arXiv subjects

Shahab Oveis Gharan

Publications and source records attributed to Shahab Oveis Gharan.

15 recordsLinked to original sources

arXiv2025

Architecture Design for Rise/Fall Asymmetry Glitch Minimization in Current-Steering DACs

Current-steering digital-to-analog converter (DAC) is a prominent architecture that is commonly used in high-speed applications such as optical communications. One of the shortcomings of this architecture is the output glitches that are input dependent and degrade the dynamic performance of the DAC. We investigate DAC glitches that arise from asymmetry in the fall/rise response of DAC switches. We formulate a glitch metric that defines the overall DAC performance, which is then used to find a novel DAC weighting scheme. Numerical simulations show that the proposed architecture can potentially provide a significant performance advantage compared to the segmented structure.

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arXiv2025

Timing-Error Optimized Architecture for Current-Steering DACs

We propose a novel digital-to-analog converter (DAC) weighting architecture that statistically minimizes the distortion caused by random timing mismatches among current sources. To decode the DAC input codewords into corresponding DAC switches, we present three algorithms with varying computational complexities. We perform high-level Matlab simulations to illustrate the dynamic performance improvement over the segmented structure.

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arXiv2025

Current-Steering DAC Architecture Design for Amplitude Mismatch Error Minimization

We propose a novel digital-to-analog converter (DAC) weighting architecture that statistically minimizes the distortion caused by random current mismatches. Unlike binary, thermometer-coded, and segmented DACs, the current weights of the proposed architecture are not an integer power of 2 or any other integer number. We present a heuristic algorithm for a static mapping of DAC input codewords into corresponding DAC switches. High-level Matlab simulations are performed to illustrate the static performance improvement over the segmented structure.

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arXiv2009

Diversity-Multiplexing Tradeoff in Multi-Antenna Multi-Relay Networks: Improvements and Some Optimality Results

This paper investigates the benefits of Amplify-and-Forward (AF) relaying in the setup of multi-antenna wireless networks. The concept of Random Sequential (RS) relaying is previously introduced in the literature and showed that it achieves the maximum diversity gain in a general multi-antenna network. Here, we show that random unitary matrix multiplication at the relay nodes empowers the RS scheme to achieve a better Diversity-Multiplexing Tradeoff (DMT) as compared to the traditional AF relaying. First, we study the case of a multi-antenna full-duplex single-relay two-hop network, for which we show that the RS achieves the optimum DMT. Applying this result, we derive a new achievable DMT for the case of multi-antenna half-duplex parallel relay network. Interestingly, it turns out that the DMT of the RS scheme is optimum for the case of multi-antenna two parallel non-interfering half-duplex relays. Next, we show that random unitary matrix multiplication also improves the DMT of the Non-Orthogonal AF relaying scheme in the case of a multi-antenna single relay channel. Finally, we study the general case of multi-antenna full-duplex relay networks and derive a new lower-bound on its DMT using the RS scheme.

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arXiv2009

Multiplexing Gain of Amplify-Forward Relaying in Wireless Multi-Antenna Relay Networks

This paper studies the general multi-antenna multiple-relay network. Every two nodes of the network are either connected together through a Rayleigh fading channel or disconnected. We study the ergodic capacity of the network in the high SNR regime. We prove that the traditional amplify-forward relaying achieves the maximum multiplexing gain of the network. Furthermore, we show that the maximum multiplexing gain of the network is equal to the minimum vertex cut-set of the underlying graph of the network, which can be computed in polynomial time in terms of the number of network nodes. Finally, the argument is extended to the multicast and multi-access scenarios.

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arXiv2009

Real Interference Alignment: Exploiting the Potential of Single Antenna Systems

In this paper, the available spatial Degrees-Of-Freedoms (DOF) in single antenna systems is exploited. A new coding scheme is proposed in which several data streams having fractional multiplexing gains are sent by transmitters and interfering streams are aligned at receivers. Viewed as a field over rational numbers, a received signal has infinite fractional DOFs, allowing simultaneous interference alignment of any finite number of signals at any finite number of receivers. The coding scheme is backed up by a recent result in the field of Diophantine approximation, which states that the convergence part of the Khintchine-Groshev theorem holds for points on non-degenerate manifolds. The proposed coding scheme is proved to be optimal for three communication channels, namely the Gaussian Interference Channel (GIC), the uplink channel in cellular systems, and the $X$ channel. It is proved that the total DOF of the $K$-user GIC is $\frac{K}{2}$ almost surely, i.e. each user enjoys half of its maximum DOF. Having $K$ cells and $M$ users within each cell in a cellular system, the total DOF of the uplink channel is proved to be $\frac{KM}{M+1}$. Finally, the total DOF of the $X$ channel with $K$ transmitters and $M$ receivers is shown to be $\frac{KM}{K+M-1}$.

