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105
Cellular Interference Alignment with Imperfect Channel Knowledge
"... Abstract—Interference alignment is evaluated as a technique to mitigate intercell interference in the downlink of a cellular network using OFDMA. The sum mutual information achieved by interference alignment together with a zeroforcing receiver is considered, and upper and lower bounds are derived ..."
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Cited by 39 (5 self)
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Abstract—Interference alignment is evaluated as a technique to mitigate intercell interference in the downlink of a cellular network using OFDMA. The sum mutual information achieved by interference alignment together with a zeroforcing receiver is considered, and upper and lower bounds are derived for the case of imperfect channel knowledge. The sum mutual information achieved by interference alignment when the base stations share their information about the channels is shown to compare favorably to the achievable sumrate of methods where the base stations do not cooperate, even under moderately accurate knowledge of the channel state. I.
MIMO minimum total MSE transceiver design with imperfect CSI at both ends
 IEEE Trans. Signal Processing
, 2009
"... Abstract—This paper presents new results on joint linear transceiver design under the minimum total meansquare error (MSE) criterion, with channel mean as well as both transmit and receive correlation information at both ends of a multipleinput multipleoutput (MIMO) link. The joint design is form ..."
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Cited by 31 (3 self)
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Abstract—This paper presents new results on joint linear transceiver design under the minimum total meansquare error (MSE) criterion, with channel mean as well as both transmit and receive correlation information at both ends of a multipleinput multipleoutput (MIMO) link. The joint design is formulated into an optimization problem. The optimum closedform precoder and decoder are derived. Compared to the case with perfect channel state information (CSI), linear filters are added at both ends to balance the suppression of channel noise and the noise from imperfect channel estimation. The impact of channel estimation error as well as channel correlation on system performance is assessed, based on analytical and simulation results. Index Terms—Channel state information (CSI), meansquare error (MSE), multipleinput multipleoutput (MIMO), precoding, spatial multiplexing. I.
Large System Analysis of Linear Precoding in MISO Broadcast Channels with Limited Feedback
, 2010
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Massive MIMO Systems with NonIdeal Hardware: Energy Efficiency, Estimation, and Capacity Limits
, 2014
"... The use of largescale antenna arrays can bring substantial improvements in energy and/or spectral efficiency to wireless systems due to the greatly improved spatial resolution and array gain. Recent works in the field of massive multipleinput multipleoutput (MIMO) show that the user channels dec ..."
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Cited by 29 (6 self)
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The use of largescale antenna arrays can bring substantial improvements in energy and/or spectral efficiency to wireless systems due to the greatly improved spatial resolution and array gain. Recent works in the field of massive multipleinput multipleoutput (MIMO) show that the user channels decorrelate when the number of antennas at the base stations (BSs) increases, thus strong signal gains are achievable with little interuser interference. Since these results rely on asymptotics, it is important to investigate whether the conventional system models are reasonable in this asymptotic regime. This paper considers a new system model that incorporates general transceiver hardware impairments at both the BSs (equipped with large antenna arrays) and the singleantenna user equipments (UEs). As opposed to the conventional case of ideal hardware, we show that hardware impairments create finite ceilings on the channel estimation accuracy and on the downlink/uplink capacity of each UE. Surprisingly, the capacity is mainly limited by the hardware at the UE, while the impact of impairments in the largescale arrays vanishes asymptotically and interuser interference (in particular, pilot contamination) becomes negligible. Furthermore, we prove that the huge degrees of freedom offered by massive MIMO can be used to reduce the transmit power and/or to tolerate larger hardware impairments, which allows for the use of inexpensive and energyefficient antenna elements.
Exponential diversity achieving spatiotemporal power allocation scheme for fading channels
 IEEE Trans. Inf. Theory
, 2008
"... Abstract — We analyze optimum (space–time) adaptive power transmission policies for Rayleigh fading MIMO channels when CSIT and CSIR are available. We show that our power allocation policy provides exponential diversity gain 2 (BER ≤ αe −f(nt,nr),whereα>0 is a constant, and f>0 is an increasin ..."
