Mehdi Torbatian

On the design of delay-tolerant distributed space-time codes with minimum length

The construction of distributed space-time codes for asynchronous relays is considered. A novel algebraic structure is proposed and shown to achieve full diversity for arbitrary number of relays, arbitrary input alphabets, and arbitrary delay profiles among the relays. Unlike previously proposed delay tolerant schemes, the new design has minimum length which translates into smaller decoding complexity at the same transmission rate. Full-rate and full-diversity are achieved by the new designs with or without the use of guard intervals between successive transmissions. Simulation results confirm the mathematical analysis of the proposed codes.

Causal coding of multiple jointly Gaussian sources

We consider causal coding of three jointly Gaussian correlated sources, X1, X2, X3, with a given covariance matrix and determine an analytic closed-form formula for its total rate distortion function subject to Mean Square Error (MSE) distortion constraints when all sources need a positive rate to be represented. It is first shown that the optimal reproduction random variables are jointly Gaussian with the sources. A novel causal coding scheme is then proposed to achieve the total rate distortion function, in which each source is first whitened with respect to all previous original sources and then encoded via encoding a proper linear combination of the residues of the previous sources with respect to all available encoded sources and the residue of the current source with respect to all previous original sources. The more-and-less coding theorem in causal coding of correlated sources - when sources do not form a Markov chain as X1 → X2 → X3, under some conditions on sources and distortion, the more sources need to be encoded, the less total rate is required - is also investigated for Gaussian sources. For the underlying scenario in which all sources need a positive rate to be represented, it is proved that the more-and-less coding is always revealed for non-Markov chain Gaussian sources.

Asynchronous Interference Alignment

A constant three-user interference channel wherein users are not symbol synchronous is considered. A novel practical interference alignment scheme for this channel is proposed wherein aligning interfering signals at each receiver is performed with the help of asynchronous delays which inherently exist among the received signals at each receiver node. Due to the existence of asynchronism among the users, the underlying quasi-static flat fading links are converted into frequency selective and accordingly into time varying channels with correlated coefficients across the time. This solves the lack of channel variation required for interference alignment in quasi-static scenarios. It is proved that the proposed scheme achieves the total degrees of freedom equal to 3/2 of this channel almost surely in the limit of codewords length. Application of the proposed scheme is not limited to high signal to noise ratio (SNR) regime and it can be used in any range of SNR.

Diversity–Multiplexing Tradeoff of Asynchronous Decode-and-Forward Cooperative Networks

The diversity-multiplexing tradeoff (DMT) of a general two-hop asynchronous cooperative network is examined for orthogonal and nonorthogonal selection decode-and-forward relaying protocols. The transmitter nodes send pulse amplitude modulation signals, in which information symbols are linearly modulated by a shaping waveform to be sent to the destination. We consider two different cases of band-limited and time-limited shaping waveforms. In each case, the DMT performance of the asynchronous and synchronous networks is compared. It is proved that in the band-limited system scenario, the asynchronism does not incur any performance loss, and the same DMT as that of the corresponding synchronous network is obtained for both protocols. In the time-limited-system scenario, the bandwidth is expanded for high values of signal-to-noise ratio. In this scenario, it is observed that only asynchronous signaling is able to exploit the extra degrees of freedom of the channel. The asynchronous network in this scenario provides better DMT performances for both protocols throughout the range of the multiplexing gain.

Asynchronous interference alignment

A constant three-user interference channel wherein users are not symbol synchronous is considered. A novel practical interference alignment scheme for this channel is proposed wherein aligning interfering signals at each receiver is performed with the help of asynchronous delays which inherently exist among the received signals at each receiver node. Due to the existence of asynchronism among the users, the underlying quasi-static flat fading links are converted into frequency selective and accordingly into time varying channels with correlated coefficients across the time. This solves the lack of channel variation required for interference alignment in quasi-static scenarios. It is proved that the proposed scheme achieves the total degrees of freedom equal to 3/2 of this channel almost surely in the limit of codewords length. Application of the proposed scheme is not limited to high signal to noise ratio (SNR) regime and it can be used in any range of SNR.

Outage analysis of general asynchronous OFDM amplify-and-forward cooperative networks

The outage behavior of non-orthogonal amplify-and-forward (NAF) and orthogonal1 amplify-and-forward (OAF) relaying protocols over a general one hop asynchronous cooperative network is examined when orthogonal frequency division multiplexing (OFDM) is used to combat synchronization error among the relays. The relays are only allowed to preform linear transformations over the received signals. It is shown that the asynchronous OFDM OAF protocol provides the same DMT as that of the corresponding synchronous counterpart; however, the asynchronous OFDM NAF protocol provides better DMT than the one of traditional NAF for large length code words and throughout the range of the multiplexing gain. In particular, in a single relay network, the asynchronous OFDM NAF provides DMT as great as the one of a 2× 1 multiple input single output (MISO) channel.

DMT analysis of asynchronous OFDM amplify-and-forward cooperative networks

The outage behavior of amplify-and-forward (AF) relaying protocol over an asynchronous cooperative network is examined when orthogonal frequency division multiplexing (OFDM) is used to combat synchronization error among the transmitting nodes. We consider non-orthogonal AF (NAF) and orthogonal1 AF (OAF) protocols, respectively, over a single relay and a two relay cooperative network and analyze the diversity multiplexing gain tradeoff (DMT) in both scenarios. It is proved that, in the limit of code words length, the asynchronous network with the OAF protocol provides the same DMT as of the corresponding synchronous network; however in case of the NAF protocol, it provides the better DMT throughout the range of multiplexing gain and as great as the one of a 2 × 1 multiple input single output channel.

DMT Analysis of Asynchronous OFDM Decode-and-Forward Cooperative Networks

The outage behavior of decode-and-forward (DF) relaying protocol over an asynchronous cooperative network is examined when orthogonal frequency division multiplexing (OFDM) is used to combat synchronization error among the transmitting nodes. We consider non-orthogonal selection DF (NSDF) and orthogonal selection DF (OSDF) protocols, respectively, over a single relay and a two relay cooperative network and analyze the diversity multiplexing gain Tradeoff (DMT) in both scenarios. It is proved that asynchronous protocols provide diversity gains greater than or equal to the one of synchronous counterparts in the limit of code word length and throughout the range of multiplexing gain.