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• 1.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
A low complexity user grouping based multiuser MISO downlink precoder2011Conference paper (Refereed)

We consider low complexity precoding for the Multiple Input Single Output (MISO)Gaussian Broadcast channel with $N_t$ antennas at the base station and $N_u$ singleantenna users in the downlink. Theoretical studies have suggested high throughputcommunication with increasing spatial dimensions i.e., $\min(N_t,N_u)$.Nevertheless, most modern communication standards are unable to exploitthe spatial dimension fully, since they are restricted to orthogonal communicationtechniques like TDMA/FDMA (Time/Frequency Division Multiplexed Access) which areknown to be sub-optimal.This restriction is mostly due to the prohibitive complexity of optimal/near-optimalprecoding schemes.On the other hand low complexity techniques like Zero Forcing (ZF) and MMSE have poor sum rate performance.In this paper, we propose a novel low-complexity user grouping based precoding scheme whichschedules all users on the same time-frequency resource (i.e., optimal utilization of resources).The proposed precoder is analytically shown to achieve a sum rate performance significantly better than the ZF precoderat similar complexity.Through simulations, it is also observed to achieve a significant fractionof the sum rate achieved by the optimal schemes.

• 2.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Constant Envelope Precoding for Power-Efficient Downlink Wireless Communicationin Multi-User MIMO Systems Using Large Antenna Arrays2012In: 2012 IEEE International Conference on Acoustics, Speech and Signal Processing, IEEE Press, 2012, p. 2949-2952Conference paper (Refereed)

We consider downlink cellular multi-user communication betweena base station (BS) having $N$ antennas and $M$ single-antenna users, i.e.,an $N \times M$ Gaussian Broadcast Channel (GBC).Under an average only total transmit power constraint (APC), large antenna arrays at the BS (having tens to a few hundred antennas) have been recently shown to achieve remarkablemulti-user interference (MUI) suppression with simple precoding techniques.However, building large arrays in practice, would require cheap/power-efficient Radio-Frequency(RF) electronic components. The type of transmitted signal that facilitates the use ofmost power-efficient RF components is a constant envelope (CE) signal (i.e.,the amplitude of the signal transmitted from each antenna is constant for every channel useand every channel realization).Under certain mild channel conditions (including i.i.d. fading), we analytically show that,even under the stringent per-antenna CE transmission constraint (compared to APC),MUI suppression can still be achieved with large antenna arrays. Our analysis also reveals that,with a fixed $M$ and increasing $N$, the total transmitted power can be reduced while maintaining a constant signal-to-interference-noise-ratio (SINR) level at each user.We also propose a novel low-complexity CE precoding scheme, using which,we confirm our analytical observations for the i.i.d. Rayleigh fading channel, through Monte-Carlo simulations.Simulation of the information sum-rate under the per-antenna CE constraint, shows that, for a fixed $M$ and a fixed desired sum-rate, the required total transmit powerdecreases linearly with increasing $N$, i.e.,an $O(N)$ array power gain.Also, in terms of the total transmit power required to achieve a fixed desired information sum-rate,despite the stringent per-antenna CE constraint, the proposed CE precoding scheme performs close to the GBC sum-capacity (under APC) achieving scheme.

• 3.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Power-Efficient Downlink Communication Using Large Antenna Arrays: The Doughnut Channel2012In: 2012 IEEE INTERNATIONAL CONFERENCE ON COMMUNICATIONS (ICC), IEEE , 2012, p. 2145-2150Conference paper (Refereed)

