Walekumsalam Saqib bhai,
I’ll share over here whatever I remember from conversations with my grad student friends about the statement of purpose…
Basically, you have to show that you are a driven and motivated individual with defined career and personal goals in life that are clearly laid out in front of you, preferably make it sound like your goals are somehow going to make a huge change in the world and be a great blessing for humanity, and then say exactly how your graduate degree will help you achieve those goals, and how your undergrad education is proving to be not sufficient because you want to expand your scope now, that your graduate education is the missing piece that you need now to move forward in life and achieve your goals.
And you can also tie your undergrad experiences, degree, and work experience you might have into your goals, and show how all of them contributed to your motivation towards getting this degree and these aims of yours in life.
If it is a particular program you are applying to, you can talk about how that particular research etc that you are interested in fits specificially with your goals.
Undergrad admissions essays were a bit immature but cute. Grad ones have to look highly mature and more concrete in defining life goals, they have to contain mature thoughts and solid plans.
This is just a random example: For example, if you were applying for a degree in Urban Planning, you could say that you are from Pakistan, you plan to get this expertise and apply it to Pakistan, which is a third world country, villages are still undeveloped, you want to go back, and contribute to turning the rural areas to developed urban centres. And then you can tie your undergrad education and job experience into it. If you don’t see a connection just think of one and write it there 
Don’t worry, not everyone applying to grad school has their whole life planned out and knows exactly what they want to do, a lot of ppl just talk like they know what they want to do whereas actually they are quite confused and unclear
That’s what you need to do too.
Also, why are you not applying to private universities? I think depending on your grades, work experience, GRE scores and references, you should apply to the appropriate private schools. In fact you should just apply, you never know where you might get in, really
I REALLYYYYYYYY encourage you to just try your luck and apply to all the good top private schools that you always thought were good.
Most people don’t pay the tuition themselves in grad school, specially the EE and CS ppl. They always get TA’ships and RA’ships. None of the Pakistani grad students I know in my college are paying for themselves, they all get TA and RA ships…so money should not be the thing stopping you.
Hmmm…hope what I wrote made some sense.
If you want, I can proof read your essay for you, I have read some grad students essays and have some ideas about what kinds of things go in there. If you need more detailed or specific tips, feel free to ask me abt any questions or confusions you might have, I know lots of grad students in my college and can easily ask them any questions you might have.
Best of luck to you
may Allah give you success in your efforts :k: