Masoud Ardakani

A more accurate one-dimensional analysis and design of irregular LDPC codes

We introduce a new one-dimensional (1-D) analysis of low-density parity-check (LDPC) codes on additive white Gaussian noise channels which is significantly more accurate than similar 1-D methods. Our method assumes a Gaussian distribution in message-passing decoding only for messages from variable nodes to check nodes. Compared to existing work, which makes a Gaussian assumption both for messages from check nodes and from variable nodes, our method offers a significantly more accurate estimate of convergence behavior and threshold of convergence. Similar to previous work, the problem of designing irregular LDPC codes reduces to a linear programming problem. However, our method allows irregular code design in a wider range of rates without any limit on the maximum variable-node degree. We use our method to design irregular LDPC codes with rates greater than 1/4 that perform within a few hundredths of a decibel from the Shannon limit. The designed codes perform almost as well as codes designed by density evolution.

Two-Way Amplify-and-Forward Multiple-Input Multiple-Output Relay Networks with Antenna Selection

Two new transmit/receive (Tx/Rx) antenna selection strategies are proposed and analyzed for two-way multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay networks. These two strategies select the best transmit and receive antennas at the two sources and the relay based on (i) minimizing the overall outage probability and (ii) maximizing the sum-rate. The performance of these selection strategies is quantified by deriving the overall outage probability, its high SNR approximation and the diversity order providing valuable insights into practical system-designs. Importantly, multiple relay and multiple user two-way relay network set-ups are also treated by proposing and analyzing (i) joint relay and antenna selection strategies, and (ii) joint user, relay and antenna selection strategies, respectively. Interestingly, our outage probability results reveal that the joint relay and antenna selection strategies achieve significant diversity and array gains over those of their single relay counterparts. In fact, the diversity orders of individual relayed-branches accumulate to yield the overall diversity of the multi-relay networks. For example, at 10-2 outage probability, the dual-antenna relay provides a 14 dB gain over a single-antenna relay, and having two dual-antenna relays improves the gain by another 5 dB. Moreover, the performance degradation due to practical transmission impairments (i) feedback delays, (ii) spatially-correlated fading and (iii) non-identically distributed fading is quantified. Impact of channel prediction to circumvent outdated channel state information for antenna selection due to feedback delay is also studied. All the derivations are validated through Monte-Carlo simulations.

Output-Threshold Multiple-Relay-Selection Scheme for Cooperative Wireless Networks

An output-threshold multiple-relay-selection (OT-MRS) scheme for dual-hop multibranch cooperative wireless networks is proposed. In this scheme, the first Lc (nonordered) relays are sequentially selected out of L relays such that the SNR of the maximal ratio combined Lc relayed paths and the direct path exceeds a preset threshold. Analytical results for the performance bounds are derived. The numerical results verify the analyses and show that OT-MRS outperforms optimal single-relay selection and generalized-selection-combining-based multiple relay-selection for low to moderately high SNRs. The proposed scheme provides more flexibility in utilizing bandwidth and spatial diversity in cooperative wireless networks.

Near-capacity coding in multicarrier modulation systems

We apply irregular low-density parity-check (LDPC) codes to the design of multilevel coded quadrature amplitude modulation (QAM) schemes for application in discrete multitone systems in frequency-selective channels. A combined Gray/Ungerboeck scheme is used to label each QAM constellation. The Gray-labeled bits are protected using an irregular LDPC code with iterative soft-decision decoding, while other bits are protected using a high-rate Reed-Solomon code with hard-decision decoding (or are left uncoded). The rate of the LDPC code is selected by analyzing the capacity of the channel seen by the Gray-labeled bits and is made adaptive by selective concatenation with an inner repetition code. Using a practical bit-loading algorithm, we apply this coding scheme to an ensemble of frequency-selective channels with Gaussian noise. Over a large number of channel realizations, this coding scheme provides an average effective coding gain of more than 7.5 dB at a bit-error rate of 10/sup -7/ and a block length of approximately 10/sup 5/ b. This represents a gap of approximately 2.3 dB from the Shannon limit of the additive white Gaussian noise channel, which could be closed to within 0.8-1.2 dB using constellation shaping.

Lifetime Analysis of Random Event-Driven Clustered Wireless Sensor Networks

Considering event-driven clustered wireless sensor networks, a probabilistic approach for analyzing the network lifetime is presented when events occur randomly over the network field. To this end, we first model the packet transmission rate of the sensors, using the theory of coverage processes and Voronoi tessellation. Then, the probability of achieving a given lifetime by individual sensors is found. This probability is then used to study the cluster lifetime. In fact, we find an accurate approximation for the probability of achieving a desired lifetime by a cluster. Our proposed analysis includes the effect of packet generation model, random deployment of sensors, dynamic cluster head assignment, data compression, and energy consumption model at the sensors. The analysis is presented for event-driven networks, but it comprises time-driven networks as a special case. Computer simulations are used to verify the results of our analysis.