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Cited by 19 (3 self)
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Abstract — We analyze optimum (space–time) adaptive power transmission policies for Rayleigh fading MIMO channels when CSIT and CSIR are available. We show that our power allocation policy provides exponential diversity gain 2 (BER ≤ αe −f(nt,nr),whereα>0 is a constant, and f>0 is an increasing function of nt & nr) if perfect CSIT is available. Exponential diversity is lost at high SNR if the quality of CSIT degrades. I. Perfect/Imperfect CSIT We consider a single user narrowband (flat fading) communication system employing nt transmit antennas and nr receive antennas. The channel between i th receive antenna and j th transmit antenna, hij is a complex Gaussian random variable (H = [hij] represents the channel). We assume i.i.d. Rayleigh fading from symbol to symbol and on each of the diversity branches. The additive noise, n, is temporally and spatially white with mean zero, i.e., n ∼NC(0,σ 2 Inr). We assume that ˆ H is the transmitter’s estimate of the channel. We assume that ˆ H and H are jointly complex Gaussian with correlation ρ. We assume perfect CSIR. ˆ H is used to get the optimal beamforming transmit weight vector w (the eigenvector of ˆ H H H ˆ corresponding to its largest eigenvalue) and transmit power P (.) for that symbol duration. The output of the matched filter sampled at symbol duration is given by y = √ P (ˆγ) Hwx+n, where x is the transmitted symbol, γ = ‖Hw ‖ 2 Ex  2 /σ 2 is the SNR, P (ˆγ) is the transmit power, and ˆγ ( = ‖ ˆ Hw ‖ 2 Ex  2 /σ 2) is the estimate of γ at the transmitter. The BER performance of the above system for the coherent ( √2γ) BPSK signaling is given by Peγ,ˆγ = Q P(ˆγ). We minimize Pe subject to the average transmit power constraint. For the perfect CSIT case (ˆγ = γ), the optimization problem is
Optimization of Training and Feedback Overhead for Beamforming over Block Fading Channels
, 2009
"... We examine the capacity of beamforming over a singleuser, multiantenna link taking into account the overhead due to channel estimation and limited feedback of channel state information. Multiinput singleoutput (MISO) and multiinput multioutput (MIMO) channels are considered subject to block Ra ..."
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Cited by 17 (0 self)
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We examine the capacity of beamforming over a singleuser, multiantenna link taking into account the overhead due to channel estimation and limited feedback of channel state information. Multiinput singleoutput (MISO) and multiinput multioutput (MIMO) channels are considered subject to block Rayleigh fading. Each coherence block contains L symbols, and is spanned by T training symbols, B feedback bits, and the data symbols. The training symbols are used to obtain a Minimum Mean Squared Error estimate of the channel matrix. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing 2B i.i.d. random vectors, and sends the corresponding B bits back to the transmitter. We derive bounds on the beamforming capacity for MISO and MIMO channels and characterize the optimal (ratemaximizing) training and feedback overhead (T and B) as L and the number of transmit antennas Nt both become large. The optimal Nt is limited by the coherence time, and increases as L / logL. For the MISO channel the optimal T/L and B/L (fractional overhead due to training and feedback) are asymptotically the same, and tend to zero at the rate 1 / logNt. For the MIMO channel the optimal feedback overhead B/L tends to zero faster (as 1 / log² Nt).
Optimal channel training in uplink network MIMO systems
 IEEE Trans. Signal Processing, to be published. THE RAPIDLY INCREASING DEMAND FOR WIRELESS DATA TRAFFIC POSES THE CHALLENGE OF HOW TO INCREASE THE CAPACITY OF CELLULAR NETWORKS IN AN ECONOMICAL AND ECOLOGICAL WAY. MARCH2011  IEEEVEHICULARTECHNOLOGYMAGAZI
"... We study a multicell frequencyselective fading uplink channel from K user terminals (UTs) to B base stations (BSs). The BSs, assumed to be oblivious of the applied encoding scheme, compress and forward their observations to a central station (CS) via capacity limited backhaul links. The CS joint ..."