Large antenna arrays at the base station can facilitate power efficient single user downlink communication due to the inherent array power gain, i.e., under an average only total transmit power constraint, for a fixed desired information rate, the required total transmit power can be reduced by increasing the number of base station antennas (e. g. with i.i.d. fading, the required total transmit power can be reduced by roughly 3 dB with every doubling in the number of base station antennas, i.e., an O(N) array power gain can be achieved with N antennas). However, in practice, building power efficient large antenna arrays would require power efficient amplifiers/analog RF components. With current technology, highly linear power amplifiers generally have low power efficiency, and therefore linearity constraints on power amplifiers must be relaxed. Under such relaxed linearity constraints, the transmit signal that suffers the least distortion is a signal with constant envelope (CE). In this paper, we consider a single user Gaussian multiple-input single-output (MISO) downlink channel where the signal transmitted from each antenna is constrained to have a constant envelope (i.e., for every channel-use the amplitude of the signal transmitted from each antenna is constant, irrespective of the channel realization). We show that under such a per-antenna CE constraint, the complex noise-free received signal lies in the interior of a "doughnut" shaped region in the complex plane. The per-antenna CE constrained MISO channel is therefore equivalent to a doughnut channel, i.e., a single-input single-output (SISO) AWGN channel where the channel input is constrained to lie inside a "doughnut" shaped region. Using this equivalence, we analytically compute a closed-form expression for an achievable information rate under the per-antenna CE constraint. We then show that, for a broad class of fading channels (i.i.d. and direct-line-of-sight (DLOS)), even under the more stringent per-antenna CE constraint (compared to the average only total power constraint), an O(N) array power gain can still be achieved with N base station antennas. We also show that with N >> 1, compared to the average only total transmit power constrained channel, the extra total transmit power required under the per-antenna CE constraint, to achieve a desired information rate is small and bounded for a broad class of fading channels (i.i.d. and DLOS). We also propose novel CE precoding algorithms. The analysis and algorithms presented are general and therefore applicable to conventional systems with a small number of antennas. Analytical results are supported with numerical results for the i.i.d. Rayleigh fading channel.

• 4.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Dept. of Electrical and Computer Systems Eng. Monash University, Melbourne, Australia. Dept. of Electrical and Computer Systems Eng. Monash University, Melbourne, Australia. Dept. of Electricam and Communication Eng. Indian Institute of Science, Bangalore, India..
MIMO Precoding with X- and Y- Codes2011In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 57, no 6, p. 3542-3566Article in journal (Refereed)

We consider a slow fading nt x nr multiple-input multiple-output (MIMO) system with channel state information (CSI) at both the transmitter and receiver. Since communication in such scenarios is subject to block fading, reception reliability, quantified in terms of the achievable diversity gain, is of importance. A simple and well known precoding scheme is based upon the singular value decomposition (SVD) of the channel matrix, which transforms the MIMO channel into parallel subchannels. Despite having low maximum likelihood decoding (MLD) complexity, this SVD based precoding scheme provides a diversity gain which is limited by the diversity gain of the weakest subchannel. We therefore propose X- and YCodes, which improve the diversity gain of the SVD precoding scheme, by jointly coding information across a pair of subchannels (i.e., pairing subchannels). In particular, subchannels with high diversity gain are paired with those having low diversitygain. A pair of subchannels is jointly encoded using a 2 x 2 real matrix, which is fixed a priori and does not change with each channel realization. For X-Codes, these matrices are 2-dimensional rotation matrices parameterized by a single angle, while for Y-Codes, these matrices are 2-dimensional upper left triangular matrices. Also, since joint coding is performed only across a pair of subchannels, the joint MLD complexity remains low. In particular, the MLD complexity of Y-Codes is even lower than that of X-Codes, and is equivalent to symbol by symbol detection. Moreover, we propose X-, Y-Precoders with the same structure as X-, Y-Codes, but with encoding matrices adapted to each channel realization. With respect to the error probability performance, the optimal encoding matrices for X-, YCodes/ Precoders are derived analytically and numerically. Whencompared to other precoding schemes reported in the literature, it is observed that X-Codes/Precoders perform better in wellconditioned channels, while Y-Codes/Precoders perform better in ill-conditioned channels.

