We experimentally and numerically demonstrated the generation of a (3, 1) vector signal by a single Mach-Zehnder modulator (MZM) without pre-coding. The MZM is driven by the (3, 1) modulated signal after photoelectric conversion by the "square law" of a photodetector. Although the phase changes, the corresponding constellation distribution is consistent with that of the regular signal. Our proposed scheme effectively avoids the pre-coding process with a simple architecture. The bit-error-ratio (BER) results indicate that the (3, 1) signal has a better BER performance than the pre-coded quadrature phase shift keying vector signal, and both are below ${3.8}\times {{10}^{ - 3}}$3.8×10-3 after 25 km optical fiber transmission.