no one cant tell you exactly how long it will take for background checks. it depends on applicants travel history.
if its 1-2 years it can take 2-3 months but if its more than 2-3 years you might have to wait for 5-6 months. as you can see in new delhi thread, there are some applicants with travel history of 3-5 years and waiting for last 6-7 months. someone has 2 years travel history in UK and they got visa within 4 months of PPR.
you dont need to worry about anything because your process has been started but we are still waiting for any response from cic. Our application was received on jan 26 at Mississauga.
best of luck