Author: PuTI
How Frontier Firms are rebuilding the operating model for the age of AI
Spend time with any software engineering team right now and you’ll see something worth paying attention to. Over the last few years, the way software gets built has moved through four distinct patterns of human-agent collaboration — and the same patterns are beginning to show up across other functions of the firm.
- Author: You’re producing the work, calling on AI to help as needed — a line of code, a sentence, a chart.
- Editor: You set the intent and AI creates the first draft for you to edit and approve.
- Director: You create a spec and hand off entire tasks for AI to execute in the background.
- Orchestrator: You design a system where multiple agents run in parallel across a workflow, flagging exceptions and escalations to you.
Every business leader knows the world is changing, but far fewer have a clear picture of what to do about it. These four patterns are the place to start. The real work ahead for leaders is redesigning their firm’s operating model around the collaboration patterns.
As agent use increases, human involvement doesn’t disappear — it changes shape. What declines is the amount of tactical, step-by-step execution work humans do themselves. And what rises is the need for humans to set direction, define standards and evaluate outcomes.
Ultimately, the goal is not to move every task and business process to the fourth pattern. Instead, it’s up to leaders to help their organizations develop clarity around matching workstreams to the right collaboration pattern. That’s the shape of the Frontier Firm: defined by how deliberately leaders design work across functions, matching the level of human involvement to the outcome.
What the data shows
Our 2026 Work Trend Index research reinforces this shift across roles and industries. We analyzed trillions of anonymized Microsoft 365 productivity signals and surveyed 20,000 workers using AI across 10 countries. We also spoke with leading experts in AI, work and organizational psychology to help us unpack the insights from the data and understand where all this is going. The conclusion is consistent: the constraint is no longer what people can do, it is how work is structured around them.
- AI lifts individual potential. A privacy-preserving analysis of more than 100,000 chats in Microsoft 365 Copilot shows that 49% of all conversations support cognitive work — helping workers analyze information, solve problems, evaluate and think creatively. This shift is already visible in output, with 58% of AI users saying they’re producing work they couldn’t have a year ago, rising to 80% among Frontier Professionals, the most advanced AI users in our research. Additionally, when AI users were asked which human skills are most important as AI takes on more work, they said two topped the list: quality control of AI output (50%) and critical thinking — that is, analyzing information objectively and making a reasoned judgment (46%).
- The Transformation Paradox. We are seeing a pressure point emerge within the organization where the pull to perform collides with the push to transform. 65% of AI users surveyed fear falling behind if they don’t use AI to adapt quickly, yet 45% say it feels safer to focus on current goals than to redesign work with AI. And only 13% of workers say they’re rewarded for reinvention of work with AI even if results aren’t met. The same forces accelerating AI adoption are holding it back.
- Every organization is a learning system. Our results show that organizational factors like culture, manager support and talent practices account for more than 2X the AI impact of individual factors like mindset and behavior (67% vs. 32%). Specifically, the findings underscore the importance of an AI-ready environment: a culture that treats AI as a strategic advantage and encourages experimentation, managers who model and incentivize AI use and talent practices that build skills and create space to apply them. The real question isn’t whether people have the right skills, it’s whether the organization is built to unlock them.
The firms that build a new operating model today won’t just move faster in the short term. They’ll build something more durable, setting themselves up to create value in ways that we can’t yet conceive of: an organization that learns faster than its competitors, compounds its own intelligence and gets harder to catch with every cycle.
For deeper analysis, see the 2026 Work Trend Index Report.
Enabling the Frontier Firm with Copilot Cowork — now mobile, extensible and enterprise-ready
None of an organization’s system scales without infrastructure that brings people and agents into the same flow of work with connected data and the ability to manage and govern it all. Microsoft 365 Copilot is built for exactly that.
Today, we’re expanding Copilot Cowork with new capabilities for Frontier customers to help organizations move from isolated AI tasks to coordinated, multistep work. Cowork enables people to define outcomes and delegate work across apps, business systems and data, with execution that stays directed and controlled throughout.
This update introduces Copilot Cowork Mobile for iOS and Android, along with a growing plugin ecosystem for Cowork, bringing more of an organization’s tools and data into these experiences. This includes native plugins across Microsoft services like Dynamics 365 and Fabric, and partner integrations available in the coming weeks like LSEG (London Stock Exchange Group), Miro, monday.com, S&P Global Energy and more. Organizations can also build custom plugins to turn their own workflows and expertise into reusable, scalable processes. Additionally, a first wave of federated Copilot connectors in Researcher and Microsoft 365 Copilot Chat is generally available today from partners like HubSpot, LSEG (London Stock Exchange Group), Moody’s, Notion and more.
Together, these updates extend Copilot Cowork from a task-based assistant into an extensible platform that helps orchestrate work across Microsoft and third-party systems. With management and governance through Microsoft Agent 365, organizations can deploy and scale agents across core business functions like sales, service and operations.