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arXiv2009

Real Interference Alignment with Real Numbers

A novel coding scheme applicable in networks with single antenna nodes is proposed. This scheme converts a single antenna system to an equivalent Multiple Input Multiple Output (MIMO) system with fractional dimensions. Interference can be aligned along these dimensions and higher Multiplexing gains can be achieved. Tools from the field of Diophantine approximation in number theory are used to show that the proposed coding scheme in fact mimics the traditional schemes used in MIMO systems where each data stream is sent along a direction and alignment happens when several streams arrive at the same direction. Two types of constellation are proposed for the encoding part, namely the single layer constellation and the multi-layer constellation. Using the single layer constellation, the coding scheme is applied to the two-user $X$ channel and the three-user Gaussian Interference Channel (GIC). In case of the two-user $X$ channel, it is proved that the total Degrees-of-Freedom (DOF), i.e. 4/3, of the channel is achievable almost surely. This is the first example in which it is shown that a time invariant single antenna system does not fall short of achieving its total DOF. Using the multi-layer constellation, the coding scheme is applied to the symmetric three-user GIC. Achievable DOFs are derived for all channel gains. As a function of the channel gain, it is observed that the DOF is everywhere discontinuous.

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arXiv2009

A New Achievable Rate for the Gaussian Parallel Relay Channel

Schein and Gallager introduced the Gaussian parallel relay channel in 2000. They proposed the Amplify-and-Forward (AF) and the Decode-and-Forward (DF) strategies for this channel. For a long time, the best known achievable rate for this channel was based on the AF and DF with time sharing (AF-DF). Recently, a Rematch-and-Forward (RF) scheme for the scenario in which different amounts of bandwidth can be assigned to the first and second hops were proposed. In this paper, we propose a \emph{Combined Amplify-and-Decode Forward (CADF)} scheme for the Gaussian parallel relay channel. We prove that the CADF scheme always gives a better achievable rate compared to the RF scheme, when there is a bandwidth mismatch between the first hop and the second hop. Furthermore, for the equal bandwidth case (Schein's setup), we show that the time sharing between the CADF and the DF schemes (CADF-DF) leads to a better achievable rate compared to the time sharing between the RF and the DF schemes (RF-DF) as well as the AF-DF.

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arXiv2008

Cooperative Strategies for the Half-Duplex Gaussian Parallel Relay Channel: Simultaneous Relaying versus Successive Relaying

This study investigates the problem of communication for a network composed of two half-duplex parallel relays with additive white Gaussian noise. Two protocols, i.e., \emph{Simultaneous} and \emph{Successive} relaying, associated with two possible relay orderings are proposed. The simultaneous relaying protocol is based on \emph{Dynamic Decode and Forward (DDF)} scheme. For the successive relaying protocol: (i) a \emph{Non-Cooperative} scheme based on the \emph{Dirty Paper Coding (DPC)}, and (ii) a \emph{Cooperative} scheme based on the \emph{Block Markov Encoding (BME)} are considered. Furthermore, the composite scheme of employing BME at one relay and DPC at another always achieves a better rate when compared to the \emph{Cooperative} scheme. A \emph{"Simultaneous-Successive Relaying based on Dirty paper coding scheme" (SSRD)} is also proposed. The optimum ordering of the relays and hence the capacity of the half-duplex Gaussian parallel relay channel in the low and high signal-to-noise ratio (SNR) scenarios is derived. In the low SNR scenario, it is revealed that under certain conditions for the channel coefficients, the ratio of the achievable rate of the simultaneous relaying based on DDF to the cut-set bound tends to be 1. On the other hand, as SNR goes to infinity, it is proved that successive relaying, based on the DPC, asymptotically achieves the capacity of the network.

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arXiv2008

On the Diversity-Multiplexing Tradeoff in Multiple-Relay Network

This paper studies the setup of a multiple-relay network in which $K$ half-duplex multiple-antenna relays assist in the transmission between a/several multiple-antenna transmitter(s) and a multiple-antenna receiver. Each two nodes are assumed to be either connected through a quasi-static Rayleigh fading channel, or disconnected. We propose a new scheme, which we call \textit{random sequential} (RS), based on the amplify-and-forward relaying. We prove that for general multiple-antenna multiple-relay networks, the proposed scheme achieves the maximum diversity gain. Furthermore, we derive diversity-multiplexing tradeoff (DMT) of the proposed RS scheme for general single-antenna multiple-relay networks. It is shown that for single-antenna two-hop multiple-access multiple-relay ($K>1$) networks (without direct link between the transmitter(s) and the receiver), the proposed RS scheme achieves the optimum DMT. However, for the case of multiple access single relay setup, we show that the RS scheme reduces to the naive amplify-and-forward relaying and is not optimum in terms of DMT, while the dynamic decode-and-forward scheme is shown to be optimum for this scenario.

