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This is the second of a two-part series on communications over the European 240 V domestic powerline, in the frequencies identified by the CENELEC European mains signalling standard, suitable for low-cost equipment in applications requiring data rates of no more than hundreds of bits per second (b/s). To minimize costs, narrow-band modulation techniques are considered. The series of two papers identifies the key impairments introduced by the channel, proposes a novel model structure to simulate them, and describes modulation techniques. The first paper describes the principal linear impairments; cyclic noise power variation and linear signal attenuation. The present paper describes nonlinear multiplicative signal fading and shows how orthogonal frequency division modulation (OFDM) can be used to overcome these impairments.