Acquisition of frequency-hopping spread-spectrum (FH/SS) signals based on autoregressive spectral estimation is addressed for nonfading and Rayleigh-fading channels. The hopped frequency is synthesized using a linear feedback shift register (LFSR). The most significant bit (MSB) of the frequency estimate is loaded into the LFSR. A new acquisition logic is devised for the acquisition scheme that employs the autoregressive spectral-estimation acquisition technique (ASEAT). To characterize the statistical distributions of the frequency estimation error, the truncated Gaussian and uniform distributions are considered. The probability of the MSB error and the mean acquisition time of the acquisition logic are derived. For the ASEAT with the acquisition logic, the acquisition scheme that uses multiple antennas is also addressed. Numerical results for the probability of the MSB error and the corresponding mean acquisition time are illustrated for the performance evaluation of both cases.