Corneliu Eugen D. Sterian

Super-orthogonal space-time codes with rectangular constellations and two transmit antennas for high data rate wireless communications

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

New super-orthogonal space-time trellis codes with 32QAM and two transmit antennas for five bits per signalling interval

In this paper, we focus on the design of super-orthogonal space-time (ST) trellis codes with a 32-point quadrature amplitude modulation (QAM) signal constellation, allowing wireless communication with a data rate of 5 bits per signalling interval. Considering a mobile wireless communications system with two transmit antennas, we form a four-dimensional (4D) signal constellation as a Cartesian product of two 2D rectangular signal sets. The first antenna transmits a 4D point as two concatenated 2D points in two consecutive baud intervals. 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 × 2 orthogonal matrix. For a rectangular constellation, as much as four sets of 2 × 2 orthogonal matrices can be built. To obtain a higher data rate, the union of two of them is used to construct a super-orthogonal signal set. With 2 × 2 orthogonal matrices, we then label the state transitions of a trellis diagram describing the operation of the encoder. For the performance analysis, two different channel models are employed. The first channel model is based on the assumption that the paths between different pairs of transmit–receive antennas are uncorrelated, while the second model takes into account the effect of spatial antenna correlation at both the base station (BS) and at the mobile station (MS). The analysis of the frame-error rate (FER) and the bit-error rate (BER) demonstrates the excellent performance of the proposed high data rate super-orthogonal ST trellis code. Copyright

Rotationally invariant space-time trellis codes with 4-D rectangular constellations for high data rate wireless communications

We demonstrate rotationally invariant space-time (ST) trellis codes with a 4-D rectangular signal constellation for data transmission over fading channels using two transmit antennas. The rotational invariance is a good property to have that may alleviate the task of the carrier phase tracking circuit in the receiver. The transmitted data stream is segmented into eight bit blocks and quadrature amplitude modulated using a 256 point 4-D signal constellation whose 2-D constituent constellation is a 16 point square constellation doubly partitioned. The 4-D signal constellation is simply the Cartesian product of the 2-D signal constellation with itself and has 32 subsets. The partition is performed on one side into four subsets A, B, C, and D with increased minimum-squared Euclidian distance, and on the other side into four rings, where each ring includes four points of equal energy. We propose both linear and nonlinear ST trellis codes and perform simulations using an appropriate multiple-input multiple-output (MIMO) channel model. The 4-D ST codes constructed here demonstrate about the same frame error rate (FER) performance as their 2-D counterparts, having however the added value of rotational invariance.

Reducing the peak and average power for OFDM systems using QAM by constellation shaping

In this paper, we present a shell mapping scheme to reduce the peak and average power of orthogonal frequency division multiplexing (OFDM) signals using quadrature amplitude modulation (QAM) by constellation shaping. Our approach can be considered as an extension of the shell mapping technique introduced originally in the V.34 recommendation of ITU-T. The shell mapping method uses multiple cost functions, each having the OFDM block length N as a parameter. The cost functions are presented in closed form for any N. The main advantage of the proposed scheme is that the peak and average power can be reduced without sacrificing the data rate, and no side information is needed at the receive side. We apply our constellation shaping technique to OFDM systems with N equal to 16, 32 and 128 subcarriers. The results show that the peak and average power decrease with increasing values of N. This advantage is partly offset by a slightly higher system complexity. Copyright

Super-orthogonal space-time trellis codes with eight dimensional phase-shift keying signal constellations

