Early every morning and again in late afternoon, the quiet of the Saudi capital is broken by the rumble of U.S. Airborne Warning and Control Systems (AWACS) aircraft as they take off or land at the old airport on the city's northern outskirts.

The odd-shaped planes, carrying a disk-like radar on their backs and packed with electronic equipment, lumber off to the eastern coast where they become the kingdom's eyes and ears over the troubled Persian Gulf.

The AWACS are the centerpiece of the Saudi air defense system against any potential Iranian attack on the kingdom or its neighbors.

In addition to serving as Saudi Arabia's "sky sentinels," the AWACS symbolize the continuing special relationship between the United States and this key Arab desert nation on the Persian Gulf, the world's oil heartland. It has its roots in 50 years of history and has survived the test of time and many storms.

A striking demonstration of this U.S.-Saudi partnership came in June, when one of the AWACS planes assisted two Saudi-piloted F15 interceptors that shot down two intruding Iranian warplanes.

While U.S. dependence on Saudi oil has dropped from more than 2 million barrels a day in 1980 to 378,000 today, a coincidence of security concerns in the Persian Gulf has kept the two countries close.

Increasing Saudi anxiety about subversion or air attack from Iran combined with a warm official friendship between King Fahd and President Reagan have breathed new life into the oft-strained U.S.-Saudi relationship. A special American role in the Saudi thrust to develop high technology industries has added an extra dimension.

By all accounts, Fahd has high respect for and confidence in Reagan. He reportedly confided to a visiting American official last spring that if he could vote in the U.S. presidential election, he would vote for Reagan. After the election, Fahd was one of the first foreign dignitaries to send a congratulatory telegram to Reagan, and he telephoned him as well.

Despite periodic Saudi doubts about U.S. reliability and a strong distaste for congressional scrutiny of every major U.S. arms deal, Fahd repeatedly has turned to Reagan for help in recent crises, and so far Reagan has responded.

Last spring, Reagan answered Fahd's emergency request for Stinger missiles despite strong opposition in Congress. In August, on Fahd's appeal, he sent U.S. warships to hunt for mysterious mines in Saudi territorial waters.

The full extent of Saudi reliance on the United States for security is held in deep secrecy by both sides, but it is understood to include extensive contingency planning for joint operations in a full-scale crisis.

The Saudis are not depending solely on the United States for external backing, however, particularly in manpower. They have entered a secret agreement with Pakistan, which has sent several thousand, and possibly as many as 10,000, troops here. Most are in the southwest along the North Yemeni border, where they are inconspicuous. Their presence came to light early this year when some of them reportedly were captured by the Yemenis in a border incident.

The Saudis also are upgrading their relations with Turkey, which like Pakistan is a Moslem country, thus making its troops far more acceptable here than those of the United States.

Nonetheless, as the presence of the four AWACS planes and the 500 U.S. officers and support personnel make clear, the American role is extensive and likely to remain so.

Earlier, the Saudis used the U.S. Army Corps of Engineers to oversee $19 billion worth of military construction. The activities of the corps are now scheduled to be phased out by 1987-88, but the U.S. Air Force has been retained to award and implement a $4 billion contract for construction of a kingdom-wide central command-and-control system.

This and the $8.5 billion sale in 1981 of five AWACS aircraft and other sophisticated equipment for Saudi Arabia's 60 U.S.-built jet fighters seem to ensure a long-term, close U.S.-Saudi relationship in military and intelligence matters.

Significantly, only three American firms -- Hughes Aircraft, Litton and Boeing -- are in the race for what is believed to be the last of the big Saudi defense contracts.

The contract features a new twist that is expected to strengthen the American connection in another field: the bidders must come up with ideas for investment in high technology industries that they will build and become partners in.

This is expected to generate between $500 million and $1 billion in new investment in advanced U.S. industrial technology, a sum that the Saudis will match.

In addition to purchasing the best security system U.S. companies can provide, Saudi Arabia clearly is determined to bring about a transfer of U.S. industrial technology to the kingdom.

This already is being done in the petrochemical sector, where U.S. companies such as Mobil, Exxon, Shell, Texas Eastern and Celanese, in 50-50 partnership with the Saudis, are building major plants based on the latest processes.

Despite the current recession and the Saudi takeover of the big Arabian-American oil company Aramco, there are still 60,000 Americans living or working here, the biggest contingent of Westerners by far. Half of them are connected to programs for the Saudi armed forces, according to a 1981 House subcommittee report.

Saudi Arabia is the sixth most important overseas market for the United States and one of the few where the balance of trade is in U.S. favor. While estimated U.S. exports to the kingdom dropped slightly last year from a 1982 high of about $8 billion, U.S. imports reached only $3.8 billion, almost all of it oil.