Shama N. Islam

Error performance analysis of decode-and-forward and amplify-and-forward multi-way relay networks with binary phase shift keying modulation

In this study, we analyse the error performance of decode and forward (DF) and amplify and forward (AF) multi-way relay networks (MWRNs). The authors consider a MWRN with pair-wise data exchange protocol using binary phase shift keying (BPSK) modulation in both additive white Gaussian noise (AWGN) and Rayleigh fading channels. The authors quantify the possible error events in an L-user DF or AF MWRN and derive accurate asymptotic bounds on the probability for the general case that a user incorrectly decodes the messages of exactly k (k ∈ [1, L − 1]) users. They show that at high signal-to-noise ratio (SNR), the higher order error events (k ≥ 3) are less probable in AF MWRN, but all error events are equally probable in a DF MWRN. They derive the average BER of a user in a DF or AF MWRN in both AWGN and Rayleigh fading channels under high SNR conditions. Simulation results validate the correctness of the derived expressions. The authors results show that at medium to high SNR, DF MWRN provides better error performance than AF MWRN in AWGN channels even with a large number of users (e.g. L = 100). Whereas, AF MWRN outperforms DF MWRN in Rayleigh fading channels even for much smaller number of users (e.g. L > 10).

A novel user pairing scheme for functional decode-and-forward multi-way relay network

In this paper, we consider a functional decode and forward (FDF) multi-way relay network (MWRN) where a common user facilitates each user in the network to obtain messages from all other users. We propose a novel user pairing scheme, which is based on the principle of selecting a common user with the best average channel gain. This allows the user with the best channel conditions to contribute to the overall system performance. Assuming lattice code based transmissions, we derive upper bounds on the average common rate and the average sum rate with the proposed pairing scheme. Considering M -ary quadrature amplitude modulation with square constellation as a special case of lattice code transmission, we derive asymptotic average symbol error rate (SER) of the MWRN. We show that in terms of the achievable rates, the proposed pairing scheme outperforms the existing pairing schemes under a wide range of channel scenarios. The proposed pairing scheme also has lower average SER compared to existing schemes. We show that overall, the MWRN performance with the proposed pairing scheme is more robust, compared to existing pairing schemes, especially under worst case channel conditions when majority of users have poor average channel gains.

Error propagation in a multi-way relay channel

This paper studies the error propagation phenomenon for a multi-way relay channel based on binary phase shift keying (BPSK) modulation and network coding in the physical layer. Though physical layer network coding enhances the throughput of a multi-way relay system by reducing number of time slots, its error performance can be highly degraded since decision about a users message depends on previous decisions. In this paper, the error probability of a multi-way relay system is examined through both analytical and numerical methods. We show that the system performance is significantly controlled by signal power and number of users accessing the single relay. Based on numerical analysis, the critical number of users to limit the error rate within an acceptable upper bound is found.

Optimal User Pairing to Improve the Sum Rate of a Pairwise AF Multi-Way Relay Network

In this letter, we propose a novel user pairing scheme for improving the average sum rate in an amplify and forward (AF) multi-way relay network (MWRN). We consider generalized lattice code based transmissions and derive upper bounds on the common rate and sum rate with the proposed scheme. We prove that pairing each user with the maximum average channel gain user is the optimal pairing scheme for an AF MWRN in terms of the average sum rate. Our results show that improving the overall channel conditions of the users results in greater benefits in terms of the average common rate and sum rate for the proposed pairing scheme, compared to the existing scheme.

Joint decoding: Extracting the correlation among user pairs in a multi-way relay channel

This paper describes a novel mechanism for joint decoding of the network coded symbols in a multi-way relay node. The mechanism, based on belief propagation algorithm, utilizes the correlation between adjacent network coded symbols to minimize the error propagation problem significantly, compared with previous methods. In case of increasing degree of asynchrony, disjoint decoding exhibits poorer error performance, whereas joint decoding helps to maintain the performance level close to that in the synchronous case both in additive white Gaussian noise and fading channels. Thus, this method adds robustness to the multi-way relay channel against channel imperfections like asynchronism and fading in practical propagation environments.

