Military Embedded Systems

Empirically Based Multichannel Phase Noise Model Validated in a 16-Channel Demonstrator

Whitepaper

March 14, 2023

Multichannel systems and compares it with measurements on a 16-channel S-band demonstrator.


This analytic approach is based on a small set of measurements that can be used to estimate correlated vs. uncorrelated noise contributions. Based on only a few measurements, phase noise under a wide range of conditions can be predicted. The view is that any specific design will need its own system noise analysis, with the 16-channel demonstrator providing a specific design example to use as a basis. Assumptions based on the 16-channel demonstrator are discussed along with limitations about when the assumptions apply and when to add additional noise terms as system complexity grows. The description provided builds on a body of work describing phase noise optimization in RF systems.1–6 Where appropriate, references describing the foundational principles used in this analysis are provided.

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      • select * from `categories` where `categories`.`id` in (1, 2, 3, 4, 6)
        1.19ms/app/Models/Article.php:375mes
        Metadata
        Backtrace
        • 24. /app/Models/Article.php:375
        • 25. view::theme::layouts.components.sidebar:8
        • 27. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 28. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 29. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `article_types` where `article_types`.`id` in (2, 3, 4, 5)
        1.95ms/app/Models/Article.php:375mes
        Metadata
        Backtrace
        • 19. /app/Models/Article.php:375
        • 20. view::theme::layouts.components.sidebar:8
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select `id`, `name`, `shortname` from `categories` where `parent_id` is null and `id` not in (999, 100) and exists (select * from `articles` where `categories`.`id` = `articles`.`primary_category` and `publish_at` < '2025-04-02 04:43:48' and `primary_image` is not null and (`primary_image` is not null and `primary_image` not in ('', '0')))
        41.97ms/app/View/Composers/SubfooterComposer.php:38mes
        Metadata
        Bindings
        • 0. 999
        • 1. 100
        • 2. 2025-04-02 04:43:48
        • 3. 
        • 4. 0
        Backtrace
        • 14. /app/View/Composers/SubfooterComposer.php:38
        • 15. /app/View/Composers/SubfooterComposer.php:19
        • 16. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 17. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 20. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `categories` where `categories`.`parent_id` in (1, 2, 3, 4, 5, 6) order by `shortname` asc
        1.6ms/app/View/Composers/SubfooterComposer.php:38mes
        Metadata
        Backtrace
        • 19. /app/View/Composers/SubfooterComposer.php:38
        • 20. /app/View/Composers/SubfooterComposer.php:19
        • 21. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 22. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 25. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `articles` where `primary_image` is not null and (`primary_image` is not null and `primary_image` not in ('', '0')) and `primary_category` in (1, 1000, 1003, 7, 1001, 9, 1002, 8) limit 5
        3.17ms/app/View/Composers/SubfooterComposer.php:63mes
        Metadata
        Bindings
        • 0. 
        • 1. 0
        • 2. 1
        • 3. 1000
        • 4. 1003
        • 5. 7
        • 6. 1001
        • 7. 9
        • 8. 1002
        • 9. 8
        Backtrace
        • 14. /app/View/Composers/SubfooterComposer.php:63
        • 15. /app/View/Composers/SubfooterComposer.php:19
        • 16. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 17. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 20. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `categories` where `categories`.`id` in (7, 8, 9, 1000)
        3.41ms/app/View/Composers/SubfooterComposer.php:63mes
        Metadata
        Backtrace
        • 19. /app/View/Composers/SubfooterComposer.php:63
        • 20. /app/View/Composers/SubfooterComposer.php:19
        • 21. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 22. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 25. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `categories` where `categories`.`id` in (1)
        1.98ms/app/View/Composers/SubfooterComposer.php:63mes
        Metadata
        Backtrace
        • 24. /app/View/Composers/SubfooterComposer.php:63
        • 25. /app/View/Composers/SubfooterComposer.php:19
        • 26. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 27. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 30. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `article_types` where `article_types`.`id` in (2)
        2.57ms/app/View/Composers/SubfooterComposer.php:63mes
        Metadata
        Backtrace
        • 19. /app/View/Composers/SubfooterComposer.php:63
        • 20. /app/View/Composers/SubfooterComposer.php:19
        • 21. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 22. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 25. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `articles` where `primary_image` is not null and (`primary_image` is not null and `primary_image` not in ('', '0')) and `primary_category` in (3, 1005, 23, 26, 25, 21, 20, 24, 22) limit 5
        3ms/app/View/Composers/SubfooterComposer.php:63mes
        Metadata
        Bindings
        • 0. 
        • 1. 0
        • 2. 3
        • 3. 1005
        • 4. 23
        • 5. 26
        • 6. 25
        • 7. 21
        • 8. 20
        • 9. 24
        • 10. 22
        Backtrace
        • 14. /app/View/Composers/SubfooterComposer.php:63
        • 15. /app/View/Composers/SubfooterComposer.php:19
        • 16. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 17. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 20. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `categories` where `categories`.`id` in (20, 23)
        1.3ms/app/View/Composers/SubfooterComposer.php:63mes