For more on these product innovations: Microsoft 365 blog.
AI is no longer an experiment. It is an execution challenge. Employees are already working across all four patterns. The open question for every leadership team is whether they can catch up. Access to AI won’t be the advantage for much longer. How the work is designed around it will be.
Jared Spataro, CMO, AI at Work at Microsoft, shapes how every organization applies AI and agents to reduce costs, create new value and define the future of work. He leads research, strategy and product across Copilot, Copilot Studio, Microsoft 365, Dynamics 365 and Power Platform.
The post How Frontier Firms are rebuilding the operating model for the age of AI appeared first on The Official Microsoft Blog.
Spend time with any software engineering team right now and you’ll see something worth paying attention to. Over the last few years, the way software gets built has moved through four distinct patterns of human-agent collaboration — and the same patterns are beginning to show up across other functions of the firm. Author: You’re producing…
The post How Frontier Firms are rebuilding the operating model for the age of AI appeared first on The Official Microsoft Blog.
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how to find optimum solution to the variable
i want to know the step for find the optimum value of t1,T by using this algorithmi want to know the step for find the optimum value of t1,T by using this algorithm i want to know the step for find the optimum value of t1,T by using this algorithm optimum, optimal, total cost MATLAB Answers — New Questions
No fullscreen of test sequence and assessment in 2025a
Hello,
actually we switched from 2022b to 2025a a couple of month ago and when I want to make a test harness with a test sequence and a test assessment, it is not possible to increase the window size to full screen on a large monitor. In 2022b it worked. What can I do?Hello,
actually we switched from 2022b to 2025a a couple of month ago and when I want to make a test harness with a test sequence and a test assessment, it is not possible to increase the window size to full screen on a large monitor. In 2022b it worked. What can I do? Hello,
actually we switched from 2022b to 2025a a couple of month ago and when I want to make a test harness with a test sequence and a test assessment, it is not possible to increase the window size to full screen on a large monitor. In 2022b it worked. What can I do? simulink, test sequence, test assessment MATLAB Answers — New Questions
2-d lookup table block codegeneration
my 2d lookup table is set as so.
the generated code from this block is as below.
Even though the input parameter is 8X6 array which should be defined as [0][0],
the generated code defines the input as a 1-dimension array [0].
This results in polyspace defect category "Unreliable cast of pointer"
Is there a way to match the generated code to the parameter’s actual size?my 2d lookup table is set as so.
the generated code from this block is as below.
Even though the input parameter is 8X6 array which should be defined as [0][0],
the generated code defines the input as a 1-dimension array [0].
This results in polyspace defect category "Unreliable cast of pointer"
Is there a way to match the generated code to the parameter’s actual size? my 2d lookup table is set as so.
the generated code from this block is as below.
Even though the input parameter is 8X6 array which should be defined as [0][0],
the generated code defines the input as a 1-dimension array [0].
This results in polyspace defect category "Unreliable cast of pointer"
Is there a way to match the generated code to the parameter’s actual size? code generation MATLAB Answers — New Questions
GPS HDL Reference Applications Overview Not Working
I am working with the GPS HDL reference example from MathWorks:
GPS HDL Reference Applications Overview – MATLAB & Simulink
I am implementing this design on ZCU48DR hardware with the following configuration:
RFDC configured for 4 samples per stream and 5× decimation
Input sample rate: 3922.168 MSPS
After additional decimation, the signal enters the acquisition and tracking IP GPS HDL Acquisition and Tracking Using C/A Code – MATLAB & Simulink at 32.768 MHz
The clock provided to the IP is 196.608 MHz
GPS HDL Acquisition and Tracking Using C/A Code – MATLAB & Simulink, and GPS HDL Data Decode and Position Estimation – MATLAB & Simulink are integrated into a single IP, similar to the reference design
I have also verified the 1 kHz navigation data rate on hardware
Issue:
The acquisition stage works correctly (satellites are detected and tracking is stable)
However, in the decoding stage, frame synchronization fails
This suggests that the LNAV data is not valid
To further debug, I generated an 8-second LNAV signal from the acquisition and tracking HDL model in simulation, but the decoder still fails to decode that LNAV signal.
Questions:
Has this GPS HDL reference example been validated on hardware (particularly ZCU48DR or RFSoC platforms)?
What could cause frame synchronization failure even when acquisition and tracking appear correct?
Could there be an issue with bit alignment, timing, or scaling between tracking output and decoder input?
Is there any recommended method to verify LNAV integrity before decoding?
