NEW DELHI — In the past decade, nearly 1 billion people have been connected to wireless phone service as part of India’s mobile communications revolution , making it the second-largest mobile phone market in the world. But a recent combination of rapidly rising growth and bad infrastructure has turned India’s dreams of wireless phone expansion into something of a nightmare.

Anguish over dropped calls has cut across income levels and social strata and led to unkind jokes about the country as the “call drop nation.” The government-run national consumer complaints help line reported that dropped calls ranked near the top of the list of all grievances in July and August. The issue was the cover story of a national newsmagazine in July. And a TV station has launched a social media campaign called #NoCallDrops

The trouble, technology analysts said, is threatening Modi’s pet project called Digital India: an $18 billion plan to connect India’s cities and villages to the Internet with a combination of broadband connectivity and WiFi. Today, most of India’s 350 million Internet users access the Web on their mobile devices.

“India’s mobile network is under tremendous stress,” Prasanto K. Roy, a technology consultant, said. “And if we fail to address mobile connectivity problems, it will directly hit the government’s Digital India initiative.” Mobile connectivity is key because the number of land lines and broadband users has remained stagnant, with WiFi hot spots few and far between, he said.

Radhika Misra, 41, a businesswoman who works from her home in the upscale suburb of Gurgaon, said dropped calls and patchy signals are affecting her discussions with clients.

“This is hugely frustrating,” Misra said. “I have to sit in one corner of my home, tilt my neck to 45 degrees in one direction to catch the signal.”

In a New Delhi neighborhood, residents said they must roam the streets to find a spot where their cellphones can connect. Shop owners complain their business is down.

“In India, the government agencies like police, military, railways and airlines are squatting on more than 60 percent of spectrum,” said Rajan Mathews, director general of the Cellular Operators Association of India. “We carry an inordinate amount of traffic on just one-third of the spectrum that most global companies have.”

A public-health scare among middle-class Indians has also compounded the situation.

Communities across Indian cities are saying they do not want to have a cellphone transmission tower in their densely populated neighborhoods because they fear that its radiation may harm their health. Resident groups, activists and a Bollywood star have campaigned against the towers.

Mumbai has banned towers near schools and hospitals.

And in the past year, about 1,700 sites have been shut down across India, said Mathews.