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Cited by 15 (6 self)
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We study a multicell frequencyselective fading uplink channel from K user terminals (UTs) to B base stations (BSs). The BSs, assumed to be oblivious of the applied encoding scheme, compress and forward their observations to a central station (CS) via capacity limited backhaul links. The CS jointly decodes the messages from all UTs. Since we assume no prior channel state information, the channel needs to be estimated during its coherence time. Based on a lower bound of the ergodic mutual information, we determine the optimal fraction of the coherence time used for channel training. We then study how the optimal training length is impacted by the backhaul capacity. Our analysis is based on large random matrix theory but shown by simulations to be tight for even small system dimensions. Index Terms — Coordinated MultiPoint (CoMP), network MIMO, channel estimation, random matrix theory
On Uplink Network MIMO under a Constrained Backhaul and Imperfect Channel Knowledge
"... Abstract — It is known that next generation mobile comunications systems will most likely employ multicell signal processingoften referred to as network MIMO in order to improve spectral efficiency and fairness. Many publications exist that predict strong achievable rate improvements, but usually ..."
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Cited by 13 (7 self)
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Abstract — It is known that next generation mobile comunications systems will most likely employ multicell signal processingoften referred to as network MIMO in order to improve spectral efficiency and fairness. Many publications exist that predict strong achievable rate improvements, but usually neglecting various practical issues connected to network MIMO. In this paper, we analyse the impact of a constrained backhaul infrastructure and imperfect channel knowledge on uplink network MIMO from an information theoretical point of view. Especially the latter aspect leads to the fact that the channel conditions for which network MIMO is reasonably beneficial are strongly constrained. We observe different base station cooperation schemes in scenarios of maximal 3 base stations and 3 terminals, provide simulation results, and discuss the practicability of the discussed schemes and the implications of our results. I.
Maximum mutual information design for MIMO systems with imperfect channel knowledge
 IEEE Transactions on Information Theory
, 2010
"... Abstract—New results on maximum mutual information design for multipleinput multipleoutput (MIMO) systems are presented, assuming that both transmitter and receiver know only an estimate of the channel state as well as the transmit and receive correlation. Since an exact capacity expression is dif ..."
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Cited by 12 (1 self)
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Abstract—New results on maximum mutual information design for multipleinput multipleoutput (MIMO) systems are presented, assuming that both transmitter and receiver know only an estimate of the channel state as well as the transmit and receive correlation. Since an exact capacity expression is difficult to obtain for this case, a tight lowerbound on the mutual information between the input and the output of a MIMO channel has been previously formulated as a design criterion. However, in the previous literature, there has been no analytical expression of the optimum transmit covariance matrix for this lowerbound. Here it is shown that for the general case with channel correlation at both ends, there exists a unique and globally optimum transmit covariance matrix whose explicit expression can be conveniently determined. For the special case with transmit correlation only, the closedform optimum transmit covariance matrix is presented. Interestingly, the optimal transmitters for the maximum mutual information design and the minimum total meansquare error design share the same structure, as they do in the case with perfect channel state information. Simulation results are provided to demonstrate the effects of channel estimation errors and channel correlation on the mutual information. Index Terms—Channel state information (CSI), meansquare error (MSE), multipleinput multipleoutput (MIMO), mutual information, optimization. I.
Outage probability of multipleinput and singleoutput (MISO) systems with delayed feedback
 IEEE Trans. Commun
, 2009
"... Abstract—We investigate the effect of feedback delay on the outage probability of multipleinput singleoutput (MISO) fading channels. Channel state information at the transmitter (CSIT) is a delayed version of the channel state information available at the receiver (CSIR). We consider two cases of ..."
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Cited by 9 (2 self)
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Abstract—We investigate the effect of feedback delay on the outage probability of multipleinput singleoutput (MISO) fading channels. Channel state information at the transmitter (CSIT) is a delayed version of the channel state information available at the receiver (CSIR). We consider two cases of CSIR: (a) perfect CSIR and (b) CSI estimated at the receiver using training symbols. With perfect CSIR, under a shortterm power constraint, we determine: (a) the outage probability for beamforming with imperfect CSIT (BFIC) analytically, and (b) the optimal spatial power allocation (OSPA) scheme that minimizes outage numerically. Results show that, for delayed CSIT, BFIC is close to optimal for low SNR and uniform spatial power allocation (USPA) is close to optimal at high SNR. Similarly, under a longterm power constraint, we show that BFIC is better for low SNR and USPA is better at high SNR. With imperfect CSIR, we obtain an upper bound on the outage probability with USPA and BFIC. Results show that the loss in performance due to imperfection in CSIR is not significant, if the training power is chosen appropriately. Index Terms—Multiple antenna systems, beamforming, feedback delay, outage probability, power allocation. I.