Any guidance on where to debug this issue would be greatly appreciated.I am working with the GPS HDL reference example from MathWorks:
GPS HDL Reference Applications Overview – MATLAB & Simulink
I am implementing this design on ZCU48DR hardware with the following configuration:
RFDC configured for 4 samples per stream and 5× decimation
Input sample rate: 3922.168 MSPS
After additional decimation, the signal enters the acquisition and tracking IP GPS HDL Acquisition and Tracking Using C/A Code – MATLAB & Simulink at 32.768 MHz
The clock provided to the IP is 196.608 MHz
GPS HDL Acquisition and Tracking Using C/A Code – MATLAB & Simulink, and GPS HDL Data Decode and Position Estimation – MATLAB & Simulink are integrated into a single IP, similar to the reference design
I have also verified the 1 kHz navigation data rate on hardware
Issue:
The acquisition stage works correctly (satellites are detected and tracking is stable)
However, in the decoding stage, frame synchronization fails
This suggests that the LNAV data is not valid
To further debug, I generated an 8-second LNAV signal from the acquisition and tracking HDL model in simulation, but the decoder still fails to decode that LNAV signal.
Questions:
Has this GPS HDL reference example been validated on hardware (particularly ZCU48DR or RFSoC platforms)?
What could cause frame synchronization failure even when acquisition and tracking appear correct?
Could there be an issue with bit alignment, timing, or scaling between tracking output and decoder input?
Is there any recommended method to verify LNAV integrity before decoding?
Any guidance on where to debug this issue would be greatly appreciated. I am working with the GPS HDL reference example from MathWorks:
GPS HDL Reference Applications Overview – MATLAB & Simulink
I am implementing this design on ZCU48DR hardware with the following configuration:
RFDC configured for 4 samples per stream and 5× decimation
Input sample rate: 3922.168 MSPS
After additional decimation, the signal enters the acquisition and tracking IP GPS HDL Acquisition and Tracking Using C/A Code – MATLAB & Simulink at 32.768 MHz
The clock provided to the IP is 196.608 MHz
GPS HDL Acquisition and Tracking Using C/A Code – MATLAB & Simulink, and GPS HDL Data Decode and Position Estimation – MATLAB & Simulink are integrated into a single IP, similar to the reference design
I have also verified the 1 kHz navigation data rate on hardware
Issue:
The acquisition stage works correctly (satellites are detected and tracking is stable)
However, in the decoding stage, frame synchronization fails
This suggests that the LNAV data is not valid
To further debug, I generated an 8-second LNAV signal from the acquisition and tracking HDL model in simulation, but the decoder still fails to decode that LNAV signal.
Questions:
Has this GPS HDL reference example been validated on hardware (particularly ZCU48DR or RFSoC platforms)?
What could cause frame synchronization failure even when acquisition and tracking appear correct?
Could there be an issue with bit alignment, timing, or scaling between tracking output and decoder input?
Is there any recommended method to verify LNAV integrity before decoding?
Any guidance on where to debug this issue would be greatly appreciated. rfsoc, simulink, matlab function, hdl coder, navigation toolbox, satellite communication toolbox, fpga, hdl, c/a code, gps, gnss, vivado MATLAB Answers — New Questions
How to debug test discovery error
In the MATLAB Test Browser, when an error occurs during test discovery (for example while creating test parameters or peforming test class setup), I don’t know how to effectively debug the error or reproduce it in a controlled environment. It just gives me the message and no context, no location or stack info. Adding a breakpoint in the setup code does not help. It does not pause there.
How can I get more information on the error that occurs during test discovery?
This is really frustrating to debug at the moment.In the MATLAB Test Browser, when an error occurs during test discovery (for example while creating test parameters or peforming test class setup), I don’t know how to effectively debug the error or reproduce it in a controlled environment. It just gives me the message and no context, no location or stack info. Adding a breakpoint in the setup code does not help. It does not pause there.
How can I get more information on the error that occurs during test discovery?
This is really frustrating to debug at the moment. In the MATLAB Test Browser, when an error occurs during test discovery (for example while creating test parameters or peforming test class setup), I don’t know how to effectively debug the error or reproduce it in a controlled environment. It just gives me the message and no context, no location or stack info. Adding a breakpoint in the setup code does not help. It does not pause there.
How can I get more information on the error that occurs during test discovery?
This is really frustrating to debug at the moment. test discovery, unittest, test browser MATLAB Answers — New Questions
How to read and write AXI4/AXI4-Lite registers from code generated by Embedded Coder R2025b on a bare-metal MicroBlaze processor?
I have a Simulink model where one part is implemented with Embedded Coder on a bare-metal MicroBlaze soft processor, and another part is implemented with HDL Coder as an IP core that exposes AXI4/AXI4-Lite memory-mapped registers.
How can I read and write those registers from the C code generated by Embedded Coder running on the MicroBlaze?I have a Simulink model where one part is implemented with Embedded Coder on a bare-metal MicroBlaze soft processor, and another part is implemented with HDL Coder as an IP core that exposes AXI4/AXI4-Lite memory-mapped registers.