        Metadata
        Backtrace
        • 19. /app/View/Composers/SubfooterComposer.php:63
        • 20. /app/View/Composers/SubfooterComposer.php:19
        • 21. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 22. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 25. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `categories` where `categories`.`id` in (3)
        1.71ms/app/View/Composers/SubfooterComposer.php:63mes
        Metadata
        Backtrace
        • 24. /app/View/Composers/SubfooterComposer.php:63
        • 25. /app/View/Composers/SubfooterComposer.php:19
        • 26. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 27. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 30. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `article_types` where `article_types`.`id` in (2)
        2.14ms/app/View/Composers/SubfooterComposer.php:63mes
        Metadata
        Backtrace
        • 19. /app/View/Composers/SubfooterComposer.php:63
        • 20. /app/View/Composers/SubfooterComposer.php:19
        • 21. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 22. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 25. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `articles` where `primary_image` is not null and (`primary_image` is not null and `primary_image` not in ('', '0')) and `primary_category` in (4, 32, 31, 30, 29, 27) limit 5
        12.62ms/app/View/Composers/SubfooterComposer.php:63mes
        Metadata
        Bindings
        • 0. 
        • 1. 0
        • 2. 4
        • 3. 32
        • 4. 31
        • 5. 30
        • 6. 29
        • 7. 27
        Backtrace
        • 14. /app/View/Composers/SubfooterComposer.php:63
        • 15. /app/View/Composers/SubfooterComposer.php:19
        • 16. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 17. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 20. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `categories` where `categories`.`id` in (30, 32)
        1.27ms/app/View/Composers/SubfooterComposer.php:63mes
        Metadata
        Backtrace
        • 19. /app/View/Composers/SubfooterComposer.php:63
        • 20. /app/View/Composers/SubfooterComposer.php:19
        • 21. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 22. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 25. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `categories` where `categories`.`id` in (4)
        2.35ms/app/View/Composers/SubfooterComposer.php:63mes
        Metadata
        Backtrace
        • 24. /app/View/Composers/SubfooterComposer.php:63
        • 25. /app/View/Composers/SubfooterComposer.php:19
        • 26. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 27. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 30. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `article_types` where `article_types`.`id` in (2, 3)
        2.57ms/app/View/Composers/SubfooterComposer.php:63mes
        Metadata
        Backtrace
        • 19. /app/View/Composers/SubfooterComposer.php:63
        • 20. /app/View/Composers/SubfooterComposer.php:19
        • 21. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 22. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 25. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `articles` where `primary_image` is not null and (`primary_image` is not null and `primary_image` not in ('', '0')) and `primary_category` in (6, 45, 44, 46, 1008, 1006, 40, 43, 47, 39, 41, 42, 1007) limit 5
        2.88ms/app/View/Composers/SubfooterComposer.php:63mes
        Metadata
        Bindings
        • 0. 
        • 1. 0
        • 2. 6
        • 3. 45
        • 4. 44
        • 5. 46
        • 6. 1008
        • 7. 1006
        • 8. 40
        • 9. 43
        • 10. 47
        • 11. 39
        • 12. 41
        • 13. 42
        • 14. 1007
        Backtrace
        • 14. /app/View/Composers/SubfooterComposer.php:63
        • 15. /app/View/Composers/SubfooterComposer.php:19
        • 16. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 17. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 20. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `categories` where `categories`.`id` in (43, 44, 46)
        1.21ms/app/View/Composers/SubfooterComposer.php:63mes
        Metadata
        Backtrace
        • 19. /app/View/Composers/SubfooterComposer.php:63
        • 20. /app/View/Composers/SubfooterComposer.php:19
        • 21. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 22. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 25. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `categories` where `categories`.`id` in (6)
        1.95ms/app/View/Composers/SubfooterComposer.php:63mes
        Metadata
        Backtrace
        • 24. /app/View/Composers/SubfooterComposer.php:63
        • 25. /app/View/Composers/SubfooterComposer.php:19
        • 26. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 27. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 30. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `article_types` where `article_types`.`id` in (2)
        890μs/app/View/Composers/SubfooterComposer.php:63mes
        Metadata
        Backtrace
        • 19. /app/View/Composers/SubfooterComposer.php:63
        • 20. /app/View/Composers/SubfooterComposer.php:19
        • 21. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 22. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 25. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `categories` where `parent_id` is null and `id` not in (999, 100, 1061)
        1.59msview::theme::layouts.components.category_subfooter:6mes
        Metadata
        Bindings
        • 0. 999
        • 1. 100
        • 2. 1061
        Backtrace
        • 14. view::theme::layouts.components.category_subfooter:6
        • 16. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 17. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 19. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `categories` where `categories`.`id` = 1 limit 1
        850μs/app/Models/Category.php:142mes
        Metadata
        Bindings
        • 0. 1
        Backtrace
