This paper presents a new idea to detect a continuous-wave (CW) burst with unknown frequency using the discrete Fourier transform. Given a CW burst of certain length, an obvious detection scheme would be to compute the DFT power over the whole burst and in the given frequency bins that cover the total frequency uncertainty range. This may result in poor performance when the CW frequency is not exactly in one of the DFT bins. The new scheme divides the CW burst into L sub-bursts and computes the summation of the DFT power in each sub-burst. With very little increase on the DFT computation complexity, the overall detection performance can he greatly improved. The analysis employs a unified approach to derive the expressions of probabilities of false alarm and miss detection for both the conventional and the new schemes over the additive white Gaussian noise (AWGN) channel. Simulations are done for both the AWGN channel and the satellite fading channel.

In this paper, we develop a new multistage detector to approach the optimal solution of the detection problem in a synchronous code division multiple access (CDMA) system. The transformation modifies the diagonal elements of the Hessian matrix of the quadratic likelihood function and brings the continuous minimum of the transformed function as close to the optimal solution as possible. The computational complexity is essentially linear with the number of users, except that a few computations of a quadratic function are needed.

Although the optimal detection of signals in a K-user CDMA synchronous system has been proved to be NP-hard, some suboptimal methods do exist to approximate the optimal one. The authors develop a new multistage detector using the transformation proposed by Carter (1984) to approach the optimal solution. The transformation modifies the diagonal elements of the hessian matrix of the quadratic function corresponding to the optimal receiver and brings the continuous minimum of the transformed function as closely to the optimal solution as possible. The convergence of the new multistage algorithms is studied. The computational complexity is essentially linear with the number of users except that a few computations of a quadratic function are needed. The numerical results for the detection of synchronous CDMA signals are shown to be very encouraging.>