Min-Chul Ju

Outage Probability and Optimum Power Allocation for Analog Network Coding

We study the analog network coding (ANC), which is a well-known amplify-and-forward (AF)-based bidirectional protocol, for a bidirectional network consisting of two different sources and a relay. In this protocol, the two sources exchange information with the help of the relay during two time slots in a half-duplex mode. For this system, we first derive a tight lower bound of outage probability, which is very close to the exact outage probability in the whole signal-to-noise ratio (SNR) range irrespective of the values of channel variances. Using the tight lower bound, we obtain finite-SNR diversity-multiplexing tradeoff of the ANC protocol. Furthermore, we propose an optimum power allocation scheme, which simultaneously minimizes the outage probability and maximizes the total mutual information of the ANC protocol.

Error Performance Analysis of BPSK Modulation in Physical-Layer Network-Coded Bidirectional Relay Networks

We analyze the error performance of the physical-layer network coding (PNC) protocol without channel coding in bidirectional relay networks for binary phase shift keying (BPSK) over Rayleigh fading channels. It is assumed that a bidirectional relay network consists of two sources and a relay, where each node has a single antenna and operates in a half-duplex mode, and the PNC over finite GF(2) is employed. In this system, since the maximum-likelihood (ML) detection metric of the multiple access channel (MAC) at the relay is given by the sum of two exponential functions, it is not possible to utilize the classical Euclidean distance rule. To make the performance analysis tractable, we approximate the ML detection metric by adopting the max-log approximation. Then we derive tight upper and lower bounds in closed form for the average symbol error probability of the MAC at the relay. Finally, we obtain tight upper and lower bounds in closed form for the end-to-end average bit-error rate (BER).

Relay Selection with ANC and TDBC Protocols in Bidirectional Relay Networks

We study relay selection (RS) with the analog network coding (ANC) and time division broadcast (TDBC), which are two major amplify-and-forward (AF)-based protocols in bidirectional relay networks. We consider a bidirectional network consisting of two different end-sources and multiple relays, where each terminal has a single antenna and operates in a half-duplex mode. In this network, a single best relay is selected depending on channel conditions to help bidirectional communication between the two end-sources. Specifically, we first consider RS schemes for the ANC and TDBC protocols based on a max-min criterion to minimize the outage probabilities. Then, for the RS in the ANC protocol, we derive a closed-form expression of the outage probability; for the RS in the TDBC protocol, we derive a one-integral form of the outage probability and its lower bound in closed-form. Numerical results confirm that the closed-form expression of the ANC protocol and the one-integral form of the TDBC protocol are very accurate, and that the closed-form lower bound of the TDBC protocol is also tight.

ML performance analysis of the decode-and-forward protocol in cooperative diversity networks

We analyze the maximum-likelihood (ML) performance of the decode-and-forward protocol in a cooperative diversity network which consists of a source, a relay, and a destination with a direct path signal, but which is not equipped with cyclicredundancy- check (CRC) codes. In this system, due to a symbol error at the relay, the ML receiver at the destination needs to consider all the possible symbol detection scenarios at the relay as well as at the destination. Therefore, the ML detection metric is given by a linear combination of exponential functions, which prevents the use of the classical minimum Euclidean distance rule. Adopting the max-log approximation, we approximate the ML detection rule which makes the ML performance analysis tractable. In order to facilitate the derivation of decision regions, we simplify the ML detection rule in the two-dimensional real space such that two metric values of two adjacent constellation points are sequentially compared. Then we obtain decision regions in a form without union and intersection. Finally, based on the decision regions, we derive a very accurate closedform BER approximation for M-pulse amplitude modulation (PAM) and M-quadrature amplitude modulation (QAM). The obtained BER expression can serve as the error performance upper-bound of the decode-and-forward protocol in cooperative diversity networks.

Outage Probability and Optimum Combining for Time Division Broadcast Protocol

Time division broadcasting (TDBC) is a well-known bidirectional protocol. In this protocol, two sources exchange information with the help of a relay terminal. For amplify-and-forward (AF)-based TDBC, we first derive a tight lower bound of the outage probability in closed-form, and it is very close to the exact outage probability in the whole signal-to-noise ratio (SNR) range irrespective of the values of channel variances. Using the tight lower bound, diversity-multiplexing tradeoff of the TDBC protocol is obtained for finite-SNR. Furthermore, we investigate how to optimize the TDBC protocol; specifically, an optimum method to combine the received signals at the relay terminal is developed. This method minimizes the outage probability and maximizes the total mutual information of the TDBC protocol at the same time.

