This work aims to assess the potential value of using successive interference cancellation (SIC) and opportunistic spectrum access techniques (OSA) in cognitive heterogeneous wireless networks composed of primary users and wideband (e.g., UWB) cognitive (secondary) users. In particular, we consider a dense fading multiuser network, where a wideband cognitive transmit-receive pair terminals communicate in an underlay fashion, while co-existing over the same spectrum with K narrowband transmit-receive pair terminals occupying K orthogonal channel bands. We use Shannon-theoretic tools to analyze the tradeoff between energy efficiency and spectral efficiency (known as the power-bandwidth tradeoff) in meaningful asymptotic regimes of signal-to-noise ratio (SNR) and number of users (K), with special focus on the power-limited wideband regime. Our analytical and numerical results yield new insights on the spectral efficiency vs. Eb/No performance of various SIC and OSA techniques in cognitive radio networks.