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A simple transmit diversity technique for wireless communications
 IEEE Journal on Selected Areas in Communications
, 1998
"... Abstract — This paper presents a simple twobranch transmit diversity scheme. Using two transmit antennas and one receive antenna the scheme provides the same diversity order as maximalratio receiver combining (MRRC) with one transmit antenna, and two receive antennas. It is also shown that the sch ..."
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Cited by 1266 (0 self)
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Abstract — This paper presents a simple twobranch transmit diversity scheme. Using two transmit antennas and one receive antenna the scheme provides the same diversity order as maximalratio receiver combining (MRRC) with one transmit antenna, and two receive antennas. It is also shown that the scheme may easily be generalized to two transmit antennas and M receive antennas to provide a diversity order of 2M. The new scheme does not require any bandwidth expansion any feedback from the receiver to the transmitter and its computation complexity is similar to MRRC. Index Terms—Antenna array processing, baseband processing, diversity, estimation and detection, fade mitigation, maximalratio combining, Rayleigh fading, smart antennas, space block coding, space–time coding, transmit diversity, wireless communications. I.
Spacetime codes for high data rate wireless communication: Performance criterion and code construction
 IEEE Trans. Inform. Theory
, 1998
"... Abstract — We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into � streams that are simultaneously transmitted using � tr ..."
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Cited by 1225 (25 self)
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Abstract — We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into � streams that are simultaneously transmitted using � transmit antennas. The received signal at each receive antenna is a linear superposition of the � transmitted signals perturbed by noise. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices constructed from pairs of distinct code sequences. The minimum rank among these matrices quantifies the diversity gain, while the minimum determinant of these matrices quantifies the coding gain. The results are then extended to fast fading channels. The design criteria are used to design trellis codes for high data rate wireless communication. The encoding/decoding complexity of these codes is comparable to trellis codes employed in practice over Gaussian channels. The codes constructed here provide the best tradeoff between data rate, diversity advantage, and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2–3 dB of the outage capacity for these channels using only 64 state encoders.
Spacetime block codes from orthogonal designs
 IEEE Trans. Inform. Theory
, 1999
"... Abstract — We introduce space–time block coding, a new paradigm for communication over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space–time block code and the encoded data is split into � streams which are simultaneously transmitted using � transmit antennas. ..."
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Cited by 996 (24 self)
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Abstract — We introduce space–time block coding, a new paradigm for communication over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space–time block code and the encoded data is split into � streams which are simultaneously transmitted using � transmit antennas. The received signal at each receive antenna is a linear superposition of the � transmitted signals perturbed by noise. Maximumlikelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection. This uses the orthogonal structure of the space–time block code and gives a maximumlikelihood decoding algorithm which is based only on linear processing at the receiver. Space–time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm. The classical mathematical framework of orthogonal designs is applied to construct space–time block codes. It is shown that space–time block codes constructed in this way only exist for few sporadic values of �. Subsequently, a generalization of orthogonal designs is shown to provide space–time block codes for both real and complex constellations for any number of transmit antennas. These codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as PAM. For an arbitrary complex constellation such as PSK and QAM, space–time block codes are designed that achieve IaP of the maximum possible transmission rate for any number of transmit antennas. For the specific cases of two, three, and four transmit antennas, space–time block codes are designed that achieve, respectively, all, QaR, and QaR of maximum possible transmission rate using arbitrary complex constellations. The best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well. Index Terms — Codes, diversity, multipath channels, multiple antennas, wireless communication.
HighRate Codes that are Linear in Space and Time
 IEEE Trans. Inform. Theory
, 2000
"... Multipleantenna systems that operate at high rates require simple yet effective spacetime transmission schemes to handle the large traffic volume in real time. At rates of tens of bits/sec/Hz, VBLAST, where every antenna transmits its own independent substream of data, has been shown to have good ..."
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Cited by 307 (9 self)
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Multipleantenna systems that operate at high rates require simple yet effective spacetime transmission schemes to handle the large traffic volume in real time. At rates of tens of bits/sec/Hz, VBLAST, where every antenna transmits its own independent substream of data, has been shown to have good performance and simple encoding and decoding. Yet VBLAST suffers from its inability to work with fewer receive antennas than transmit antennasthis deficiency is especially important for modern cellular systems where a basestation typically has more antennas than the mobile handsets. Furthermore, because VBLAST transmits independent data streams on its antennas there is no builtin spatial coding to guard against deep fades from any given transmit antenna. On the other hand, there are many previouslyproposed spacetime codes that have good fading resistance and simple decoding, but these codes generally have poor performance at high data rates or with many antennas. We propose a highrate coding scheme that can handle any...
Spacetime block coding for wireless communications: performance results
 IEEE J. Select. Areas. Commun
, 1999
"... Abstract—We document the performance of space–time block codes [13], [14], which provide a new paradigm for transmission over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space–time block code, and the encoded data is split into n streams which are simultaneousl ..."
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Cited by 221 (7 self)
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Abstract—We document the performance of space–time block codes [13], [14], which provide a new paradigm for transmission over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space–time block code, and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. Maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection. This uses the orthogonal structure of the space–time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver. We review the encoding and decoding algorithms for various codes and provide simulation results demonstrating their performance. It is shown that using multiple transmit antennas and space–time block coding provides remarkable performance at the expense of almost no extra processing. Index Terms — Diversity, multipath channels, multiple antennas, space–time codes, wireless communication. I.
