Melda Yuksel

Multiple-Antenna Cooperative Wireless Systems: A Diversity–Multiplexing Tradeoff Perspective

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.

The Relay Channel with a Wire-tapper

In this work a relay channel with a wire-tapper is studied for both discrete memoryless and Gaussian channels. The wire-tapper receives a physically degraded version of the destinations signal. We find inner and outer bounds for the capacity-equivocation rate region. We also argue that when the destination receives a physically degraded version of the relays signal, inner and outer bounds meet for some special cases.

Diversity-Multiplexing Tradeoff for the Multiple-Antenna Wire-tap Channel

In this paper the fading multiple antenna (MIMO) wire-tap channel is investigated under short term power constraints. The secret diversity gain and the secret multiplexing gain are defined. Using these definitions, the secret diversity-multiplexing tradeoff (DMT) is calculated analytically for no transmitter side channel state information (CSI) and for full CSI. When there is no CSI at the transmitter, under the assumption of Gaussian codebooks, it is shown that the eavesdropper steals both transmitter and receiver antennas, and the secret DMT depends on the remaining degrees of freedom. When CSI is available at the transmitter (CSIT), the eavesdropper steals only transmitter antennas. This dependence on the availability of CSI is unlike the DMT results without secrecy constraints, where the DMT remains the same for no CSI and full CSI at the transmitter under short term power constraints. A zero-forcing type scheme is shown to achieve the secret DMT when CSIT is available.

Secure Communication with a Relay Helping the Wire-tapper

A four terminal Gaussian network, composed of a single source-destination pair, a relay and a wire-tapper is considered. Unlike the relay channel with a wire-tapper, it is assumed that the relay assists the wire-tapper, not the destination. The relays objective is to decrease the achievable secrecy rates. However, since the destination is also allowed to listen to the relays transmission, it also benefits from the relay in terms of achievable rates. Direct transmission, amplify-and-forward (AF), decode-and-forward (DF) and compress-and-forward (CF) relaying schemes are compared in terms of secrecy rates. It is shown that the best relaying strategy depends on relays location. Comparison of relaying protocols and best power allocation schemes, when the relay assists the source-destination communication, do not readily extend to the case when the relay assists the wire-tapper.

Diversity in relaying protocols with amplify and forward

We examine a network consisting of one source, one destination and two amplifying and forwarding relays and consider a scenario in which destination and relays can have various processing limitations. For all possible diversity combining schemes at the relays and at the destination, we find diversity order results analytically and confirm our findings through numerical calculations of bit error rate (BER) versus signal-to-noise-ratio (SNR) curves. We compare our results with direct transmission, well known transmit diversity methods and traditional multihop transmission and conclude that diversity reception in multihop networks provides the lowest error rate.

Diversity-Multiplexing Tradeoff in Cooperative Wireless Systems

We first examine a system with a single source-destination pair and two relays, each node with a single antenna, and explore whether this virtual multi-input multi-output (MIMO) system can mimic a physical MIMO in terms of diversity-multiplexing tradeoff (DMT). We show that even under the idealistic assumption of full-duplex relays and a clustered network, the relay system can never fully mimic a real MIMO DMT, it is multiplexing gain limited. The limitation comes from the fact that source and destination are connected to relays with finite capacity links. We provide communication strategies that achieve the best DMT of this relay system. We extend our work to cover cooperative systems with multiple sources and multiple destinations and show that the same limitation is still in effect. Our results suggest that while cooperative relaying is able to provide high spatial diversity for low multiplexing gains, it can never mimic a physical MIMO for large multiplexing gains.

Diversity gains and clustering in wireless relaying

We consider a wireless system consisting of one source, one destination and M relays. Assuming path loss and Rayleigh fading, we use the cutset upper bound to show that no matter where the relays are located, the maximum diversity one can obtain is M+1. However, one can achieve a higher diversity gain, namely /spl lfloor/(M+2/2)/sup 2//spl rfloor/, if /spl lfloor/M/2/spl rfloor/ of the relays are clustered with the source and /spl lceil/M/2/spl rceil/ with the destination. This result utilizes the observation that if two wireless nodes are very close, Rayleigh assumption breaks and the proper channel model is additive white Gaussian noise (AWGN). Hence to realize a virtual multiinput multioutput (MIMO) system, clustering is essential.

A Secure Communication Game With a Relay Helping the Eavesdropper

In this work, a four-terminal complex Gaussian network composed of a source, a destination, an eavesdropper, and a jammer relay is studied under two different set of assumptions: 1) The jammer relay does not hear the source transmission, and 2) The jammer relay is causally given the source message. In both cases, the jammer relay assists the eavesdropper and aims to decrease the achievable secrecy rates. The source, on the other hand, aims to increase it. To help the eavesdropper, the jammer relay can use pure relaying and/or send interference. Each of the problems is formulated as a two-player, noncooperative, zero-sum continuous game. Assuming Gaussian strategies at the source and the jammer relay in the first problem, the Nash equilibrium is found and shown to be achieved with mixed strategies in general. The optimal cumulative distribution functions (cdfs) for the source and the jammer relay that achieve the value of the game, which is the Nash equilibrium secrecy rate, are found. For the second problem, the Nash equilibrium solution is found and the results are compared to the case when the jammer relay is not informed about the source message.

On channel output feedback in deterministic interference channels

In this paper, we study the effect of channel output feedback on the sum capacity in a two-user symmetric deterministic interference channel. We find that having a single feedback link from one of the receivers to its own transmitter results in the same sum capacity as having a total of 4 feedback links from both the receivers to both the transmitters. Hence, from the sum capacity point of view, the three additional feedback links are not helpful. We also consider a half-duplex feedback model, where the forward and the feedback resources are symmetric and time-shared. Surprisingly, we find that there is no gain in sum-capacity with feedback in a half-duplex feedback model, when interference links have more capacity than direct links.

Diversity-Multiplexing Tradeoff in Multiple-Antenna Relay Systems

We study the diversity-multiplexing tradeoff (DMT) for the full-duplex relay channel when the source and the destination have multiple antennas, and the relay has 1 or more. We find DMT upper bounds and investigate the achievable performance of decode-and-forward (DF), partial decode-and-forward (PDF), and compress-and-forward (CF) protocols. We study the effect of increased degrees of freedom in the direct link and the source-relay channel when multiple antennas are introduced. Our results suggest that while DF is DMT optimal when all terminals have one antenna each, it cannot maintain its good performance when the degrees of freedom in the direct link is increased. CF proves to be a more robust strategy, which works well in multi-antenna scenarios studied in this paper. We also extend our results for clustered relay networks to find DMT upper bounds and achievable performances