Distributed Space-time Trellis Codes Research Articles

Circulation Technique of Distributed Space Time Trellis Codes with AF Relaying

In this letter, a circulation-based distributed space time trellis code (DSTTC) technique for amplify-and-forward (AF) relaying is proposed. The proposed circulation technique is a method of configuring new protocols from the existing protocols of which the performance is dependent on specific source to relay links. The simulation results show that the newly developed protocol is less dependent on weak conditions of specific links and a performance gain in frame error rate (FER) can be obtained over the original protocol.

Novel Distributed Space-Time Trellis Codes for Relay Systems over Cascaded Rayleigh Fading

In this letter, we consider the deployment of distributed space-time trellis codes (STTCs) for user cooperation. We derive a pairwise error probability (PEP) expression for distributed STTCs over cascaded Rayleigh fading channels. Using the derived PEP expression, we determine a code design criterion and propose novel 4-/8-/16-state 4-PSK and 8-/16-state 8-PSK distributed STTCs through a systematic code search. We confirm the superiority of the proposed codes through extensive Monte-Carlo simulations.

Distributed space-time trellis codes for a cooperative system

In this paper, we propose a novel distributed spacetime trellis code (DSTTC) structure, and analyze its error performance in both slow and quasi-slow Rayleigh fading channels. The protocol adopted is decode-and-forward (DAF) with a single relay between the source and destination. Both scenarios with perfect and imperfect decoding at the relay are investigated. For imperfect decoding at the relay node, we consider an equivalent one-hop link model for the source-relay-destination path, and use it to modify the maximum likelihood detection metric by taking into account the equivalent signal-to-noise ratio (SNR) of the link model. The upper bounds of pairwise error probability (PEP) are derived for slow and quasi-slow Rayleigh fading channels, and the DSTTC design criteria are formulated accordingly. Based on the proposed design criteria, new DSTTCs are constructed by computer search. Simulation results demonstrate the superiority of the designed codes.

Distributed space-time trellis code for asynchronous cooperative communications under frequency-selective channels

In most cooperative communication works, perfect synchronization among relay nodes is assumed in order to achieve the cooperative diversity. However, this assumption is not realistic due to the distributed nature of each relay node. In this paper, we propose a family of distributed space-time trellis code (DSTTC) that does not require the synchronization assumption. It is shown that the proposed DSTTC has minimum memory order, and the construction of such DSTTCs is equivalent to using the generator matrices that have full row rank, regardless of sub-matrices shifting problem. Here, a sub-matrix corresponds to the generator matrix of a relay node under frequency-selective channels. We derive sufficient conditions on the code design such that the full cooperative and multipath diversities can be achieved. By further studying the diversity product, we design the DSTTCs which can achieve full diversity and the maximum coding gain through the exhaustive computer search. The newly proposed codes exhibit good properties, e.g., high energy efficiency and low synchronization cost, and can be applied to distributed wireless networks. Finally, various numerical examples are provided to corroborate the analytical studies.

Cooperative Relaying with CPFSK and Distributed Space-Time Trellis Codes

Cooperative relaying allows single antenna users to achieve diversity and coding gains by utilizing nearby users' transmitting capabilities. We consider a relay system employing constant envelope continuous phase frequency shift keying. Distributed space-time trellis codes are implemented with a novel multiple relay protocol.

Decentralized distributed space-time trellis coding

In this paper, we introduce a new class of distributed space-time trellis codes (DSTTCs) for wireless networks with a large set of decode-and-forward relay nodes N. We consider the general case where each relay node is equipped with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> antennas and the destination node is equipped with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> antennas. It is assumed that at any given time only a small, a priori unknown subset of nodes S ∈ N is active and neither the relay nodes nor the destination node know which relay nodes are active. In the proposed scheme, each node is assigned a signature matrix and the signal transmitted by an active node is the product of the signature matrix and a space-time trellis code (STTC) matrix originally designed for N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> co-located antennas. It is shown that existing full-rank STTCs designed for N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ⩾ 2 co-located antennas are a favorable choice for the code matrix. Two practical designs for good deterministic signature matrix sets are provided and compared with random signature matrices. If the signature matrices are properly optimized, the proposed DSTTCs achieve a diversity order of d = min{N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> , N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> } if N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</sub> nodes are active. Simulation results confirm that DSTTCs yield significant performance gains over distributed space-time block codes and distributed space-time filtering. Furthermore, equipping relay nodes with a second antenna can be highly beneficial especially if only few nodes can be active at any given time.

Analysis and Design of Distributed Space–Time Trellis Codes With Amplify-and-Forward Relaying

We study the asymptotic behavior of a cooperative scheme operating in amplify-and-forward (AF) mode when the number of relay terminals tends to infinity. We consider three time-division-multiple-access-based cooperation protocols which realize different degrees of broadcasting and receive collision. Optimal design rules for distributed space-time codes (STCs) are derived through the investigation of pairwise error probability expression for each considered protocol. The derived design rules reveal a Euclidean-distance-type performance metric, including some scaling terms due to the effects of AF operation mode and cooperation protocols as well as path loss/shadowing effects associated with the underlying relay links. Based on the derived criteria, an exhaustive computer code search is conducted to find out optimal distributed STCs. Our search results indicate the optimality of conventional designs, i.e., based on classical Euclidean distance, for relay numbers larger than two in a distributed scenario. For the special cases of one and two relays, we present novel distributed codes which are able to outperform their conventional counterparts and demonstrate robustness against distributed implementation.

A Family of Distributed Space-Time Trellis Codes With Asynchronous Cooperative Diversity

In current cooperative communication schemes, to achieve cooperative diversity, synchronization between terminals is usually assumed, which may not be practical since each terminal has its own local oscillator. In this paper, based on the stack construction proposed by Hammons and El Gamal, we first construct a family of space-time trellis codes for BPSK modulation scheme that is characterized to possess the full cooperative diversity order without the synchronization assumption. We then generalize this family of the space-time trellis codes from BPSK to higher order QAM and PSK modulation schemes based on the unified construction proposed by Lu and Kumar. Some diversity product properties of space-time trellis codes are studied and simplified decoding methods are discussed. Simulation results are given to illustrate the performance of the newly proposed codes