A differential detection scheme for transmit diversity
 IEEE J. Select. Areas Commun
, 2000
"... Abstract—We present a transmission scheme for exploiting diversity given by two transmit antennas when neither the transmitter nor the receiver has access to channel state information. The new detection scheme can use equal energy constellations and encoding is simple. At the receiver, decoding is a ..."
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Cited by 160 (5 self)
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Abstract—We present a transmission scheme for exploiting diversity given by two transmit antennas when neither the transmitter nor the receiver has access to channel state information. The new detection scheme can use equal energy constellations and encoding is simple. At the receiver, decoding is achieved with low decoding complexity. The transmission provides full spatial diversity and requires no channel state side information at the receiver. The scheme can be considered as the extension of differential detection schemes to two transmit antennas. Index Terms—Antenna arrays, differential detection, spacetime codes, transmitter diversity. I.
Efficient Use of Side Information in MultipleAntenna Data Transmission over Fading Channels
, 1998
"... We derive performance limits for two closely related communication scenarios involving a wireless system with multipleelement transmitter antenna arrays: a pointtopoint system with partial side information at the transmitter, and a broadcast system with multiple receivers. In both cases, ideal be ..."
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Cited by 153 (2 self)
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We derive performance limits for two closely related communication scenarios involving a wireless system with multipleelement transmitter antenna arrays: a pointtopoint system with partial side information at the transmitter, and a broadcast system with multiple receivers. In both cases, ideal beamforming is impossible, leading to an inherently lower achievable performance as the quality of the side information degrades or as the number of receivers increases. Expected signaltonoise ratio (SNR) and mutual information are both considered as performance measures. In the pointtopoint case, we determine when the transmission strategy should use some form of beamforming and when it should not. We also show that, when properly chosen, even a small amount of side information can be quite valuable. For the broadcast scenario with an SNR criterion, we find the efficient frontier of operating points and show that even when the number of receivers is larger than the number of antenna array ...
Cayley differential unitary space–time codes
 IEEE Trans. Inform. Theory
, 2002
"... One method for communicating with multiple antennas is to encode the transmitted data differentially using unitary matrices at the transmitter, and to decode differentially without knowing the channel coefficients at the receiver. Since channel knowledge is not required at the receiver, differential ..."
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Cited by 69 (6 self)
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One method for communicating with multiple antennas is to encode the transmitted data differentially using unitary matrices at the transmitter, and to decode differentially without knowing the channel coefficients at the receiver. Since channel knowledge is not required at the receiver, differential schemes are ideal for use on wireless links where channel tracking is undesirable or infeasible, either because of rapid changes in the channel characteristics or because of limited system resources. Although this basic principle is well understood, it is not known how to generate goodperforming constellations of unitary matrices, for any number of transmit and receive antennas and for any rate. This is especially true at high rates where the constellations must be rapidly encoded and decoded. We propose a class of Cayley codes that works with any number of antennas, and has efficient encoding and decoding at any rate. The codes are named for their use of the Cayley transform, which maps the highly nonlinear Stiefel manifold of unitary matrices to the linear space of skewHermitian matrices. This transformation leads to a simple linear constellation structure in the Cayley transform domain and to an informationtheoretic design criterion based on emulating a Cauchy random matrix. Moreover, the resulting Cayley codes allow polynomialtime nearmaximumlikelihood decoding based on either successive nulling/cancelling or sphere decoding. Simulations show that the Cayley codes allow efficient and effective highrate data transmission in multiantenna communication systems without knowing the channel.
Performance Limits of Coded Diversity Methods for Transmitter Antenna Arrays
 IEEE Trans. Inform. Theory
, 1999
"... Several aspects of the design and optimization of coded multipleantenna transmission diversity methods for slowly timevarying channels are explored from an informationtheoretic perspective. Both optimized vectorcoded systems, which can achieve the maximum possible performance, and suboptimal sca ..."
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Cited by 69 (3 self)
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Several aspects of the design and optimization of coded multipleantenna transmission diversity methods for slowly timevarying channels are explored from an informationtheoretic perspective. Both optimized vectorcoded systems, which can achieve the maximum possible performance, and suboptimal scalarcoded systems, which reduce complexity by exploiting suitably designed linear precoding, are investigated. The achievable rates and associated outage characteristics of these spatial diversity schemes are evaluated and compared, both for the case when temporal diversity is being jointly exploited and for the case when it is not. Complexity and implementation issues more generally are also discussed.
Existence and Construction of Noncoherent Unitary SpaceTime Codes
 IEEE Trans. Inform. Theory
, 2000
"... We consider transmission using N transmit and reception using M receive antennas in a wireless environment assuming that neither the transmitter nor the receiver knows the channel coefficients. For the scenario that the transmission employs noncoherent T Nunit spacet codes and for a block fading c ..."
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Cited by 30 (0 self)
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We consider transmission using N transmit and reception using M receive antennas in a wireless environment assuming that neither the transmitter nor the receiver knows the channel coefficients. For the scenario that the transmission employs noncoherent T Nunit spacet codes and for a block fading channel model wherete channel is st during T channel uses and varies from T channel usest ot1 ot we est1x tt bound r # min(T  N,N) ont diversit y advantx1 rM provided byt code. Wet showt0 t requirement r # min(T  N,N) cannot be relaxed by constx1 for any given R, N , T and r # min(T N,N),unit T Nspacet0 codes of rat Rt0 guarant e diversit y adantage rM. Two constructions are given that are also amenable to simple encoding and noncoherent maximum likelihood decoding algorithms.