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This paper describes a new concept in modulation methods for high speed digital mobile communications. Linear modulation is introduced to allow amplitude variation in the modulated signal. This primarily brings the advantage that sharp cut-off band restriction can be performed to enhance the transmission efficiency. Also, we can adopt as a multipath strategy an amplitude-shift anti-multipath modulation technique, which is found to be more effective than its phase-shift counterpart. A linear modulation method is presented to meet the mobile radio requirement on power efficiency. We finally derive a narrow-band anti-multipath modulation scheme, with required bandwidth compatible with other narrow-band modulation techniques and with superior anti-multipath effect.