We introduce a new kind of adaptive equalizer that operates in the spatial-frequency domain and uses either least mean square (LMS) or recursive least squares (RLS) adaptive processing. We simulate the equalizer's performance in an 8-Mb/s quaternary phase-shift keying (QPSK) link over a frequency-selective Rayleigh fading multipath channel with similar to 3 mu s rms delay spread, corresponding to 60 symbols of dispersion. With the RLS algorithm and two diversity branches, our results show rapid convergence and channel tracking for a range of mobile speeds (up to similar to 100 mi/h), With a mobile speed of 40 mi/h, for example, the equalizer achieves an average bit error rate (BER) of 10(-4) at a signal-to-noise ratio (;SNR) of 15 dB, falling short of optimum linear receiver performance by about 4 dB, Moreover, it requires only similar to 50 complex operations per detected bit, i.e., similar to 400M operations per second, which is close to achievable with state-of-the-art digital signal processing technology. An equivalent time-domain equalizer, if it converged at all, would require orders-of-magnitude more processing.