This paper addresses the fundamental characteristics of information exchange via multihop network coding over two-way relaying in a wireless ad hoc network. The end-to-end rate regions achieved by time-division multihop (TDMH), MAC-layer network coding (MLNC) and PHY-layer network coding (PLNC) are first characterized. It is shown that MLNC does not always achieve better rates than TDMH, time sharing between TDMH and MLNC is able to achieve a larger rate region, and PLNC dominates the rate regions achieved by TDMH and MLNC. An opportunistic scheduling algorithm for MLNC and PLNC is then proposed to stabilize the two-way relaying system for Poisson arrivals whenever the rate pair is within the Shannon rate regions of MLNC and PLNC. To understand the two-way transmission limits of multihop network coding, the sum-rate optimization with or without certain traffic pattern and the end-to-end diversity-multiplexing tradeoffs (DMTs) of two-way transmission over multiple relay nodes are also analyzed.
Finally, network coding can be used to exploit cooperative diversity between source and destination nodes @cite_29 @cite_4 . Since network coding is able to provide diversity as well as throughput gain, it is of interest to understand the diversity-multiplexing tradeoffs (DMTs) The diversity-multiplexing tradeoff (DMT) for point-to-point multiple input and multiple output (MIMO) channels was found in @cite_5 , and has become a popular metric for comparing transmission protocols. of MLNC and PLNC and determine if they are better than TDMH's. Since we consider two-way transmission over multiple relays, this plurality of relays may cooperate in a number of different ways or not at all, and each cooperation scenario leads to a different DMT result for TDMH, MLNC and PLNC.
@cite_5 @cite_29 @cite_4
2099857870 2160800591 2006462346 2025889675
We consider a general multiple-antenna network with multiple sources, multiple destinations, and multiple relays in terms of the diversity-multiplexing tradeoff (DMT). We examine several subcases of this most general problem taking into account the processing capability of the relays (half-duplex or full-duplex), and the network geometry (clustered or nonclustered). We first study the multiple-antenna relay channel with a full-duplex relay to understand the effect of increased degrees of freedom in the direct link. We find DMT upper bounds and investigate the achievable performance of decode-and-forward (DF), and compress-and-forward (CF) protocols. Our results suggest that while DF is DMT optimal when all terminals have one antenna each, it may not maintain its good performance when the degrees of freedom in the direct link are increased, whereas CF continues to perform optimally. We also study the multiple-antenna relay channel with a half-duplex relay. We show that the half-duplex DMT behavior can significantly be different from the full-duplex case. We find that CF is DMT optimal for half-duplex relaying as well, and is the first protocol known to achieve the half-duplex relay DMT. We next study the multiple-access relay channel (MARC) DMT. Finally, we investigate a system with a single source-destination pair and multiple relays, each node with a single antenna, and show that even under the ideal assumption of full-duplex relays and a clustered network, this virtual multiple-input multiple-output (MIMO) system can never fully mimic a real MIMO DMT. For cooperative systems with multiple sources and multiple destinations the same limitation remains in effect. Explicit code constructions for multiple-input multiple-output (MIMO) multiple-access channels (MAC) with K users are presented in this paper. The first construction is dedicated to the case of symmetric MIMO-MAC where all the users have the same number of transmit antennas nt and transmit at the same level of per-user multiplexing gain r. Furthermore, we assume that the users transmit in an independent fashion and do not cooperate. The construction is systematic for any values of K, nt and r. It is proved that this newly proposed construction achieves the optimal MIMO-MAC diversity-multiplexing gain tradeoff (DMT) provided by Tse at high-SNR regime. In the second part of the paper we take a further step to investigate the MAC-DMT of a general MIMO-MAC where the users are allowed to have different numbers of transmit antennas and can transmit at different levels of multiplexing gain. The exact optimal MAC-DMT of such channel is explicitly characterized in this paper. Interestingly, in the general MAC-DMT, some users might not be able to achieve their single-user DMT performance as in the symmetric case, even when the multiplexing gains of the other users are close to 0. Detailed explanations of such unexpected result are provided in this paper. Finally, by generalizing the code construction for the symmetric MIMO-MAC, explicit code constructions are provided for the general MIMO-MAC and are proved to be optimal in terms of the general MAC-DMT. As one of the key technologies for future wireless communication systems, user cooperation has a great potential in improving the system performance. In this paper, the diversity benefit of user cooperation is evaluated using diversity-multiplexing tradeoff (DMT) as the performance metric. Ways of exploiting the diversity benefit are devised. We investigate two typical channel models, namely, the multiple-access channel (MAC) and the interference channel (IFC). For the MAC, all the terminals are equipped with multiple antennas and the K(K ≥ 2) sources cooperate in a full-duplex mode. We determine the optimal DMT of the channel and propose a compressed-and-forward (CF) based cooperation scheme to achieve the optimal DMT. For the IFC, we consider a two-user channel with single-antenna terminals and full-duplex source cooperation. A DMT upper bound and two DMT lower bounds are derived. The upper bound is derived based on a channel capacity upper bound, and the lower bounds are derived using decode-and-forward (DF) based cooperation schemes. In most channel scenarios, the bounds are found to be tight. This implies that under certain channel scenarios, the optimal DMT of the channel can be achieved by DF-based cooperation schemes. In this work, we extend the nonorthogonal amplify-and-forward (NAF) cooperative diversity scheme to the multiple-input multiple-output (MIMO) channel. A family of space-time block codes for a half-duplex MIMO NAF fading cooperative channel with N relays is constructed. The code construction is based on the nonvanishing determinant (NVD) criterion and is shown to achieve the optimal diversity-multiplexing tradeoff (DMT) of the channel. We provide a general explicit algebraic construction, followed by some examples. In particular, in the single-relay case, it is proved that the Golden code and the 4times4 Perfect code are optimal for the single-antenna and two-antenna cases, respectively. Simulation results reveal that a significant gain (up to 10 dB) can be obtained with the proposed codes, especially in the single-antenna case