A novel pairing scheme to reduce error propagation in an amplify and forward multi-way relay network

In this paper, we propose a novel user pairing scheme to reduce the error propagation in an amplify and forward (AF) based multi-way relay network (MWRN). We consider a user pairing scheme, where, a common user is chosen based on its average channel gain to form pairs with every other user in the MWRN. We show that choosing the common user as the user with the minimum average channel gain reduces the contribution of the interference components from the common users signal in the extracted signals of other users. This leads to better bit error rate (BER) performance for all other users. For the common user, the BER improves at high SNR but it degrades at low SNR. The results show that the proposed pairing scheme outperforms the existing pairing scheme in terms of average BER of different users at high SNR.

Achievable rate and error performance of an amplify and forward multi-way relay network in the presence of imperfect channel estimation

In this paper, we investigate the impact of channel estimation error on the achievable common rate and error performance of amplify and forward (AF) multi-way relay networks (MWRNs). Assuming lattice codes with large dimensions, we provide the analytical expressions for the end-to-end SNR at the users and obtain upper bounds on the achievable common rate for an AF MWRN. Moreover, considering binary phase shift keying (BPSK) modulation as the simplest case of lattice codes, we obtain the average bit error rate (BER) for a user in an AF MWRN. The analysis shows that the average BER is a linearly increasing function and the achievable common rate is a linearly decreasing function of the channel estimation error. On the other hand, the average BER decreases and the achievable common rate increases with increasing correlation between the true and the estimated channel. Also, we observe that the AF protocol is robust against increasing number of users in terms of error performance. We show that when the decoding user has better channel conditions compared to other users, AF relaying gives a better error performance and common rate. Finally, simulation results are provided to verify the validity of our analysis.

Joint user decoding: A technique to enhance the benefits of coding in a multi-way relay channel

In this paper, a comparative analysis between joint and disjoint user decoding of the network and channel coded symbols in a multi-way relay channel is presented. The joint user decoding mechanism implements belief propagation algorithm to utilize the correlation between adjacent network coded symbols of user pairs, whereas, disjoint decoding disregards this correlation. This feature enables joint user decoding to support larger number of users than disjoint decoding in synchronous and asynchronous, additive white Gaussian noise and fading channels. Even, this novel mechanism allows almost the same level of average bit error rate performance for small and large number of users in asynchronous fading channel. Thus, to maximize the benefits of channel coding in practical propagation environments, joint user decoding in the relay node is essential.

Error Performance Analysis of a Clustered Multiway Relay Network

In this paper, we propose a new clustered structure for a multiway relay network (MWRN) with G clusters, N users per cluster, one intracluster relay per cluster, and a single intercluster relay. The proposed structure allows private information exchange among users within a certain cluster through the corresponding intracluster relay and only public information exchange among users in different clusters through the intercluster relay. In this paper, we quantify the dominating error events in the proposed clustered MWRN and derive the expressions for the probability of these error events. Then, we use these expressions to derive the average bit error rate (BER) of a clustered MWRN. It is shown that clustering in an MWRN improves the error performance by reducing the number of dominating error events and, in effect, reducing error propagation, compared with the nonclustered counterpart. The analysis proves that the average BER of a clustered MWRN is minimized when the number of clusters and the number of users per cluster are chosen to be the closest possible factors of the total number of users, i.e., L=GN. Finally, numerical simulation results are provided to verify the validity of the analysis.

Characterization of dispersion properties of silicon nanowire considering different core geometry

Silicon nanowires on silica cladding have been simulated using finite element method in this paper. The transverse and longitudinal electric field patterns are analyzed and it has been observed that a smaller core dimension results in a larger longitudinal field. Also, dispersion engineering through configuring the nanowire structure has been discussed. It is found that a smaller core dimension would result in a larger dispersion. Method of achieving zero dispersion in either infrared or optical communication region has also been suggested.