Design of irregular LDPC codes with optimized performance-complexity tradeoff

The optimal performance-complexity tradeoff for error-correcting codes at rates strictly below the Shannon limit is a central question in coding theory. This paper proposes a numerical approach for the minimization of decoding complexity for long-block-length irregular low-density parity-check (LDPC) codes. The proposed design methodology is applicable to any binary-input memoryless symmetric channel and any iterative message-passing decoding algorithm with a parallel-update schedule. A key feature of the proposed optimization method is a new complexity measure that incorporates both the number of operations required to carry out a single decoding iteration and the number of iterations required for convergence. This paper shows that the proposed complexity measure can be accurately estimated from a density-evolution and extrinsic-information transfer chart analysis of the code. A sufficient condition is presented for convexity of the complexity measure in the variable edge-degree distribution; when it is not satisfied, numerical experiments nevertheless suggest that the local minimum is unique. The results presented herein show that when the decoding complexity is constrained, the complexity-optimized codes significantly outperform threshold-optimized codes at long block lengths, within the ensemble of irregular codes.

Performance Analysis of Zero-Forcing for Two-Way MIMO AF Relay Networks

Transmit/receive zero-forcing (ZF) is studied for multiple-input multiple-output (MIMO) amplify-and-forward (AF) two-way relay networks (TWRNs). Specifically, two sources employ transmit and receive ZF during two consecutive time-slots for transmission and reception, respectively, while the relay performs analog network coding. Each source then requires only the instantaneous respective source-to-relay channel knowledge, and hence, the complexity of practical implementation is significantly reduced. The performance of this system set-up is studied by deriving the upper and lower bounds of the overall outage probability, their high signal-to-noise ratio approximations and diversity order. To obtain valuable insights into practical MIMO TWRN implementation, the diversity-multiplexing trade-off is also quantified.

Performance Analysis Framework for Transmit Antenna Selection Strategies of Cooperative MIMO AF Relay Networks

The performance of three transmit antenna selection (TAS) strategies for dual-hop multiple-input-multiple-output (MIMO) ideal channel-assisted amplify-and-forward (AF) relay networks is analyzed. All channel fades are assumed to be Nakagami-m (integer m) fading. The source, relay, and destination are MIMO terminals. The optimal TAS and two suboptimal TAS strategies are considered. Since direct analysis of the end-to-end signal-to-noise ratio (e2e SNR) of the optimal TAS is intractable, a lower bound of the e2e SNR is derived. Its cumulative distribution function and the moment generating function (mgf) are derived and used to obtain the upper bounds of the outage probability and the average symbol error rate (SER). For the two suboptimal TAS strategies, we derive the exact mgfs of the e2e SNR and obtain accurate and efficient closed-form approximations for the outage probability and the average SER. The asymptotic outage probability and the average SER, which are exact in high SNR, are also derived, and they provide valuable insights into the system design parameters, such as diversity order and array gain. The exact outage probability, average SER, and their high SNR approximations are also derived for the optimal TAS when the direct path is ignored. The impact of outdated channel state information (CSI) on the performance of TAS is also studied. Specifically, the amount of performance degradation due to feedback delays is studied by deriving the asymptotic outage probability and the average SER and thereby quantifying the reduction of diversity order and array gain. Numerical and Monte Carlo simulation results are provided to analyze the system performance and verify the accuracy of our analysis.

Asymptotically-Exact Performance Bounds of AF Multi-Hop Relaying over Nakagami Fading

A new class of upper bounds on the end-to-end signal-to-noise ratio (SNR) of channel-assisted amplify-and-forward (AF) multi-hop (N ≥ 2) relay networks is presented. It is the half-harmonic mean of the minimum of the first P ≥ 0 hop SNRs and the minimum of the remaining N-P hop SNRs. The parameter P varies between 0 to N and may be chosen to provide the tightest bound. The closed-form cumulative distribution function and moment generating function are derived for independent and non-identically distributed Rayleigh fading and for independent and identically distributed Nakagami-m fading, where m is an integer. The resulting outage probability and the average symbol error rate bounds are asymptotically-exact. The asymptotic-exactness holds for any 0 ≤ P ≤ N. As applications, two cases of multi-hop multi-branch relay networks (i) the best branch selection and (ii) maximal ratio combining reception are treated. Numerical results are provided to verify the comparative performance against the existing bounds.

Joint Relay and Antenna Selection for Dual-Hop Amplify-and-Forward MIMO Relay Networks

Four joint relay and antenna selection strategies for dual-hop amplify-and-forward (AF) multiple-input multiple-output relay networks are studied. Two of them require full channel state information (CSI) whereas the other two require only partial CSI. The relays are either channel-assisted AF or fixed-gain AF type. The first joint selection strategy involves choosing the best relay and the best single transmit antennas at the source and the relay. The second strategy jointly involves choosing the best relay and the best single transmit/receive antenna pairs at the source-to-relay and relay-to-destination channels. Moreover, two partial selection strategies, which can be used when the global CSI is not available, are also proposed and analyzed. In order to quantify the system performance analytically, the exact outage probability of all selection strategies is derived in closed-form. Direct insights into the system-design are obtained by deriving the asymptotic outage probability, asymptotic average symbol error rate, diversity order and array gain.