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We show that space-charge instabilities (electric field domains) insemiconductor superlattices are the attribute of absolute negative conductanceinduced by small constant and large alternating electric fields. We propose theefficient method for suppression of this destructive phenomenon in order toobtain a generation at microwave and THz frequencies in devices operating atroom temperature. We theoretically proved that an unbiased superlattice with amoderate doping subjected to a microwave pump field provides a strong gain atthird, fifth, seventh, etc. harmonics of the pump frequency in the conditionsof suppressed domains.Comment: 8 pages. Development of cond-mat/0503216 . Version 2: Final version,  erratum is include

Suppressed absolute negative conductance and generation of high-frequency radiation in semiconductor superlattices