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Approximate Signal Processing
, 1997
"... It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tra ..."
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Cited by 516 (2 self)
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It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tradeoffs. One of the objectives of this paper is to suggest that there is the potential for developing a more formal approach, including utilizing current research in Computer Science on Approximate Processing and one of its central concepts, Incremental Refinement. Toward this end, we first summarize a number of ideas and approaches to approximate processing as currently being formulated in the computer science community. We then present four examples of signal processing algorithms/systems that are structured with these goals in mind. These examples may be viewed as partial inroads toward the ultimate objective of developing, within the context of signal processing design and implementation,...
Unitary SpaceTime Modulation for MultipleAntenna Communications in Rayleigh Flat Fading
 IEEE Trans. Inform. Theory
, 1998
"... Motivated by informationtheoretic considerations, we propose a signalling scheme, unitary spacetime modulation, for multipleantenna communication links. This modulation is ideally suited for Rayleigh fastfading environments, since it does not require the receiver to know or learn the propagation ..."
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Cited by 307 (19 self)
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Motivated by informationtheoretic considerations, we propose a signalling scheme, unitary spacetime modulation, for multipleantenna communication links. This modulation is ideally suited for Rayleigh fastfading environments, since it does not require the receiver to know or learn the propagation coefficients. Unitary spacetime modulation uses constellations of T \cross M spacetime signals {\Phi_l, l= 1,...L},where T represents the coherence interval during which the fading is approximately constant, and M > M . We design some multipleantenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding. We demonstrate that two antennas have a 6dB diversity gain over one antenna at 15db SNR.
Distributed spacetime coding in wireless relay networks
, 2006
"... We apply the idea of spacetime coding devised for multipleantenna systems to the problem of communications over a wireless relay network with Rayleigh fading channels. We use a twostage protocol, where in one stage the transmitter sends information and in the other, the relays encode their rece ..."
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Cited by 223 (15 self)
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We apply the idea of spacetime coding devised for multipleantenna systems to the problem of communications over a wireless relay network with Rayleigh fading channels. We use a twostage protocol, where in one stage the transmitter sends information and in the other, the relays encode their received signals into a “distributed ” linear dispersion (LD) code, and then transmit the coded signals to the receive node. We show that for high SNR, the pairwise error probability (PEP) behaves as (log P/P) min{T,R} , with T the coherence interval, that is, the number of symbol periods during which the channels keep constant, R the number of relay nodes, and P the total transmit power. Thus, apart from the log P factor, the system has the same diversity as a multipleantenna system with R transmit antennas, which is the same as assuming that the R relays can fully cooperate and have full knowledge of the transmitted signal. We further show that for a network with a large number of relays and a fixed total transmit power across the entire network, the optimal power allocation is for the transmitter to expend half the power and for the relays to collectively expend the other half. We also show that at low and high SNR, the coding gain is the same as that of a multipleantenna system with R antennas. However, at intermediate SNR, it can be quite different, which has implications for the design of distributed spacetime codes.
Outage analysis and optimal power allocation for multinode relay networks,” accepted for publication
 in IEEE Signal Processing letters
"... Abstract—In this letter, a novel approach for outage probability analysis of the multinode amplifyandforward relay network is provided. It is shown that the harmonic mean of two exponential random variables can be approximated, at high signaltonoise ratio (SNR), to be an exponential random varia ..."
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Cited by 29 (9 self)
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Abstract—In this letter, a novel approach for outage probability analysis of the multinode amplifyandforward relay network is provided. It is shown that the harmonic mean of two exponential random variables can be approximated, at high signaltonoise ratio (SNR), to be an exponential random variable. The single relay case considered before is a special case of our analysis. Based on that approximation, an outage probability bound is derived which proves to be tight at high SNR. Based on the derived outage probability bound, optimal power allocation is studied. Simulation results show a performance improvement, in terms of symbol error rate, of the optimal power allocation compared to the equal powerallocation scheme. Index Terms—Amplifyandforward protocol, outage probability, wireless relay networks. I.
Detection and estimation of improper complex random signals
 IEEE Trans. Inf. Theory
, 2005
"... Abstract—Nonstationary complex random signals are in general improper (not circularly symmetric), which means that their complementary covariance is nonzero. Since the Karhunen–Loève (KL) expansion in its known form is only valid for proper processes, we derive the improper version of this expansio ..."
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Cited by 25 (4 self)
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Abstract—Nonstationary complex random signals are in general improper (not circularly symmetric), which means that their complementary covariance is nonzero. Since the Karhunen–Loève (KL) expansion in its known form is only valid for proper processes, we derive the improper version of this expansion. It produces two sets of eigenvalues and improper observable coordinates. We then use the KL expansion to solve the problems of detection and estimation of improper complex random signals in additive white Gaussian noise. We derive a general result comparing the performance of conventional processing, which ignores complementary covariances, with processing that takes these into account. In particular, for the detection and estimation problems considered, we find that the performance gain, as measured by deflection and meansquared error (MSE), respectively, can be as large as a factor of 2. In a communications example, we show how this finding generalizes the result that coherent processing enjoys a 3dB gain over noncoherent processing. Index Terms—Detection, estimation, improper complex random signal, Karhunen–Loève (KL) expansion, nonstationary process, widely linear transformations. I.