        • 19. /app/Models/Category.php:142
        • 20. view::theme::layouts.components.category_subfooter:18
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `categories` where `categories`.`parent_id` = 1 and `categories`.`parent_id` is not null order by `shortname` asc
        1.05ms/app/Models/Category.php:148mes
        Metadata
        Bindings
        • 0. 1
        Backtrace
        • 20. /app/Models/Category.php:148
        • 21. view::theme::layouts.components.category_subfooter:18
        • 23. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 25. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select `articles`.* from `articles` where `publish_at` < '2025-04-02 04:43:48' and `primary_image` is not null and `primary_image` != '0' and `primary_image` != '' and `article_type_id` <> '8' and (`primary_category` = 1 or `primary_category` = 1000 or `primary_category` = 1003 or `primary_category` = 7 or `primary_category` = 1001 or `primary_category` = 9 or `primary_category` = 1002 or `primary_category` = 8) and `article_type_id` <> '8' order by `publish_at` desc limit 5
        67.37msview::theme::layouts.components.category_subfooter:19mes
        Metadata
        Bindings
        • 0. 2025-04-02 04:43:48
        • 1. 0
        • 2. 
        • 3. 8
        • 4. 1
        • 5. 1000
        • 6. 1003
        • 7. 7
        • 8. 1001
        • 9. 9
        • 10. 1002
        • 11. 8
        • 12. 8
        Backtrace
        • 14. view::theme::layouts.components.category_subfooter:19
        • 16. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 17. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 19. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `categories` where `categories`.`id` in (7, 8, 1000, 1001)
        1.41msview::theme::layouts.components.category_subfooter:19mes
        Metadata
        Backtrace
        • 19. view::theme::layouts.components.category_subfooter:19
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 24. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `categories` where `categories`.`id` in (1)
        2.42msview::theme::layouts.components.category_subfooter:19mes
        Metadata
        Backtrace
        • 24. view::theme::layouts.components.category_subfooter:19
        • 26. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 27. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 28. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 29. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `article_types` where `article_types`.`id` in (3)
        1.57msview::theme::layouts.components.category_subfooter:19mes
        Metadata
        Backtrace
        • 19. view::theme::layouts.components.category_subfooter:19
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 24. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `categories` where `categories`.`id` = 3 limit 1
        2.74ms/app/Models/Category.php:142mes
        Metadata
        Bindings
        • 0. 3
        Backtrace
        • 19. /app/Models/Category.php:142
        • 20. view::theme::layouts.components.category_subfooter:18
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `categories` where `categories`.`parent_id` = 3 and `categories`.`parent_id` is not null order by `shortname` asc
        1.56ms/app/Models/Category.php:148mes
        Metadata
        Bindings
        • 0. 3
        Backtrace
        • 20. /app/Models/Category.php:148
        • 21. view::theme::layouts.components.category_subfooter:18
        • 23. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 25. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select `articles`.* from `articles` where `publish_at` < '2025-04-02 04:43:48' and `primary_image` is not null and `primary_image` != '0' and `primary_image` != '' and `article_type_id` <> '8' and (`primary_category` = 3 or `primary_category` = 1005 or `primary_category` = 23 or `primary_category` = 26 or `primary_category` = 25 or `primary_category` = 21 or `primary_category` = 20 or `primary_category` = 24 or `primary_category` = 22) and `article_type_id` <> '8' order by `publish_at` desc limit 5
        78.96msview::theme::layouts.components.category_subfooter:19mes
        Metadata
        Bindings
        • 0. 2025-04-02 04:43:48
        • 1. 0
        • 2. 
        • 3. 8
        • 4. 3
        • 5. 1005
        • 6. 23
        • 7. 26
        • 8. 25
        • 9. 21
        • 10. 20
        • 11. 24
        • 12. 22
        • 13. 8
        Backtrace
        • 14. view::theme::layouts.components.category_subfooter:19
        • 16. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 17. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 19. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `categories` where `categories`.`id` in (23, 25)
        2.14msview::theme::layouts.components.category_subfooter:19mes
        Metadata
        Backtrace
        • 19. view::theme::layouts.components.category_subfooter:19
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 24. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `categories` where `categories`.`id` in (3)
        990μsview::theme::layouts.components.category_subfooter:19mes
        Metadata
        Backtrace
        • 24. view::theme::layouts.components.category_subfooter:19
        • 26. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 27. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 28. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 29. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `article_types` where `article_types`.`id` in (3)
        960μsview::theme::layouts.components.category_subfooter:19mes
        Metadata
        Backtrace
        • 19. view::theme::layouts.components.category_subfooter:19
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 24. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `categories` where `categories`.`id` = 4 limit 1
        2.31ms/app/Models/Category.php:142mes
        Metadata
        Bindings
        • 0. 4
        Backtrace
        • 19. /app/Models/Category.php:142
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