Exact BER analysis of distributed alamouti's code for cooperative diversity networks

We analyze the bit-error rate (BER) performance of the distributed Alamoutis code for cooperative diversity networks consisting of a source, two relays and a destination node over Rayleigh fading channels. It is assumed that the relays adopt the amplify-and-forward protocol. Firstly, assuming the existence of the direct path component from the source to the destination, we derive the exact BER expression in a one-integral form for M-pulse amplitude modulation (PAM) and M-quadrature amplitude modulation (QAM) constellations. We also present a series expansion of a very accurate BER approximation, which does not require any numerical calculation, and we prove this series is convergent. Secondly, considering the system where the direct path component does not exist, we obtain the exact BER expression in a one-integral form and a series expansion of the exact BER expression. Numerical results confirm that the two exact BER expressions in a one-integral form perfectly match the simulation results and the two series expressions of BER are very accurate, even with a small truncation window.

Joint Relay-and-Antenna Selection in Multi-Antenna Relay Networks

For the decode-and-forward protocol in relay networks, opportunistic relaying (OR) and selection cooperation (SC) are two major relay selection schemes, which have been studied only for single antenna terminals. We study OR and SC in a multi-antenna relay network where each terminal has multiple antennas. To fully exploit multiple antennas without incurring high feedback overhead, we adopt transmit antenna selection (TAS). Specifically, we first propose two joint relay-and-antenna selection schemes which combine OR and SC, respectively, with TAS: joint OR-TAS and joint SC-TAS. For each joint selection scheme, a single best transmit antenna at the source, a single best relay, and a single best transmit antenna at this selected relay are jointly determined in an optimum sense. In this network, at the first time slot, the selected antenna at the source transmits a symbol to the selected relay; at the second time slot, the selected antenna at the selected relay retransmits the detected symbol to the destination. We derive the outage probability of joint OR-TAS. Also, we obtain the outage probability of joint SC-TAS by proving that the outage probability of joint SC-TAS is identical to that of joint OR-TAS.

Channel estimation and DC-offset compensation schemes for frequency-hopped Bluetooth networks

This article is concerned with a Bluetooth receiver with the channel estimation and DC-offset estimation. Each of the Bluetooth devices in the connection state knows the access codes used in the ad-hoc networks, which is utilized as a reference signal for the parameter estimation. The proposed estimators can be implemented without degradation of frame and spectral efficiency thanks to using the access code specified for the Bluetooth system.

Joint Relay Selection and Relay Ordering for DF-Based Cooperative Relay Networks

Relay selection (RS) has widely been studied for both decode-and-forward (DF) and amplify-and-forward (AF) protocols, and relay ordering (RO) was recently proposed for the AF protocol only . The two strategies, RS and RO, have been individually shown to be very effective to enhance the performance of cooperative relay networks. In this letter, we first discuss the fundamental difference of the two schemes and investigate an important tradeoff in terms of spectral efficiency and energy efficiency between RS and RO. Specifically, RS is more spectrally efficient, whereas RO can be more efficient in energy consumption. Then we demonstrate that indeed RS and RO generally have different outage performance and may complement each other depending on channel conditions. To optimize the outage performance, therefore, we combine the two strategies, RS and RO, and we propose joint RS-RO, followed by exact outage probability derivation of the joint RS-RO in closed-form. Finally, we obtain some interesting insights into the issue of selecting efficient transmission schemes between RS and RO.

Joint Relay Selection and Opportunistic Source Selection in Bidirectional Cooperative Diversity Networks

Relay selection (RS) has widely been studied in the literature, and an opportunistic source selection (OSS) protocol with a single relay has recently been proposed. Since RS and OSS could individually improve the performance of cooperative diversity networks, optimum combining of RS and OSS is an interesting topic. In this paper, we optimally combine RS and OSS in the sense that the mutual information is maximized, and we propose a joint RS-OSS protocol in an amplify-and-forward (AF)-based bidirectional cooperative diversity network, which consists of two different end-sources and multiple relays. In this network, a best source is selected to transmit data to the other source with the help of a selected best relay in an opportunistic manner, depending on channel conditions. Then, to show the performance of the joint RS-OSS, we derive the outage probability and the average bit error rate (BER) for M-quadrature amplitude modulation (QAM). Numerical results confirm that the derived outage probability and the average BER expressions are very accurate. In addition, we find that the proposed joint RS-OSS considerably outperforms both RS and OSS in terms of outage probability and average BER and that the performance is highly dependent on relay location. The obtained outage probability and average BER will help the design of reliable bidirectional cooperative diversity networks in determining the system parameters, such as relay location, and the transmission power at source and relay.