• 5.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Dept. of Electrical and Computer Systems Eng. Monash University, Melbourne, Australia. Dept. of Electrical and Computer Systems Eng. Monash University, Melbourne, Australia. Dept. of Electrical and Communication Eng. Indian Institute of Science (IISc) Bangalore, India..
Precoding by Pairing Subchannels to Increase MIMO Capacity with Discrete Input Alphabets2011In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 57, no 7, p. 4156-4169Article in journal (Refereed)

We consider Gaussian multiple-input multiple-output (MIMO) channels with discrete input alphabets. We propose a non-diagonal precoder based on the X-Codes in \cite{Xcodes_paper} to increase the mutual information. The MIMO channel is transformed into a set of parallel subchannels using Singular Value Decomposition (SVD) and X-Codes are then used to pair the subchannels. X-Codes are fully characterized by the pairings and a $2\times 2$ real rotation matrix for each pair (parameterized with a single angle). This precoding structure enables us to express the total mutual information as a sum of the mutual information of all the pairs. The problem of finding the optimal precoder with the above structure, which maximizes the total mutual information, is solved by {\em i}) optimizing the rotation angle and the power allocation within each pair and {\em ii}) finding the optimal pairing and power allocation among the pairs. It is shown that the mutual information achieved with the proposed pairing scheme is very close to that achieved with the optimal precoder by Cruz {\em et al.}, and is significantly better than Mercury/waterfilling strategy by Lozano {\em et al.}. Our approach greatly simplifies both the precoder optimization and the detection complexity, making it suitable for practical applications.

• 6.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Achievable Rates of ZF Receivers in Massive MIMO with Phase Noise Impairments2013In: 2013 ASILOMAR CONFERENCE ON SIGNALS, SYSTEMS AND COMPUTERS, 2013, p. 1004-1008Conference paper (Refereed)

The effect of oscillator phase noise on the sum-rate performance of large multi-user multiple-input multiple-output (MU-MIMO) systems, termed as Massive MIMO, is studied. A Rayleigh fading MU-MIMO uplink channel is considered, where channel state information (CSI) is acquired via training. The base station (BS), which is equipped with an excess of antenna elements, M, uses the channel estimate to perform zero-forcing (ZF) detection. A lower bound on the sum-rate performance is derived. It is shown that the proposed receiver structure exhibits an O($\sqrt{M}$) array power gain. Additionally, the proposed receiver is compared with earlier studies that employ maximum ratio combining and it is shown that it can provide significant sum-rate performance gains at the medium and high signal-to-noise-ratio (SNR) regime. Further, the expression of the achievable sum rate provides new insights on the effect of various parameters on the overall system performance.

• 7.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Effect of Oscillator Phase Noise on Uplink Performance of Large MU-MIMO Systems2012In: Proceedings of the 50th Annual Allerton Conference on Communication, Control, and Computing,, IEEE , 2012, p. 1190-1197Conference paper (Refereed)

The effect of oscillator phase noise on the sumrate performance of a frequency selective multi-user multipleinputmultiple-output (MU-MIMO) uplink channel is studiedunder imperfect channel state information. A maximum ratiocombining detection strategy is employed by the base station(BS) (having a large antenna array of M elements), and ananalytical expression of a lower bound on the sum capacity ofthe system is derived. It is shown that an array power gainof O(pM) is achievable. It is also observed that phase noiseeffectively limits the fraction of the time used for informationtransmission and the number of users in the system. Finally itis concluded that, phase noise degrades the performance butdoes not eliminate the fundamental gains of a Large ScaleAntenna System (LSAS), i.e., power efficiency and high sumrate performance with low complexity receiver processing.

• 8.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
On the Optimality of Single-Carrier Transmission in Large-Scale Antenna Systems2012In: IEEE Wireless Communications Letters, ISSN 2162-2337, E-ISSN 2162-2345, Vol. 1, no 4, p. 276-279Article in journal (Other academic)

A single carrier transmission scheme is presentedfor the frequency selective multi-user (MU) multiple-input singleoutput(MISO) Gaussian Broadcast Channel (GBC) with a basestation (BS) having M antennas and K single antenna users.The proposed transmission scheme has low complexity andfor M ≫ K it is shown to achieve near optimal sum-rateperformance at low transmit power to receiver noise power ratio.Additionally, the proposed transmission scheme results in anequalization-free receiver and does not require any MU resourceallocation and associated control signaling overhead. Also, thesum-rate achieved by the proposed transmission scheme is shownto be independent of the channel power delay profile (PDP). Interms of power efficiency, the proposed transmission scheme alsoexhibits an O(M) array power gain. Simulations are used toconfirm analytical observations.