How can I read and write those registers from the C code generated by Embedded Coder running on the MicroBlaze? I have a Simulink model where one part is implemented with Embedded Coder on a bare-metal MicroBlaze soft processor, and another part is implemented with HDL Coder as an IP core that exposes AXI4/AXI4-Lite memory-mapped registers.
How can I read and write those registers from the C code generated by Embedded Coder running on the MicroBlaze? microblaze, axi4, axi4-lite, bare-metal, memorymappedregisters, devicedriverblocks, tcpclient MATLAB Answers — New Questions
Why is my 2-D array data flattened in code generation from my Simulink model using Embedded Coder but not when I use a Stateflow chart?
I am generating code for my model. When generating code normally, my 2-D array or matrix is flattened as shown below:
var1 = ((&my2DArray[0][0]))[4];
However, when my signals, which are handling the 2-D matrix data, are passed through a Stateflow chart in my model first, the data is represented as a 2-D array even in my generated C-code, as shown below:
var1 = my2DArray[1][2];
Why is my code generated with single indexing for matrices and 2-D arrays, but not when using a Stateflow?I am generating code for my model. When generating code normally, my 2-D array or matrix is flattened as shown below:
var1 = ((&my2DArray[0][0]))[4];
However, when my signals, which are handling the 2-D matrix data, are passed through a Stateflow chart in my model first, the data is represented as a 2-D array even in my generated C-code, as shown below:
var1 = my2DArray[1][2];
Why is my code generated with single indexing for matrices and 2-D arrays, but not when using a Stateflow? I am generating code for my model. When generating code normally, my 2-D array or matrix is flattened as shown below:
var1 = ((&my2DArray[0][0]))[4];
However, when my signals, which are handling the 2-D matrix data, are passed through a Stateflow chart in my model first, the data is represented as a 2-D array even in my generated C-code, as shown below:
var1 = my2DArray[1][2];
Why is my code generated with single indexing for matrices and 2-D arrays, but not when using a Stateflow? flatten, 2d-array, stateflow MATLAB Answers — New Questions
How to unload packages from an Embedded Coder Dictionary in MATLAB R2025b?
I am using Embedded Coder in MATLAB R2025b and unloaded a package from the "Memory Section" tab of the Embedded Coder Dictionary, but it still appears in the "Memory Sections" list.
How can I make sure the package is properly unloaded and removed from the "Memory Sections" list?I am using Embedded Coder in MATLAB R2025b and unloaded a package from the "Memory Section" tab of the Embedded Coder Dictionary, but it still appears in the "Memory Sections" list.
How can I make sure the package is properly unloaded and removed from the "Memory Sections" list? I am using Embedded Coder in MATLAB R2025b and unloaded a package from the "Memory Section" tab of the Embedded Coder Dictionary, but it still appears in the "Memory Sections" list.
How can I make sure the package is properly unloaded and removed from the "Memory Sections" list? embeddedcoderdictionary, unloadpackage, memorysections MATLAB Answers — New Questions
integrate the LTSpice circuit model in MatLab
It´s possible to integrate the LTSpice circuit model in MatLab.
Can LTSpice communicate with Matlab in a simple way, for example with a function in Matlab that writes a text file and LTSPICE executes, and then Matlab reads back the results generated from LTSpice?
Has Matlab a toolbox that can execute SPICE commands directly?It´s possible to integrate the LTSpice circuit model in MatLab.
Can LTSpice communicate with Matlab in a simple way, for example with a function in Matlab that writes a text file and LTSPICE executes, and then Matlab reads back the results generated from LTSpice?
Has Matlab a toolbox that can execute SPICE commands directly? It´s possible to integrate the LTSpice circuit model in MatLab.
Can LTSpice communicate with Matlab in a simple way, for example with a function in Matlab that writes a text file and LTSPICE executes, and then Matlab reads back the results generated from LTSpice?
Has Matlab a toolbox that can execute SPICE commands directly? 10 MATLAB Answers — New Questions
Matlab variable viewer does not update structure variables
I have been saving data in structures and with my version of Matlab (2025B) it does not seem to update these variables in the viewer. I am currently developing some scripts, so I am essentially just running all the code from the command line. I don’t think the code is important; it allocates matrices in a structure based on the data it reads in, and then calculates what the values are. Some psuedo code is below:
NewData=’DataSet_X’;
Data.(NewData).Value=zeros(size(X,1),2);
for I=1:length(X)
[Data.(NewData).Value(I,1),Data.(NewData).Value(I,2)] = ValueCalcFunction(Dataset X, Ith row)
end
Anyway, if I have Data open in the Variables window It shows the Value field as a matrix full of zeros even after it has been updated. If I double click the field and open just it in the variable window, it shows that it has been updated with the correct values. It would be nice to see it in the structure variable… Here is a screen capture that demonstrates what I mean:
Any ideas how can I force a refresh of the variable viewer?
