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422
Diversity and Multiplexing: A Fundamental Tradeoff in Multiple Antenna Channels
 IEEE Trans. Inform. Theory
, 2002
"... Multiple antennas can be used for increasing the amount of diversity or the number of degrees of freedom in wireless communication systems. In this paper, we propose the point of view that both types of gains can be simultaneously obtained for a given multiple antenna channel, but there is a fund ..."
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Cited by 1165 (20 self)
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Multiple antennas can be used for increasing the amount of diversity or the number of degrees of freedom in wireless communication systems. In this paper, we propose the point of view that both types of gains can be simultaneously obtained for a given multiple antenna channel, but there is a fundamental tradeo# between how much of each any coding scheme can get. For the richly scattered Rayleigh fading channel, we give a simple characterization of the optimal tradeo# curve and use it to evaluate the performance of existing multiple antenna schemes.
Distributed spacetimecoded protocols for exploiting cooperative diversity in wireless networks
 IEEE TRANS. INF. THEORY
, 2003
"... We develop and analyze space–time coded cooperative diversity protocols for combating multipath fading across multiple protocol layers in a wireless network. The protocols exploit spatial diversity available among a collection of distributed terminals that relay messages for one another in such a m ..."
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Cited by 622 (5 self)
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We develop and analyze space–time coded cooperative diversity protocols for combating multipath fading across multiple protocol layers in a wireless network. The protocols exploit spatial diversity available among a collection of distributed terminals that relay messages for one another in such a manner that the destination terminal can average the fading, even though it is unknown a priori which terminals will be involved. In particular, a source initiates transmission to its destination, and many relays potentially receive the transmission. Those terminals that can fully decode the transmission utilize a spacetime code to cooperatively relay to the destination. We demonstrate that these protocols achieve full spatial diversity in the number of cooperating terminals, not just the number of decoding relays, and can be used effectively for higher spectral efficiencies than repetitionbased schemes. We discuss issues related to space–time code design for these protocols, emphasizing codes that readily allow for appealing distributed versions.
Grassmannian beamforming for multipleinput multipleoutput wireless systems
 IEEE TRANS. INFORM. THEORY
, 2003
"... Transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multipleinput and multipleoutput (MIMO) wireless systems. Unfortunately, optimal performance requires either complete channel knowledge or knowledge of the optimal beamformi ..."
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Cited by 329 (38 self)
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Transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multipleinput and multipleoutput (MIMO) wireless systems. Unfortunately, optimal performance requires either complete channel knowledge or knowledge of the optimal beamforming vector which are not always realizable in practice. In this correspondence, a quantized maximum signaltonoise ratio (SNR) beamforming technique is proposed where the receiver only sends the label of the best beamforming vector in a predetermined codebook to the transmitter. By using the distribution of the optimal beamforming vector in independent identically distributed Rayleigh fading matrix channels, the codebook design problem is solved and related to the problem of Grassmannian line packing. The proposed design criterion is flexible enough to allow for side constraints on the codebook vectors. Bounds on the codebook size are derived to guarantee full diversity order. Results on the density of Grassmannian line packings are derived and used to develop bounds on the codebook size given a capacity or SNR loss. Monte Carlo simulations are presented that compare the probability of error for different quantization strategies.
On MaximumLikelihood Detection and the Search for the Closest Lattice Point
 IEEE TRANS. INFORM. THEORY
, 2003
"... Maximumlikelihood (ML) decoding algorithms for Gaussian multipleinput multipleoutput (MIMO) linear channels are considered. Linearity over the field of real numbers facilitates the design of ML decoders using numbertheoretic tools for searching the closest lattice point. These decoders are colle ..."
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Cited by 273 (9 self)
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Maximumlikelihood (ML) decoding algorithms for Gaussian multipleinput multipleoutput (MIMO) linear channels are considered. Linearity over the field of real numbers facilitates the design of ML decoders using numbertheoretic tools for searching the closest lattice point. These decoders are collectively referred to as sphere decoders in the literature. In this paper, a fresh look at this class of decoding algorithms is taken. In particular, two novel algorithms are developed. The first algorithm is inspired by the Pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the ViterboBoutros sphere decoder. The connection between the proposed algorithm and the stack sequential decoding algorithm is then established. This connection is utilized to construct the second algorithm which can also be viewed as an application of the SchnorrEuchner strategy to ML decoding. Aided with a detailed study of preprocessing algorithms, a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a nearML detection performance. This claim is supported by intuitive arguments and simulation results in many relevant scenarios.
Distributed spacetime coding in wireless relay networks,”IEEE Trans.
 on Wireless Communications,
, 2006
"... Abstract In this paper, we present a coding strategy for half duplex wireless relay networks, where we assume no channel knowledge at any of the transmitter, receiver or relays. The coding scheme uses distributed spacetime coding, that is, the relay nodes cooperate to encode the transmitted signal ..."
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Cited by 225 (16 self)
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Abstract In this paper, we present a coding strategy for half duplex wireless relay networks, where we assume no channel knowledge at any of the transmitter, receiver or relays. The coding scheme uses distributed spacetime coding, that is, the relay nodes cooperate to encode the transmitted signal so that the receiver senses a spacetime codeword. It is inspired by noncoherent differential techniques. The proposed strategy is available for any number of relays nodes. It is analyzed, and shown to yield a diversity linear in the number of relays. We also study the resistance of the scheme to relay node failures, and show that a network with R relay nodes and d of them down behaves, as far as diversity is concerned, as a network with R − d nodes. Finally, our construction can be easily generalized to the case where the transmitter and receiver nodes have several antennas.