• 9.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Uplink Performance of Time-Reversal MRC in Massive MIMO Systems subject to Phase Noise2015In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, p. 711-723Article in journal (Refereed)

Multi-user multiple-input multiple-output (MU-MIMO) cellular systems with an excess of base station (BS) antennas (Massive MIMO) offer unprecedented multiplexing gains and radiated energy efficiency. Oscillator phase noise is introduced in the transmitter and receiver radio frequency chains and severely degrades the performance of communication systems. We study the effect of oscillator phase noise in frequency-selective Massive MIMO systems with imperfect channel state information (CSI) and M BS antennas. In particular, we consider two distinct operation modes, namely when the phase noise processes at the BS antennas are identical (synchronous operation) and when they are independent (non-synchronous operation). We analyze a linear and low-complexity time-reversal maximum-ratio combining (TR-MRC) reception strategy. For both operation modes we derive a lower bound on the sum-capacity and we compare the performance of the two modes. Based on the derived achievable sum-rate, we show that with the proposed receive processing an O($\sqrt{M}$) array gain is achievable. Due to the phase noise drift the estimated effective channel becomes progressively outdated. Therefore, phase noise effectively limits the length of the interval used for data transmission and the number of scheduled users. The derived achievable rates provide insights into the optimum choice of the data interval length and the number of scheduled users.

• 10.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Single-User Beamforming in Large-Scale MISO Systems with Per-Antenna Constant-Envelope Constraints: The Doughnut Channel2012In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 11, no 11, p. 3992-4005Article in journal (Refereed)

Large antenna arrays at the transmitter (TX) have recently been shown to achieve remarkable intra-cell interference suppression at low complexity. However, building large arrays in practice, would require the use of power-efficient RF amplifiers, which generally have poor linearity characteristics and hence would require the use of input signals with a very small peak-to-average power ratio (PAPR). In this paper, we consider the single-user Multiple-Input Single-Output (MISO) channel for the case where the TX antennas are constrained to transmit signals having constant envelope (CE). We show that, with per-antenna CE transmission the effective channel seen by the receiver is a SISO AWGN channel with its input constrained to lie in a doughnut-shaped region. For a broad class of fading channels, analysis of the effective doughnut channel shows that under a per-antenna CE input constraint, i) compared to an average-only total TX power constrained MISO channel, the extra total TX power required to achieve a desired information rate is small and bounded, ii) with N TX antennas an O(N) array power gain is achievable, and iii) for a desired information rate, using power-efficient amplifiers with CE inputs would require significantly less total TX power when compared to using highly linear (power-inefficient) amplifiers with high PAPR inputs.

• 11.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Monash University of Clayton. Monash University of Clayton. Indian Institute Science.
Modulation Diversity in Fading Channels with a Quantized Receiver2012In: Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on, ISSN 2157-8095, Vol. 11, no 1, p. 2949-2953Article in journal (Refereed)

In this paper, we address the design of codes which achieve modulation diversity in block fading single-input single-output (SISO) channels with signal quantization at the receiver. With an unquantized receiver, coding based on algebraic rotations is known to achieve maximum modulation coding diversity. On the other hand, with a quantized receiver, algebraic rotations may not guarantee gains in diversity. Through analysis, we propose specific rotations which result in the codewords having equidistant component-wise projections. We show that the proposed coding scheme achieves maximum modulation diversity with a low-complexity minimum distance decoder and perfect channel knowledge. Relaxing the perfect channel knowledge assumption we propose a novel channel training/estimation technique to estimate the channel. We show that our coding/training/estimation scheme and minimum distance decoding achieves an error probability performance similar to that achieved with perfect channel knowledge.

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