I have a similar problem with the workspace not updating, but I found I can update it by pressing F5 or chosing Refresh from the menu. These options are not available in the variable viewer.
Thanks!I have been saving data in structures and with my version of Matlab (2025B) it does not seem to update these variables in the viewer. I am currently developing some scripts, so I am essentially just running all the code from the command line. I don’t think the code is important; it allocates matrices in a structure based on the data it reads in, and then calculates what the values are. Some psuedo code is below:
NewData=’DataSet_X’;
Data.(NewData).Value=zeros(size(X,1),2);
for I=1:length(X)
[Data.(NewData).Value(I,1),Data.(NewData).Value(I,2)] = ValueCalcFunction(Dataset X, Ith row)
end
Anyway, if I have Data open in the Variables window It shows the Value field as a matrix full of zeros even after it has been updated. If I double click the field and open just it in the variable window, it shows that it has been updated with the correct values. It would be nice to see it in the structure variable… Here is a screen capture that demonstrates what I mean:
Any ideas how can I force a refresh of the variable viewer?
I have a similar problem with the workspace not updating, but I found I can update it by pressing F5 or chosing Refresh from the menu. These options are not available in the variable viewer.
Thanks! I have been saving data in structures and with my version of Matlab (2025B) it does not seem to update these variables in the viewer. I am currently developing some scripts, so I am essentially just running all the code from the command line. I don’t think the code is important; it allocates matrices in a structure based on the data it reads in, and then calculates what the values are. Some psuedo code is below:
NewData=’DataSet_X’;
Data.(NewData).Value=zeros(size(X,1),2);
for I=1:length(X)
[Data.(NewData).Value(I,1),Data.(NewData).Value(I,2)] = ValueCalcFunction(Dataset X, Ith row)
end
Anyway, if I have Data open in the Variables window It shows the Value field as a matrix full of zeros even after it has been updated. If I double click the field and open just it in the variable window, it shows that it has been updated with the correct values. It would be nice to see it in the structure variable… Here is a screen capture that demonstrates what I mean:
Any ideas how can I force a refresh of the variable viewer?
I have a similar problem with the workspace not updating, but I found I can update it by pressing F5 or chosing Refresh from the menu. These options are not available in the variable viewer.
Thanks! variable viewer MATLAB Answers — New Questions
installation error: An attempt to create a new profile for an email address already in use was detected.
I have applied for a trial version and downloaded the installer. During installation, after I input user name and password, the installer showed the "confirm user" page, and then I clicked next step, and then the installer showed an error page: An attempt to create a new profile for an email address already in use was detected. Please help to solve this issue.
Thank you
RickI have applied for a trial version and downloaded the installer. During installation, after I input user name and password, the installer showed the "confirm user" page, and then I clicked next step, and then the installer showed an error page: An attempt to create a new profile for an email address already in use was detected. Please help to solve this issue.
Thank you
Rick I have applied for a trial version and downloaded the installer. During installation, after I input user name and password, the installer showed the "confirm user" page, and then I clicked next step, and then the installer showed an error page: An attempt to create a new profile for an email address already in use was detected. Please help to solve this issue.
Thank you
Rick installation error MATLAB Answers — New Questions
email address aleady in use
when installing the Free trial student version of matlab 2026 i get this error "An attempt to create a new profile for an email address already in use was detected." even though i am not creating a new account , i am using my account that i am signed in on matlab site to download the license how do i fix that problemwhen installing the Free trial student version of matlab 2026 i get this error "An attempt to create a new profile for an email address already in use was detected." even though i am not creating a new account , i am using my account that i am signed in on matlab site to download the license how do i fix that problem when installing the Free trial student version of matlab 2026 i get this error "An attempt to create a new profile for an email address already in use was detected." even though i am not creating a new account , i am using my account that i am signed in on matlab site to download the license how do i fix that problem matlab MATLAB Answers — New Questions
Doubt in solving nested integral
I have a query regarding MATLAB code to plot SOP using analytical expression given by :
where
begin{equation}
begin{aligned}
Theta(u,y,v)
&= frac{1}{A_k(u,y,v)}
exp!left(
frac{lambda_Y lambda_Z}{alpha A_k(u,y,v)}
– A_k(u,y,v)frac{1}{bar{gamma}} right. \
&quad left.