FullDiversity, HighRate SpaceTime Block Codes from Division Algebras
 IEEE TRANS. INFORM. THEORY
, 2003
"... We present some general techniques for constructing fullrank, minimaldelay, rate at least one spacetime block codes (STBCs) over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras (field extensions) as well as using noncommutative division algeb ..."
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Cited by 177 (55 self)
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We present some general techniques for constructing fullrank, minimaldelay, rate at least one spacetime block codes (STBCs) over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras (field extensions) as well as using noncommutative division algebras of the rational field embedded in matrix rings. The first half of the paper deals with constructions using field extensions of . Working with cyclotomic field extensions, we construct several families of STBCs over a wide range of signal sets that are of full rank, minimal delay, and rate at least one appropriate for any number of transmit antennas. We study the coding gain and capacity of these codes. Using transcendental extensions we construct arbitrary rate codes that are full rank for arbitrary number of antennas. We also present a method of constructing STBCs using noncyclotomic field extensions. In the later half of the paper, we discuss two ways of embedding noncommutative division algebras into matrices: left regular representation, and representation over maximal cyclic subfields. The 4 4 real orthogonal design is obtained by the left regular representation of quaternions. Alamouti's code is just a special case of the construction using representation over maximal cyclic subfields and we observe certain algebraic uniqueness characteristics of it. Also, we discuss a general principle for constructing cyclic division algebras using the th root of a transcendental element and study the capacity of the STBCs obtained from this construction. Another family of cyclic division algebras discovered by Brauer is discussed and several examples of STBCs derived from each of these constructions are presented.
On the Complexity of Sphere Decoding in Digital Communications
 IN DIGITAL COMMUNICATIONS,” IEEE TRANSACTIONS ON SIGNAL PROCESSING, TO APPEAR
, 2005
"... ..."
On the spheredecoding algorithm I. Expected complexity
 IEEE Trans. Sig. Proc
, 2005
"... Abstract—The problem of finding the leastsquares solution to a system of linear equations where the unknown vector is comprised of integers, but the matrix coefficient and given vector are comprised of real numbers, arises in many applications: communications, cryptography, GPS, to name a few. The ..."
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Cited by 135 (7 self)
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Abstract—The problem of finding the leastsquares solution to a system of linear equations where the unknown vector is comprised of integers, but the matrix coefficient and given vector are comprised of real numbers, arises in many applications: communications, cryptography, GPS, to name a few. The problem is equivalent to finding the closest lattice point to a given point and is known to be NPhard. In communications applications, however, the given vector is not arbitrary but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known. Therefore, in this paper, rather than dwell on the worstcase complexity of the integer leastsquares problem, we study its expected complexity, averaged over the noise and over the lattice. For the “sphere decoding” algorithm of Fincke and Pohst, we find a closedform expression for the expected complexity, both for the infinite and finite lattice.
On the capacity of spatially correlated MIMO Rayleighfading channels
 IEEE Trans. Inform. Theory
, 2003
"... Abstract—In this paper, we investigate the capacity distribution of spatially correlated, multipleinput–multipleoutput (MIMO) channels. In particular, we derive a concise closedform expression for the characteristic function (c.f.) of MIMO system capacity with arbitrary correlation among the tran ..."
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Cited by 134 (15 self)
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Abstract—In this paper, we investigate the capacity distribution of spatially correlated, multipleinput–multipleoutput (MIMO) channels. In particular, we derive a concise closedform expression for the characteristic function (c.f.) of MIMO system capacity with arbitrary correlation among the transmitting antennas or among the receiving antennas in frequencyflat Rayleighfading environments. Using the exact expression of the c.f., the probability density function (pdf) and the cumulative distribution function (CDF) can be easily obtained, thus enabling the exact evaluation of the outage and mean capacity of spatially correlated MIMO channels. Our results are valid for scenarios with the number of transmitting antennas greater than or equal to that of receiving antennas with arbitrary correlation among them. Moreover, the results are valid for an arbitrary number of transmitting and receiving antennas in uncorrelated MIMO channels. It is shown that the capacity loss is negligible even with a correlation coefficient between two adjacent antennas as large as 0 5 for exponential correlation model. Finally, we derive an exact expression for the mean value of the capacity for arbitrary correlation matrices. Index Terms—Eigenvalues distribution, multiple input–multiple output (MIMO), multiple antennas, Rayleighfading channels, Shannon capacity, Wishart matrices. I.
SpaceTime Diversity Systems Based on Linear Constellation Precoding
 IEEE TRANS. WIRELESS COMMUN
, 2003
"... We present a unified approach to designing spacetime (ST) block codes using linear constellation precoding (LCP). Our designs are based either on parameterizations of unitary matrices, or on algebraic numbertheoretic constructions. With an arbitrary number of transmit and receiveantennas, STLCP ..."
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Cited by 128 (8 self)
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We present a unified approach to designing spacetime (ST) block codes using linear constellation precoding (LCP). Our designs are based either on parameterizations of unitary matrices, or on algebraic numbertheoretic constructions. With an arbitrary number of transmit and receiveantennas, STLCP achieves rate 1 symbol/s/Hz and enjoys diversity gain as high as over (possibly correlated) quasistatic and fast fading channels. As figures of merit, we use diversity and coding gains, as well as mutual information of the underlying multipleinputmultipleoutput system. We show that over quadratureamplitude modulation and pulseamplitude modulation, our LCP achieves the upper bound on the coding gain of all linear precoders for certain values of and comes close to this upper bound for other values of , in both correlated and independent fading channels. Compared with existing ST block codes adhering to an orthogonal design (STOD), STLCP offers not only better performance, but also higher mutual information for...