We propose a new method of designing super-orthogonal space-time trellis codes (SOSTTCS) by labeling each state transition of the trellis diagram with an ordered pair of 2×2 orthogonal matrices instead of only a single 2×2 orthogonal matrix. An 8D instead of a 4D signal constellation is thus used for modulation and the delay elements of the trellis encoder are 4T instead of 2T, where T is the 2D symbol duration. Therefore, at the receiver, the sequence decoding using Viterbi algorithm requires two times less frequent updating of the branch metrics. We investigate by computer simulation the performance of the new sosttcs compared to sosttcs designed by the known method. The frame error rate (fer) and the bit error rate (ber) simulation results show that the performance of the new sosttcs is practically as good as that of the sosttcs of similar complexity designed along classical lines, with the advantage that the number of arithmetic and logic operations performed by the decoder per time unit is smaller, which is crucial in high data-rate applications.RésuméNous proposons une nouvelle méthode pour concevoir des codes espace-temps superorthogonaux (sosttcs) en étiquetant chaque transition du diagramme en treillis par une paire ordonnée de matrices orthogonales 2×2 à la place d’une seule matrice orthogonale 2×2. On emploie donc pour la modulation une constellation de signaux 8D à la place d’une 4D, ce qui fait que les éléments de retard sont 4T à la place de 2T, où T est la durée d’un symbole. Pour cette raison, au récepteur, le décodage séquentiel utilisant l’algorithme de Viterbi demande une actualisation deux fois moins fréquente des métriques de branche. Par simulation au moyen d’un ordinateur, nous étudions la performance de nos nouveaux codes en treillis espace-temps super-orthogonaux en les comparant aux codes conçus par la méthode connue. Les résultats des simulations concernant le taux d’erreurs de trames et le taux d’erreurs de bits (teb) montrent que la performance de nos nouveaux codes espace-temps super-orthogonaux est, d’un point de vue pratique, aussi bonne que celle des codes de complexité similaire conçus de manière classique, avec l’avantage d’un nombre réduit d’opérations arithmétiques et logiques à effectuer par le décodeur par unité de temps, ce qui compte le plus dans les applications à débit élevé.

Using Constellation Shaping to Reduce the Peak and Average Power of OFDM Signals

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.

256‐state trellis code with 12‐D rectangular constellation using an extended wei method

The Weis method of constructing trellis codes with 2N-D rectangular constellations is limited to N being an integer power of two. In the present letter to the editor, this limitation is removed and the example of a 256-state, rate 4/5 linear trellis code with 12-D rectangular signal set is given.

On designing fully rotationally invariant trellis-coded modulation using Wei functions

A desirable property trellis-coded modulation (TCM) should have the invariance to rotations of the signal constellation by symmetry angles. Two methods are known to provide rotational invariance: one is that of the parity-check equation and other is that of bijective functions defined on the set of states of the sequence encoder. Whilst both approaches express different facets of the same reality, we emphasize in this letter the greater usefulness of the second one and demonstrate fully rotationally invariant TCM for 2D 16-phase shift keying (PSK) using an algebraic group of 16 bijective functions, which seems not possible to design otherwise, since a rate 3/4 parity-check equation is not mathematically tractable. The design methodology, we demonstrate, is general and does not exclude combining the two methods when performing computer searches for good TCM codes. Copyright

Combining super-orthogonal space-frequency trellis coding, constellation shaping by shell mapping, and OFDM for high data rate broadband mobile communications

In this paper, we seamlessly combine three transmission techniques to design an improved performance broadband mobile communication system with two transmit antennas. In so doing, we took inspiration from the V.34 data modem toolbox designed for public switched telephone network. We modified the constellation shaping by shell mapping algorithm to apply it only to the orthogonal frequency division multiplexing (OFDM) frame sent by the first antenna, in such a way that the peak-to-average power ratio (PAPR) is also reduced for the second antenna. We use a 24-point quadrature amplitude modulation (QAM) signal constellation on each subcarrier, while the reference system employs 16 QAM for the same data rate. The 24 QAM constellation is partitioned into four subsets and six rings of four two-dimensional points each. Two adjacent OFDM frequencies form with the symbols transmitted on them the entries of a 2 × 2 matrix similar to Alamoutis scheme. Two rings corresponding to adjacent OFDM frequencies form a super-ring. The constellation shaping algorithm is applied to shells made up of super-rings instead of rings as usual. Super-orthogonal space-frequency trellis coding is used on pairs of subcarriers. The proposed system was simulated using two channel models, and the performance was evaluated against the uncoded OFDM reference system. It has both reduced PAPR, and better bit error rate and frame error rate performances. Copyright

A new method of decoding space-time trellis codes using differential M-PSK for noncoherent mobile communication systems

This paper proposes a new method of decoding space-time trellis codes using differential modulation for noncoherent mobile communication systems.