  This paper proposes novel spectrum sensing algorithms for cognitive radio
networks. By assuming known transmitter pulse shaping filter, synchronous and
asynchronous receiver scenarios have been considered. For each of these
scenarios, the proposed algorithm is explained as follows: First, by
introducing a combiner vector, an over-sampled signal of total duration equal
to the symbol period is combined linearly. Second, for this combined signal,
the Signal-to-Noise ratio (SNR) maximization and minimization problems are
formulated as Rayleigh quotient optimization problems. Third, by using the
solutions of these problems, the ratio of the signal energy corresponding to
the maximum and minimum SNRs are proposed as a test statistics. For this test
statistics, analytical probability of false alarm ($P_f$) and detection ($P_d$)
expressions are derived for additive white Gaussian noise (AWGN) channel. The
proposed algorithms are robust against noise variance uncertainty. The
generalization of the proposed algorithms for unknown transmitter pulse shaping
filter has also been discussed. Simulation results demonstrate that the
proposed algorithms achieve better $P_d$ than that of the Eigenvalue
decomposition and energy detection algorithms in AWGN and Rayleigh fading
channels with noise variance uncertainty. The proposed algorithms also
guarantee the desired $P_f(P_d)$ in the presence of adjacent channel
interference signals.
