This paper presents the design and the experimental demonstration of transmission of spectrally efficient frequency division multiplexing (SEFDM) signals, using a single 5-GHz channel, from 81 to 86 GHz in the E-band frequency allocation. A purpose-built E-band SEFDM experimental demonstrator, consisting of transmitter and receiver GaAs microwave integrated circuits, along with a complete chain of digital signal processing is explained. Solutions are proposed to solve the channel and phase offset estimation and equalization issues, which arise from the well-known intercarrier interference between the SEFDM signal subcarriers. This paper shows the highest transmission rate of 12 Gb/s over a bandwidth varying between 2.67 to 4 GHz depending on the compression level of the SEFDM signals, which results in a spectral efficiency improvement by up to 50%, compared to the conventional orthogonal frequency division multiplexing modulation format.