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25
Asymptotic Performance of Linear Receivers in MIMO Fading Channels
 IEEE TRANS. ON INFO THEORY
, 2009
"... Linear receivers are an attractive lowcomplexity alternative to optimal processing for multiantenna MIMO communications. In this paper we characterize the informationtheoretic performance of MIMO linear receivers in two different asymptotic regimes. For fixed number of antennas, we investigate th ..."
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Linear receivers are an attractive lowcomplexity alternative to optimal processing for multiantenna MIMO communications. In this paper we characterize the informationtheoretic performance of MIMO linear receivers in two different asymptotic regimes. For fixed number of antennas, we investigate the limit of error probability in the highSNR regime in terms of the DiversityMultiplexing Tradeoff (DMT). Following this, we characterize the error probability for fixed SNR in the regime of large (but finite) number of antennas. As far as the DMT is concerned, we report a negative result: we show that both linear ZeroForcing (ZF) and linear Minimum MeanSquare Error (MMSE) receivers achieve the same DMT, which is largely suboptimal even in the case where outer coding and decoding is performed across the antennas. We also provide an approximate quantitative analysis of the markedly different behavior of the MMSE and ZF receivers at finite rate and nonasymptotic SNR, and show that while the ZF receiver achieves poor diversity at any finite rate, the MMSE receiver error curve slope flattens out progressively, as the coding rate increases. When SNR is fixed and the number of antennas becomes large, we show that the mutual information
Spatial multiplexing architectures with jointly designed ratetailoring and ordered BLAST decoding part—II: A practical method for rate and power allocation
 IEEE Trans. Wireless Commun
, 2008
"... ered SpaceTime) architecture involves independent coding/decoding per antenna (layer) with equal rate and power per antenna and a fixed order of nulling/canceling decoding but is known to suffer from poor performance; for example, in a multiinput multioutput (MIMO) Rayleigh fading channel with ..."
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Cited by 14 (1 self)
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ered SpaceTime) architecture involves independent coding/decoding per antenna (layer) with equal rate and power per antenna and a fixed order of nulling/canceling decoding but is known to suffer from poor performance; for example, in a multiinput multioutput (MIMO) Rayleigh fading channel with Mt transmit and Mr receive antennas (Mr ≥ Mt), the diversitymultiplexing gain (DM) tradeoff is just (Mr−Mt+1)(1−r/Mt) for r ∈ [0,Mt]. There are two remedies available, namely, (i) channeldependent ordered decoding at the receiver and (ii) allocation of rates and powers across the transmit antennas. However, the former doesn’t improve the DM tradeoff curve and while the latter does (with maximum diversity gainMr and maximummultiplexing gain Mt), its tradeoff curve is still significantly inferior compared to the DM tradeoff curve of the optimum (unconstrained)
Channel state feedback over the MIMOMAC
 in Proc. IEEE Int. Symp. Information Theory
, 2009
"... We consider the problem of designing low latency and low complexity schemes for channel state feedback over the MIMOMAC (multipleinput multipleoutput multiple access channel). We develop a framework for analyzing this problem in terms of minimizing the MSE distortion, and come up with separated s ..."
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We consider the problem of designing low latency and low complexity schemes for channel state feedback over the MIMOMAC (multipleinput multipleoutput multiple access channel). We develop a framework for analyzing this problem in terms of minimizing the MSE distortion, and come up with separated sourcechannel schemes and joint sourcechannel schemes that perform better than analog feedback. We also develop a strikingly simple code design based on scalar quantization and uncoded QAM modulation that achieves the theoretical asymptotic performance limit of the separated approach with very low complexity and latency, in the case of singleantenna users.
Exact MIMO zeroforcing detection analysis for transmitcorrelated Rician fading
 IEEE Transactions on Wireless Communications
, 2014
"... Abstract—We analyze the performance of multiple input/multiple output (MIMO) communications systems employing spatial multiplexing and zeroforcing detection (ZF). The distribution of the ZF signaltonoise ratio (SNR) is characterized when either the intended stream or interfering streams experien ..."
