consequently comparable with that of an antenna using TR Modules which are all stable with temperature and all identical in behaviour. Such ‘ideal’ TR Modules are not a practical option, but the technique described provides a practical alternative. The improvement in antenna performance has been achieved by making use of a priori knowledge of TR Module behaviour. Since the modelling of optimum control setting data incurs only a small degradation in error, the performance of the technique is close to optimal. The pre-processing of the measurement data to yield optimum control setting data permits a fast, single-shot solution algorithm to be utilised, whilst requiring only a relatively small amount of data to be stored. Thus, the potential responsiveness of the compensation process to rapid temperature change is also improved. The compensation method described has been ‘fine tuned’ for a specific application, but the principles used in the development of the technique are
potentially very valuable. The fundamental requirement to control imperfect devices with accuracy and speed in varying conditions is common to many engineering systems. The ability to exploit the apriori knowledge of device characteristics in the modelling process provides a powerful means by which to ‘squeeze’ the maximum amount of performance from the minimum of device complexity. Acknowledgements-This work has been carried out under contract to the European Space Agency (ESA). The author would like to thank colleagues in the Systems Group at Matra Marconi Space, and at Dornier and the European Space Technology Centre (ESTEC) for their support and encouragement. The author would also like to thank Alcatel Espace for providing the TR Module characterisation data.
APPENDIX Abbreciations
SAR ASAR
Synthetic Aperture Radar Advanced SAR (instrument)
TR TxV TxH RxV RxH
Transmit/Receive Transmit Vertical Transmit Horizontal Receive Vertical Receive Horizontal