When did Dish state that it had set aside $5.6B for its LTE network? As far as I can tell, the most recent 10Q shows that Dish doesn't even have $5.7B in available assets. Total assets is about $9.2B, with current liabilities of $3B, and property and equipment valued at around $3B. This leaves dish with about $3.2B in assets that could possibly be converted to cash. Unless they plan to sell off some property and equipment there is no way they could possibly spend that much on an LTE network build.
All of this on top of the fact that their customer base is dwindling, leading to greatly reduced profits, leads me to believe that Dish needs to do something drastic, and fast if it wants to maintain its viability. Now the question is, if Dish's profits are dwindling, why purchase Clearwire's debt?