We demonstrate a super-quasi-orthogonal space- time (ST) trellis code for four transmit antennas with rectangular signal constellations for wireless communications with a spectral efficiency of 5bits/s/Hz, thus larger than only 4 bits/s/Hz as shown in our previous conference paper. Considering a mobile wireless communications system with four transmit antennas, we form an 8D signal constellation as Cartesian product of four 2D rectangular signal sets, an 8D point being transmitted by the first antenna as four concatenated 2D points in four consecutive channel uses. The 2D symbols transmitted by the other three antennas are not independent, but so chosen as to form, together with the symbols transmitted by the first antenna, the entries of a 4times4 quasi-orthogonal matrix. The union of two sets of quasi-orthogonal matrices forms a super-quasi-orthogonal signal set. With 4x4 quasi-orthogonal matrices, we then label the state transitions of a trellis diagram describing the operation of the encoder. The frame error rate (FER) and the bit error rate (BER) performance results show an excellent behavior of our proposed super-quasi-orthogonal ST trellis codes.

We demonstrate a super-quasi-orthogonal space- time (ST) trellis code for four transmit antennas with rectangular signal constellations for wireless communications with a spectral efficiency of 4 bits/s/Hz. Considering a mobile wireless communications system with four transmit antennas, we form an 8D signal constellation as Cartesian product of four 2D rectangular signal sets, an 8D point being transmitted by the first antenna as four concatenated 2D points in four consecutive channel uses. The 2D symbols transmitted by the other three antennas are not independent, but so chosen as to form, together with the symbols transmitted by the first antenna, the entries of a 4 times 4 quasi- orthogonal matrix. The union of two sets of quasi-orthogonal matrices forms a super-quasi-orthogonal signal set. With 4times4 quasi-orthogonal matrices, we then label the state transitions of a trellis diagram describing the operation of the encoder. The frame error rate (FER) and the bit error rate (BER) performance results show an excellent behavior of our proposed super-quasi- orthogonal ST trellis codes.

We suggest applying constellation shaping to reduce the peak and average power of orthogonal frequency division multiplexing (OFDM) signals using quadrature amplitude modulation (QAM) in all subcarriers without clipping or reducing the data rate. Adopting the successful shell mapping algorithm for high data rate transmission over telephone channels, as described in the V.34 Recommendation of ITU-T, we build a shell mapping algorithm for multidimensional constellation in the frequency domain for OFDM communication systems with N subcarriers. We give closed-form expressions of the functions needed to apply the constellation shaping algorithm for any N being a power of two. No side information needs to be transmitted and the data rate remains the same as for the basic OFDM system. Our simulation results show that we are able to reduce the peak and mean power by about 1 dB for OFDM signals with N = 16. For a higher number of subcarriers, we expect that we obtain more freedom in power minimization and the resulting gain will be higher. The only price to be paid is the enhanced complexity of the system by an amount that is rather acceptable.

We demonstrate super-orthogonal space-time (ST) trellis codes with rectangular signal constellations for wireless communications with a spectral efficiency of 4 bits/s/Hz. Considering a mobile wireless communications system with two transmit antennas, we form a 4D signal constellation as Cartesian product of two 2D rectangular signal sets, a 4D point being transmitted by the first antenna as two concatenated 2D points in two consecutive channel uses. The 2D symbols transmitted by the second antenna are not independent, but so chosen as to form, together with the symbols transmitted by the first antenna, the entries of a 2 times 2 orthogonal matrix. This can be done in four different ways, resulting in four sets of 2 times 2 orthogonal matrices. To obtain a higher data rate, the union of two of them forms a super-orthogonal signal set. With 2 times 2 orthogonal matrices, we then label the state transitions of a trellis diagram describing the operation of the encoder. We perform simulations using a model that takes into account the Doppler effect as well as the effect of spatial antenna correlation at both the base station (BS) and at the mobile station (MS). The frame error rate (FER) and the bit error rate (BER) performance results show an excellent behaviour of our proposed super-orthogonal ST trellis code, which clearly outperforms all known simple ST trellis codes of same spectral efficiency using 16QAM or 16PSK

The V.34 high-speed modem combines a number of advanced techniques including constellation shaping by shell mapping. This technique makes use of some functions representing the number of ring combinations with a given cost. In this correspondence, closed-form expressions for these functions are given and used in the constellation shaping by the shell-mapping algorithm.

The Wei method of constructing trellis codes with 2N-dimensional rectangular signal constellations is limited to N being an integer power of two. In the present correspondence, this limitation is removed and examples of six-dimensional (6-D) and twelve-dimensional (12-D) trellis codes are given.