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Abstract—We analyze the performance of multiple input/multiple output (MIMO) communications systems employing spatial multiplexing and zeroforcing detection (ZF). The distribution of the ZF signaltonoise ratio (SNR) is characterized when either the intended stream or interfering streams experience Rician fading, and when the fading may be correlated on the transmit side. Previously, exact ZF analysis based on a wellknown SNR expression has been hindered by the noncentrality of the Wishart distribution involved. In addition, approximation with a centralWishart distribution has not proved consistently accurate. In contrast, the following exact ZF study proceeds from a lesserknown SNR expression that separates the intended and interfering channelgain vectors. By first conditioning on, and then averaging over the interference, the ZF SNR distribution for Rician–Rayleigh fading is shown to be an infinite linear combination of gamma distributions. On the other hand, for Rayleigh–Rician fading, the ZF SNR is shown to be gammadistributed. Based on the SNR distribution, we derive new series expressions for the ZF average error probability, outage probability, and ergodic capacity. Numerical results confirm the accuracy of our new expressions, and reveal effects of interference and channel statistics on performance. Index Terms—Azimuth spread, Kfactor, gamma distribution, MIMO, Rayleigh and Rician (Ricean) fading, transmit correla
Integerforcing MIMO linear receivers based on lattice reduction
 IEEE Trans. Wireless Commun
, 2013
"... Abstract—A new architecture called integerforcing (IF) linear receiver has been recently proposed for multipleinput multipleoutput (MIMO) fading channels, wherein an appropriate integer linear combination of the received symbols has to be computed as a part of the decoding process. In this paper, ..."
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Abstract—A new architecture called integerforcing (IF) linear receiver has been recently proposed for multipleinput multipleoutput (MIMO) fading channels, wherein an appropriate integer linear combination of the received symbols has to be computed as a part of the decoding process. In this paper, we propose a method based on HermiteKorkineZolotareff (HKZ) and Minkowski lattice basis reduction algorithms to obtain the integer coefficients for the IF receiver. We show that the proposed method provides a lower bound on the ergodic rate, and achieves the full receive diversity. Suitability of complex LenstraLenstraLovasz (LLL) lattice reduction algorithm (CLLL) to solve the problem is also investigated. Furthermore, we establish the connection between the proposed IF linear receivers and lattice reductionaided MIMO detectors (with equivalent complexity), and point out the advantages of the former class of receivers over the latter. For the 2 × 2 and 4 × 4 MIMO channels, we compare the codedblock error rate and bit error rate of the proposed approach with that of other linear receivers. Simulation results show that the proposed approach outperforms the zeroforcing (ZF) receiver, minimum mean square error (MMSE) receiver, and the lattice reductionaided MIMO detectors. Index Terms—MIMO, integerforcing, lattice reduction, Minkowski reduction, HermiteKorkineZolotareff reduction, complex LenstraLenstraLovasz lattice reduction, linear receivers. I.
On Performance of Vector OFDM With Linear Receivers
"... (OFDM) for single transmit antenna systems is a general transmission scheme, where OFDM and SingleCarrier Frequency Domain Equalization (SCFDE) can be treated as two special/extreme cases. Due to its flexibility, it has drawn more and more attention recently. So far, all the studies about Vector O ..."
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(OFDM) for single transmit antenna systems is a general transmission scheme, where OFDM and SingleCarrier Frequency Domain Equalization (SCFDE) can be treated as two special/extreme cases. Due to its flexibility, it has drawn more and more attention recently. So far, all the studies about Vector OFDM assume the Maximum Likelihood (ML) receiver. In this paper, we investigate the performance of Vector OFDM with linear receivers, i.e., the ZeroForcing (ZF) and Minimum Mean Square Error (MMSE) receivers. We first show that the detection SNR gap between the MMSE and ZF receivers increases with both channel SNR and the vector blocks (VB) size defined in Vector OFDM. Then, it is proved that for both ZF and MMSE receivers, all the transmitted symbols have equal performance. This is different from the Vector OFDM with ML receiver, where different VBs may have different coding gain, and thus may have different performances. We analyze the diversity order for Vector OFDM with MMSE receiver, and show that, regardless of the Vector OFDM symbol length,thediversity order can be represented as,where is the VB size, is the spectrum efficiency in bits/symbol, and is the maximum delay of the multipath channel. For Vector OFDM with ZF receiver, we show that the diversity order equals 1 and the performance is the same as the conventional OFDM at high SNR.
MIMO zeroforcing performance evaluation using the holonomic gradient method
 IEEE Transactions on Wireless Communications
, 2015
"... Abstract—For multipleinput multipleoutput (MIMO) spatialmultiplexing transmission, zeroforcing detection (ZF) is appealing because of its low complexity. Our recent MIMO ZF performance analysis for Rician–Rayleigh fading, which is relevant in heterogeneous networks, has yielded for the ZF outa ..."