– lambda_U u – lambda_V v
right)
E_1!left(
frac{lambda_Y lambda_Z}{alpha A_k(u,y,v)}
right).
end{aligned}
end{equation}
Here is what i tried for code of SOP (analytical):
% This code is for analytical expression of SOP of user k
clc; clear all; close all;
%% Parameters
lambda_X = 1; % rate parameter of the exponential distribution
lambda_Y = 1;
lambda_Z = 1;
lambda_U = 1;
lambda_V = 1;
alpha = 0.1;
k = 1;
a1 = 0.1;
a2= 0.3;
a3 = 0.6;
a = [a1 a2 a3];
R1 = 0.1; % nearest
R2 = 0.2; % middle
R3 = 0.3; % farthest
R = [R1 R2 R3];
beta = 0.8;
t1 = 1*1e5; % samples
t2 = 1e4;
D = (1 – beta) + beta * sum(a(1:k-1));
SOP_ana = [];
for snr_user_dB = 0:5:80
snr_user = 10^(snr_user_dB/10);
snr_eve_dB = 0; % in dB
snr_eve = 10^(snr_eve_dB/10);
accum = 0;
for iter = 1:t1
% Generate all RVs together
y = exprnd(1/lambda_Y);
u = exprnd(1/lambda_U);
v = exprnd(1/lambda_V);
% Gamma_e
Gamma_e = (beta * a(k) * u) / …
(u*D + alpha*y*v + (1/snr_eve));
% t(u,y,v)
t_val = (2^R(k))*(1 + Gamma_e) – 1;
% A_k
if beta*a(k) – t_val*D <= 0
continue;
end
A_k = (lambda_X * t_val) / (beta*a(k) – t_val*D);
% Theta
arg = (lambda_Y * lambda_Z)/(alpha*A_k);
Theta = (1/A_k) * …
exp(arg – A_k*(1/snr_user) …
– lambda_U*u – lambda_V*v) …
* expint(arg);
accum = accum + Theta;
end
SOP = 1 – (lambda_U * lambda_V * lambda_Y * lambda_Z / alpha) …
* (accum / t1);
SOP_ana = [SOP_ana SOP];
end
snr_axis = 0:5:80;
figure;
%semilogy(snr_axis, SOP_ana, ‘r-o’,’LineWidth’,1.5);
plot(snr_axis, SOP_ana, ‘r-o’,’LineWidth’,1.5);
grid on;
xlabel(‘SNR (dB)’);
ylabel(‘SOP’);
title(‘SOP vs SNR’);
The output of above code should match the simulation of SOP whose code is given by
% This code is for simulation expression of SOP of user k
%clc; clear all; close all;
%% Parameters
lambda_X = 1; % rate parameter of the exponential distribution
lambda_Y = 1;
lambda_Z = 1;
lambda_U = 1;
lambda_V = 1;
alpha = 0.1;
k = 1;
a1 = 0.1;
a2= 0.3;
a3 = 0.6;
a = [a1 a2 a3];
R1 = 0.1; % nearest
R2 = 0.2; % middle
R3 = 0.3; % farthest
R = [R1 R2 R3];
beta = 0.8;
t1 = 10*1e4; % samples
D = (1 – beta) + beta * sum(a(1:k-1));
SOP_sim = []; count = 0;
for snr_user_dB = 0:5:80
snr_user = 10^(snr_user_dB/10);
snr_eve_dB = 0; % in dB
snr_eve = 10^(snr_eve_dB/10);
for iter = 1:t1
X = exprnd(1/lambda_X); % mean is 1/lambda
Y = exprnd(1/lambda_Y);
Z = exprnd(1/lambda_Z);
U = exprnd(1/lambda_U);
V = exprnd(1/lambda_V);
Gamma_k = (beta * a(k) * X) / …
( X * D + alpha * Y * Z + (1/snr_user));
Gamma_e = (beta * a(k) * U) / …
( U * D + alpha * Y * V + (1/snr_eve));
if Gamma_k < ((2^R(k))*(1+Gamma_e)-1)
%if Gamma_k < (2^R(k)-1)
count = count + 1;
end
end
SOP = count / t1;
SOP_sim = [SOP_sim SOP];
count = 0;
end
snr_axis = 0:5:80;
figure;
%semilogy(snr_axis, SOP_sim, ‘r-o’,’LineWidth’,1.5);
plot(snr_axis, SOP_sim, ‘r-o’,’LineWidth’,1.5);
grid on;
xlabel(‘SNR (dB)’);
ylabel(‘SOP’);
title(‘SOP vs SNR’);
I am not getting what wrong i am doing in analytical SOP code…
Any help in this regard is highly appreciatedI have a query regarding MATLAB code to plot SOP using analytical expression given by :
where
begin{equation}
begin{aligned}
Theta(u,y,v)
&= frac{1}{A_k(u,y,v)}
exp!left(
frac{lambda_Y lambda_Z}{alpha A_k(u,y,v)}
– A_k(u,y,v)frac{1}{bar{gamma}} right. \
&quad left.
