Cognitive radios have emerged as an attractive solution to the spectral congestion problem by opportunistically using the frequency bands that are not heavily occupied by the licensed users. In cognitive radio networks multiband spectrum sensing provides the capability to sense the available channel over a wideband. In this work, an optimal multiband sensing-time adaptive framework is used to jointly detect a wideband Gaussian primary M-QAM signal over multiple non-overlapping narrowband Gaussian channels so as to maximize the throughput in cognitive radio networks. Under some specific primary user and channel conditions the framework which appeared to be non-convex is explored to determine convexity range. Furthermore, a multiband cyclostationary joint detection framework is proposed which jointly detects the BPSK primary signal over a wideband Gaussian channel using cyclostationary detection technique so as to maximize the aggregate opportunistic throughput of secondary network in cognitive radio environment.