  In this paper we expand our recently introduced concept of UW-OFDM (unique
word orthogonal frequency division multiplexing). In UW-OFDM the cyclic
prefixes (CPs) are replaced by deterministic sequences, the so-called unique
words (UWs). The UWs are generated by appropriately loading a set of redundant
subcarriers. By that a systematic complex number Reed Solomon (RS) code
construction is introduced in a quite natural way, because an RS code may be
defined as the set of vectors, for which a block of successive zeros occurs in
the other domain w.r.t. a discrete Fourier transform. (For a fixed block
different to zero, i.e., a UW, a coset code of an RS code is generated.) A
remaining problem in the original systematic coded UW-OFDM concept is the fact
that the redundant subcarrier symbols disproportionately contribute to the mean
OFDM symbol energy. In this paper we introduce the concept of non-systematic
coded UW-OFDM, where the redundancy is no longer allocated to dedicated
subcarriers, but distributed over all subcarriers. We derive optimum complex
valued code generator matrices matched to the BLUE (best linear unbiased
estimator) and to the LMMSE (linear minimum mean square error) data estimator,
respectively. With the help of simulations we highlight the advantageous
spectral properties and the superior BER (bit error ratio) performance of
non-systematic coded UW-OFDM compared to systematic coded UW-OFDM as well as to
CP-OFDM in AWGN (additive white Gaussian noise) and in frequency selective
environments.
