Sprint announced a layoff it calculates will save the company at least $350 million (annualized), even as Clearwire confirmed yesterday’s report that Sprint is investing another $1.18 billion in the WiMAX company.

Sprint said it will eliminate 2,000 to 2,500 positions, or about 6 percent of its total workforce, during the fourth quarter. The company said the reduction “impacts positions companywide” and includes cuts in the company’s wholesale organization that were announced earlier this month.

Sprint vowed the cuts would not affect customer service, improvements in which have led to steadily increasing customer satisfaction – to the point where the company has been able to close 27 call centers “as call volume has decreased in the wake of service improvements.”

Clearwire also specified the amounts its three cable investors will be contributing: Comcast is ponying up $196 million, Time Warner Cable $103 million and Bright House Networks $19 million.

Intel is going to toss in $50 million, according to Clearwire, and Eagle River Holdings another $20 million (Eagle River is run by Clearwire founder Craig McCaw). The total new investment will exceed $1.5 billion. The investors will be buying new shares in Clearwire at about $7.33 each.

The success of Clearwire is extremely important for Sprint. The wireless carrier has been losing 3G customers, even as it tries to steal a march on AT&T Wireless and Verizon Wireless by getting a nationwide 4G network up and running (via Clearwire) before its larger rivals can establish their 4G networks.

"This additional level of strategic funding marks another important milestone in the progress of Clearwire and will enable us to maintain our leadership and aggressive 4G WiMAX network build plans," said Bill Morrow, CEO of Clearwire. "Today's news is also further validation of the importance of our 4G network to our strategic investors. We all benefit from this robust, all-IP, high-bandwidth network that delivers an unmatched combination of Internet speed and mobility.”

Shares of Sprint and Clearwire gained Monday, thanks to reports suggesting Sprint and its partner investors would put more money into Clearwire.

Investors cheered the move, sending Sprint up 32 cents, or 11 percent, to $3.17 in afternoon trading, while Clearwire rose 34 cents, or 5.2 percent, to $6.84.

Conspicuously absent from the funding contributors is Google, which invested $500 million in Clearwire last December only to have to write-down that investment by $355 million.

"[Google is] the least desperate of the financing group," says analyst Chris King with Stifel Nicolaus. "It's nice for Google if Clearwire works, but not hugely necessary to its business model. For everyone else, it's hugely important. My sense is that Google has been as exposed [to risk] as they feel they need to get."

Google landed several business deals with its investment in Clearwire, including agreements for mobile advertising and search. In addition, Clearwire will carry devices based on Google's Android operating system.

Meanwhile, on the verge of reporting its Q3 financials, Clearwire also announced plans to launch an offering for a minimum of $1.45 billion in new senior secured notes, with net proceeds to be used to pay off the company’s existing $1.4 billion credit facility.

– Wireless Week’s Maisie Ramsay and The Associated Press contributed to this report