Cooperative diversity in wireless relay networks with multipleantenna nodes
 In preparation
"... Abstract — In [1], the idea of distributed spacetime coding was proposed to achieve a degree of cooperative diversity in a wireless relay network. In particular, for a relay network with a singleantenna transmitter and receiver and R singleantenna relays, it was shown that the pairwise error prob ..."
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Cited by 19 (4 self)
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Abstract — In [1], the idea of distributed spacetime coding was proposed to achieve a degree of cooperative diversity in a wireless relay network. In particular, for a relay network with a singleantenna transmitter and receiver and R singleantenna relays, it was shown that the pairwise error probability (PEP) decays as () log P R, where P is the total transmit power. In this P paper, we extend the results to wireless relay networks where the transmitter, receiver, and/or relays may have multiple antennas. Assuming that the transmitter has M antennas, the receiver has N antennas, the sum of all the antennas at the relay nodes is R, and the coherence interval is long enough, we show that the log
ProtocolAware Design Criteria and Performance Analysis for Distributed SpaceTime Coding
"... Abstract — In this paper, we consider the design of distributed spacetime codes for wireless networks. Distributed spacetime coding (DSTC) can be achieved through node cooperation to emulate multiple transmit antennas. We derive the distributed spacetime codes design criteria for different scenari ..."
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Cited by 16 (9 self)
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Abstract — In this paper, we consider the design of distributed spacetime codes for wireless networks. Distributed spacetime coding (DSTC) can be achieved through node cooperation to emulate multiple transmit antennas. We derive the distributed spacetime codes design criteria for different scenarios based on the pairwise error probability (PEP) analysis. First, we consider the decodeandforward (DAF) protocol and prove that spacetime codes, designed to achieve full diversity and maximum coding gain in the MIMO channels, will achieve full diversity but not necessarily maximizing the coding gain if used with the DAF protocol. Next, we consider the amplifyandforward (AAF) protocol and prove that a spacetime code designed to achieve full diversity and maximum coding gain in MIMO channels will achieve the same if used with the AAF protocol. I.
Fingerprinting and Forensic Analysis of Multimedia
 ACM MULTIMEDIA
, 2004
"... One of the prime reasons movie and music studios have ignored the Internet for opennetworked multimedia content delivery, has been the lack of a technology that can support a secure digital rights management (DRM) system on a general purpose computer. The difficulty ..."
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Cited by 12 (2 self)
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One of the prime reasons movie and music studios have ignored the Internet for opennetworked multimedia content delivery, has been the lack of a technology that can support a secure digital rights management (DRM) system on a general purpose computer. The difficulty
Securing OFDM over Wireless TimeVarying Channels Using Subcarrier Overloading with Joint Signal Constellations
, 2009
"... A method of overloading subcarriers by multiple transmitters to secure OFDM in wireless timevarying channels is proposed and analyzed. The method is based on reverse piloting, superposition modulation, and joint decoding. It makes use of channel randomness, reciprocity, and fast decorrelation in sp ..."
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Cited by 8 (6 self)
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A method of overloading subcarriers by multiple transmitters to secure OFDM in wireless timevarying channels is proposed and analyzed. The method is based on reverse piloting, superposition modulation, and joint decoding. It makes use of channel randomness, reciprocity, and fast decorrelation in space to secure OFDM with low overheads on encryption, decryption, and key distribution. These properties make it a good alternative to traditional softwarebased information security algorithms in systems where the costs associated with such algorithms are an implementation obstacle. A necessary and sufficient condition for achieving information theoretic security in accordance with channel and system parameters is derived. Security by complexity is assessed for cases where the condition for information theoretic security is not satisfied. In addition, practical means for implementing the method are derived including generating robust joint constellations, decoding data with low complexity, and mitigating the effects of imperfections due to mobility, power control errors, and synchronization errors.
Distributed spacefrequency coding over broadband relay channels
 IEEE Trans. Wireless Commun
, 2008
"... Abstract—Designing diversity achieving schemes over the wireless broadband fading relay channels is crucial to achieve higher diversity gains. These gains are achieved by exploiting the multipath (frequency) and cooperative diversities to combat the fading nature of wireless channels. The challenge ..."
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Cited by 4 (0 self)
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Abstract—Designing diversity achieving schemes over the wireless broadband fading relay channels is crucial to achieve higher diversity gains. These gains are achieved by exploiting the multipath (frequency) and cooperative diversities to combat the fading nature of wireless channels. The challenge is how to design spacefrequency codes, distributed among randomly located nodes that can exploit the frequency diversity of the wireless broadband channels. In this paper, the design of distributed spacefrequency codes (DSFCs) for wireless relay networks is considered. The proposed DSFCs are designed to achieve the frequency and cooperative diversities of the wireless relay channels. The use of DSFCs with the decodeandforward (DAF) and amplifyandforward (AAF) protocols is considered. The code design criteria to achieve full diversity, based on the pairwise error probability (PEP) analysis, are derived. For DSFC with the DAF protocol, a twostage coding scheme, with source node coding and relay nodes coding, is proposed. We derive sufficient conditions for the proposed code structures at the source and relay nodes to achieve full diversity of order NL,whereNis the number of relay nodes and L is the number of paths per channel. For the case of DSFC with the AAF protocol, a structure for distributed spacefrequency coding is proposed. Index Terms—Amplifyandforward, broadband channels, decodeandforward, relay channels, spacefrequency coding. I.