Add a vocal Carl Icahn-style activist investor to the long list of issues Sprint needs to tackle in 2007: build WiMAX, fix the Nextel integration, cut workers, coax back those high-end customers . . . now also figure out how to manage press-friendly pissed off shareholders.

The Wall Street Journal published an article this morning about disgruntled investor Ralph Whitworth, who’s investment firm reportedly owns a $500 million stake, or almost 1%, of Sprint (Reuters report here). Whitworth wants changes at the recently poor performing carrier, including less spending on capex and a sale of its fiber-optic network and long-distance business.

The interesting part is that Sprint hopes its WiMAX network will help with its lagging numbers behind Cingular and Verizon Wireless. And Sprint plans to spend around $3 billion on the rollout.

But Whitworth sees WiMAX as “a drain on the company’s overall cashflow” and “too speculative an investment,” according to an unnamed source in the WSJ. (In double PR talk that could easily be Whitworth himself.)

Sprint’s shares actually rose 2.97% (and rising) today, likely as a result of the report. That could mean the street agrees with the uncertain WiMAX assessment, or just that Sprint needs more drastic changes. Or likely both. (For what it is worth, the rise in shares means Whitworth’s firm’s $500 million stake went up to $515 million – after the story appeared.)

Interestingly Sprint actually sees its WiMAX investment as less of an investment than it would make on other forms of network upgrades. Sprint says it will overlay its WiMAX network onto its 3G network at one tenth the cost of what it takes to build out its 3G network. I’m not sure capital expenses are Sprint’s issue, just spending money on networks (Nextel, WiMAX) that might have integration issues, is a bigger problem.