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Abstract—For multipleinput multipleoutput (MIMO) spatialmultiplexing transmission, zeroforcing detection (ZF) is appealing because of its low complexity. Our recent MIMO ZF performance analysis for Rician–Rayleigh fading, which is relevant in heterogeneous networks, has yielded for the ZF outage probability and ergodic capacity infiniteseries expressions. Because they arose from expanding the confluent hypergeometric function 1F1(·, ·, σ) around 0, they do not converge numerically at realisticallyhigh Rician Kfactor values. Therefore, herein, we seek to take advantage of the fact that 1F1(·, ·, σ) satisfies a differential equation, i.e., it is a holonomic function. Holonomic functions can be computed by the holonomic gradient method (HGM), i.e., by numerically solving the satisfied differential equation. Thus, we first reveal that the moment generating function (m.g.f.) and probability density function (p.d.f.) of the ZF signaltonoise ratio (SNR) are holonomic. Then, from the differential equation for 1F1(·, ·, σ), we deduce those satisfied by the SNR m.g.f. and p.d.f., and demonstrate that the HGM helps compute the p.d.f. accurately at practicallyrelevant values of K. Finally, numerical integration of the SNR p.d.f. output by the HGM yields accurate ZF outage probability and ergodic capacity results. Index Terms—Holonomic gradient method, hypergeometric function, MIMO, Rayleigh–Rician fading, zeroforcing.
Multiuser Relaying over Mixed RF/FSO Links
"... Abstract—A multiuser dualhop relaying system over mixed radio frequency/freespace optical (RF/FSO) links is investigated. Specifically, the system consists of m singleantenna sources, a relay node equipped with n ≥ m receive antennas and a single photoaperture transmitter, and one destination eq ..."
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Abstract—A multiuser dualhop relaying system over mixed radio frequency/freespace optical (RF/FSO) links is investigated. Specifically, the system consists of m singleantenna sources, a relay node equipped with n ≥ m receive antennas and a single photoaperture transmitter, and one destination equipped with a single photodetector. RF links are used for the simultaneous data transmission from multiple sources to the relay. The relay operates under the decodeandforward protocol and utilizes the popular VBLAST technique by successively decoding each user’s transmitted stream. Two common normbased orderings are adopted, i.e., the streams are decoded in an ascending or a descending order. After VBLAST, the relay retransmits the decoded information to the destination via a pointtopoint FSO link in m consecutive timeslots. Analytical expressions for the endtoend outage probability and average symbol error probability of each user are derived, while closedform asymptotic expressions are also presented. Capitalizing on the derived results, some engineering insights are manifested, such as the coding and diversity gain of each user, the impact of the pointing error displacement on the FSO link and the VBLAST ordering effectiveness at the relay. Index Terms—Decodeandforward (DF), dualhop communication, mixed RF/FSO systems, ordered successive interference cancellation (SIC), VBLAST reception. I.
Performance analysis of dualuser macrodiversity MIMO systems with linear receivers in flat Rayleigh fading,” submitted to
 IEEE Trans. Wireless Commun
, 2012
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"... In wireless communication networks, performance goals are often conflicting with each other. For example, in pointtopoint multiinputmultioutput (MIMO) links, spectrum efficiency and reliability are in a tradeoff relation; in adhoc wireless networks, we need to sacrifice throughput to decrease ..."
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In wireless communication networks, performance goals are often conflicting with each other. For example, in pointtopoint multiinputmultioutput (MIMO) links, spectrum efficiency and reliability are in a tradeoff relation; in adhoc wireless networks, we need to sacrifice throughput to decrease packet delay. In this dissertation, we investigate problems on the diversitymultiplexing tradeoff (DMT) in cellular wireless communication networks and problems on the throughputdelay tradeoff in adhoc wireless networks. We first consider two topics on the DMT in cellular uplinks (or multipleaccess channels, MACs): (1) the diversitymultiplexingdelay tradeoff (DMDT) in a randomaccess scenario and (2) an explicit construction of spacetime coding scheme achieving the DMT. For the randomaccess scenario, we propose an incrementalredundancy automatic repeat request (IRARQ) scheme. We prove that our scheme successfully exploits both ARQ diversity and jointdecoding advantage, and achieves a better DMT than other existing protocols, such as Tsatsanis et al.’s networkassisted diversity