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The objective of this work is to assess some fundamental limits for opportunistic spectrum reuse via cognitive radio in a frequency-planned environment. We present a first order analysis of the signal-to-noise-and-interference situation in a wireless cellular network, and analyze the impact of cognitive users starting to transmit. Two main conclusions emerge from our study. First, obtaining any substantial benefits from opportunistic spatial spectrum reuse in a frequency-planned network without causing substantial interference is going to be very challenging. Second, the cognitive users need to be more sensitive, by orders of magnitude, than the receivers in the primary system, especially if there is significant shadow fading. This latter problem can be alleviated by having cognitive users cooperate, but only if they are separated far apart so that they experience independent shadowing.