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arXiv2008

Optimal Coding for the Erasure Channel with Arbitrary Alphabet Size

An erasure channel with a fixed alphabet size $q$, where $q \gg 1$, is studied. It is proved that over any erasure channel (with or without memory), Maximum Distance Separable (MDS) codes achieve the minimum probability of error (assuming maximum likelihood decoding). Assuming a memoryless erasure channel, the error exponent of MDS codes are compared with that of random codes and linear random codes. It is shown that the envelopes of all these exponents are identical for rates above the critical rate. Noting the optimality of MDS codes, it is concluded that both random codes and linear random codes are exponentially optimal, whether the block sizes is larger or smaller than the alphabet size.

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arXiv2008

Path Diversity over Packet Switched Networks: Performance Analysis and Rate Allocation

Path diversity works by setting up multiple parallel connections between the end points using the topological path redundancy of the network. In this paper, \textit{Forward Error Correction} (FEC) is applied across multiple independent paths to enhance the end-to-end reliability. Network paths are modeled as erasure Gilbert-Elliot channels. It is known that over any erasure channel, \textit{Maximum Distance Separable} (MDS) codes achieve the minimum probability of irrecoverable loss among all block codes of the same size. Based on the adopted model for the error behavior, we prove that the probability of irrecoverable loss for MDS codes decays exponentially for an asymptotically large number of paths. Then, optimal rate allocation problem is solved for the asymptotic case where the number of paths is large. Moreover, it is shown that in such asymptotically optimal rate allocation, each path is assigned a positive rate \textit{iff} its quality is above a certain threshold. The quality of a path is defined as the percentage of the time it spends in the bad state. Finally, using dynamic programming, a heuristic suboptimal algorithm with polynomial runtime is proposed for rate allocation over a finite number of paths. This algorithm converges to the asymptotically optimal rate allocation when the number of paths is large. The simulation results show that the proposed algorithm approximates the optimal rate allocation (found by exhaustive search) very closely for practical number of paths, and provides significant performance improvement compared to the alternative schemes of rate allocation.

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arXiv2007

Channel Code Design with Causal Side Information at the Encoder

The problem of channel code design for the $M$-ary input AWGN channel with additive $Q$-ary interference where the sequence of i.i.d. interference symbols is known causally at the encoder is considered. The code design criterion at high SNR is derived by defining a new distance measure between the input symbols of the Shannon's \emph{associated} channel. For the case of binary-input channel, i.e., M=2, it is shown that it is sufficient to use only two (out of $2^Q$) input symbols of the \emph{associated} channel in the encoding as far as the distance spectrum of code is concerned. This reduces the problem of channel code design for the binary-input AWGN channel with known interference at the encoder to design of binary codes for the binary symmetric channel where the Hamming distance among codewords is the major factor in the performance of the code.

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arXiv2007

Optimum Diversity-Multiplexing Tradeoff in the Multiple Relays Network

In this paper, a multiple-relay network in considered, in which $K$ single-antenna relays assist a single-antenna transmitter to communicate with a single-antenna receiver in a half-duplex mode. A new Amplify and Forward (AF) scheme is proposed for this network and is shown to achieve the optimum diversity-multiplexing trade-off curve.

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arXiv2007

Asymptotic Analysis of Amplify and Forward Relaying in a Parallel MIMO Relay Network

This paper considers the setup of a parallel MIMO relay network in which $K$ relays, each equipped with $N$ antennas, assist the transmitter and the receiver, each equipped with $M$ antennas, in the half-duplex mode, under the assumption that $N\geq{M}$. This setup has been studied in the literature like in \cite{nabar}, \cite{nabar2}, and \cite{qr}. In this paper, a simple scheme, the so-called Incremental Cooperative Beamforming, is introduced and shown to achieve the capacity of the network in the asymptotic case of $K\to{\infty}$ with a gap no more than $O(\frac{1}{\log(K)})$. This result is shown to hold, as long as the power of the relays scales as $ω(\frac{\log^9(K)}{K})$. Finally, the asymptotic SNR behavior is studied and it is proved that the proposed scheme achieves the full multiplexing gain, regardless of the number of relays.

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