– lambda_U u – lambda_V v
right)
E_1!left(
frac{lambda_Y lambda_Z}{alpha A_k(u,y,v)}
right).
end{aligned}
end{equation}
Here is what i tried for code of SOP (analytical):
% This code is for analytical expression of SOP of user k
clc; clear all; close all;
%% Parameters
lambda_X = 1; % rate parameter of the exponential distribution
lambda_Y = 1;
lambda_Z = 1;
lambda_U = 1;
lambda_V = 1;
alpha = 0.1;
k = 1;
a1 = 0.1;
a2= 0.3;
a3 = 0.6;
a = [a1 a2 a3];
R1 = 0.1; % nearest
R2 = 0.2; % middle
R3 = 0.3; % farthest
R = [R1 R2 R3];
beta = 0.8;
t1 = 1*1e5; % samples
t2 = 1e4;
D = (1 – beta) + beta * sum(a(1:k-1));
SOP_ana = [];
for snr_user_dB = 0:5:80
snr_user = 10^(snr_user_dB/10);
snr_eve_dB = 0; % in dB
snr_eve = 10^(snr_eve_dB/10);
accum = 0;
for iter = 1:t1
% Generate all RVs together
y = exprnd(1/lambda_Y);
u = exprnd(1/lambda_U);
v = exprnd(1/lambda_V);
% Gamma_e
Gamma_e = (beta * a(k) * u) / …
(u*D + alpha*y*v + (1/snr_eve));
% t(u,y,v)
t_val = (2^R(k))*(1 + Gamma_e) – 1;
% A_k
if beta*a(k) – t_val*D <= 0
continue;
end
A_k = (lambda_X * t_val) / (beta*a(k) – t_val*D);
% Theta
arg = (lambda_Y * lambda_Z)/(alpha*A_k);
Theta = (1/A_k) * …
exp(arg – A_k*(1/snr_user) …
– lambda_U*u – lambda_V*v) …
* expint(arg);
accum = accum + Theta;
end
SOP = 1 – (lambda_U * lambda_V * lambda_Y * lambda_Z / alpha) …
* (accum / t1);
SOP_ana = [SOP_ana SOP];
end
snr_axis = 0:5:80;
figure;
%semilogy(snr_axis, SOP_ana, ‘r-o’,’LineWidth’,1.5);
plot(snr_axis, SOP_ana, ‘r-o’,’LineWidth’,1.5);
grid on;
xlabel(‘SNR (dB)’);
ylabel(‘SOP’);
title(‘SOP vs SNR’);
The output of above code should match the simulation of SOP whose code is given by
% This code is for simulation expression of SOP of user k
%clc; clear all; close all;
%% Parameters
lambda_X = 1; % rate parameter of the exponential distribution
lambda_Y = 1;
lambda_Z = 1;
lambda_U = 1;
lambda_V = 1;
alpha = 0.1;
k = 1;
a1 = 0.1;
a2= 0.3;
a3 = 0.6;
a = [a1 a2 a3];
R1 = 0.1; % nearest
R2 = 0.2; % middle
R3 = 0.3; % farthest
R = [R1 R2 R3];
beta = 0.8;
t1 = 10*1e4; % samples
D = (1 – beta) + beta * sum(a(1:k-1));
SOP_sim = []; count = 0;
for snr_user_dB = 0:5:80
snr_user = 10^(snr_user_dB/10);
snr_eve_dB = 0; % in dB
snr_eve = 10^(snr_eve_dB/10);
for iter = 1:t1
X = exprnd(1/lambda_X); % mean is 1/lambda
Y = exprnd(1/lambda_Y);
Z = exprnd(1/lambda_Z);
U = exprnd(1/lambda_U);
V = exprnd(1/lambda_V);
Gamma_k = (beta * a(k) * X) / …
( X * D + alpha * Y * Z + (1/snr_user));
Gamma_e = (beta * a(k) * U) / …
( U * D + alpha * Y * V + (1/snr_eve));
if Gamma_k < ((2^R(k))*(1+Gamma_e)-1)
%if Gamma_k < (2^R(k)-1)
count = count + 1;
end
end
SOP = count / t1;
SOP_sim = [SOP_sim SOP];
count = 0;
end
snr_axis = 0:5:80;
figure;
%semilogy(snr_axis, SOP_sim, ‘r-o’,’LineWidth’,1.5);
plot(snr_axis, SOP_sim, ‘r-o’,’LineWidth’,1.5);
grid on;
xlabel(‘SNR (dB)’);
ylabel(‘SOP’);
title(‘SOP vs SNR’);
I am not getting what wrong i am doing in analytical SOP code…
Any help in this regard is highly appreciated I have a query regarding MATLAB code to plot SOP using analytical expression given by :
where
begin{equation}
begin{aligned}
Theta(u,y,v)
&= frac{1}{A_k(u,y,v)}
exp!left(
frac{lambda_Y lambda_Z}{alpha A_k(u,y,v)}
– A_k(u,y,v)frac{1}{bar{gamma}} right. \
&quad left.
