A constellation shaping scheme is proposed. The motivation is to decrease the required transmit power for a specified spectral efficiency. Instead of imposing a non-uniform distribution on the constellation or using non-uniformly spaced symbols, a sphere constraint is employed on the n-dimensional signal space. An efficient algorithm called enumerative amplitude shaping is given to find and index all signal points in the sphere. A comparison with a prominent probabilistic shaping algorithm is provided. The enumerative approach achieves the target rate more efficiently for small block lengths. To introduce error correction, the convolutional encoder used in IEEE Std 802.11 is combined with the shaper in a novel way. Instead of utilizing a larger constellation in combination with shaping, a higher code rate is used by puncturing. Gains up to 1.61 dB are observed for the rates 3 to 6 bits/2-D with 64- and 256-QAM schemes in AWGN channels. The contribution of puncturing in these gains is discussed.
Gültekin, Y. C., Van Houtum, W. J., Şerbetli, S., & Willems, F. M. J. (2018). Constellation shaping for IEEE 802.11. In IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC (Vol. 2017-October, pp. 1–7). Institute of Electrical and Electronics Engineers Inc. https://doi.org/10.1109/PIMRC.2017.8292338