– lambda_U u – lambda_V v
right)
E_1!left(
frac{lambda_Y lambda_Z}{alpha A_k(u,y,v)}
right).
end{aligned}
end{equation}
Here is what i tried for code of SOP (analytical):
% This code is for analytical expression of SOP of user k
clc; clear all; close all;
%% Parameters
lambda_X = 1; % rate parameter of the exponential distribution
lambda_Y = 1;
lambda_Z = 1;
lambda_U = 1;
lambda_V = 1;
alpha = 0.1;
k = 1;
a1 = 0.1;
a2= 0.3;
a3 = 0.6;
a = [a1 a2 a3];
R1 = 0.1; % nearest
R2 = 0.2; % middle
R3 = 0.3; % farthest
R = [R1 R2 R3];
beta = 0.8;
t1 = 1*1e5; % samples
t2 = 1e4;
D = (1 – beta) + beta * sum(a(1:k-1));
SOP_ana = [];
for snr_user_dB = 0:5:80
snr_user = 10^(snr_user_dB/10);
snr_eve_dB = 0; % in dB
snr_eve = 10^(snr_eve_dB/10);
accum = 0;
for iter = 1:t1
% Generate all RVs together
y = exprnd(1/lambda_Y);
u = exprnd(1/lambda_U);
v = exprnd(1/lambda_V);
% Gamma_e
Gamma_e = (beta * a(k) * u) / …
(u*D + alpha*y*v + (1/snr_eve));
% t(u,y,v)
t_val = (2^R(k))*(1 + Gamma_e) – 1;
% A_k
if beta*a(k) – t_val*D <= 0
continue;
end
A_k = (lambda_X * t_val) / (beta*a(k) – t_val*D);
% Theta
arg = (lambda_Y * lambda_Z)/(alpha*A_k);
Theta = (1/A_k) * …
exp(arg – A_k*(1/snr_user) …
– lambda_U*u – lambda_V*v) …
* expint(arg);
accum = accum + Theta;
end
SOP = 1 – (lambda_U * lambda_V * lambda_Y * lambda_Z / alpha) …
* (accum / t1);
SOP_ana = [SOP_ana SOP];
end
snr_axis = 0:5:80;
figure;
%semilogy(snr_axis, SOP_ana, ‘r-o’,’LineWidth’,1.5);
plot(snr_axis, SOP_ana, ‘r-o’,’LineWidth’,1.5);
grid on;
xlabel(‘SNR (dB)’);
ylabel(‘SOP’);
title(‘SOP vs SNR’);
The output of above code should match the simulation of SOP whose code is given by
% This code is for simulation expression of SOP of user k
%clc; clear all; close all;
%% Parameters
lambda_X = 1; % rate parameter of the exponential distribution
lambda_Y = 1;
lambda_Z = 1;
lambda_U = 1;
lambda_V = 1;
alpha = 0.1;
k = 1;
a1 = 0.1;
a2= 0.3;
a3 = 0.6;
a = [a1 a2 a3];
R1 = 0.1; % nearest
R2 = 0.2; % middle
R3 = 0.3; % farthest
R = [R1 R2 R3];
beta = 0.8;
t1 = 10*1e4; % samples
D = (1 – beta) + beta * sum(a(1:k-1));
SOP_sim = []; count = 0;
for snr_user_dB = 0:5:80
snr_user = 10^(snr_user_dB/10);
snr_eve_dB = 0; % in dB
snr_eve = 10^(snr_eve_dB/10);
for iter = 1:t1
X = exprnd(1/lambda_X); % mean is 1/lambda
Y = exprnd(1/lambda_Y);
Z = exprnd(1/lambda_Z);
U = exprnd(1/lambda_U);
V = exprnd(1/lambda_V);
Gamma_k = (beta * a(k) * X) / …
( X * D + alpha * Y * Z + (1/snr_user));
Gamma_e = (beta * a(k) * U) / …
( U * D + alpha * Y * V + (1/snr_eve));
if Gamma_k < ((2^R(k))*(1+Gamma_e)-1)
%if Gamma_k < (2^R(k)-1)
count = count + 1;
end
end
SOP = count / t1;
SOP_sim = [SOP_sim SOP];
count = 0;
end
snr_axis = 0:5:80;
figure;
%semilogy(snr_axis, SOP_sim, ‘r-o’,’LineWidth’,1.5);
plot(snr_axis, SOP_sim, ‘r-o’,’LineWidth’,1.5);
grid on;
xlabel(‘SNR (dB)’);
ylabel(‘SOP’);
title(‘SOP vs SNR’);
I am not getting what wrong i am doing in analytical SOP code…
Any help in this regard is highly appreciated for loop, mathematics MATLAB Answers — New Questions
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