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Journal Article•DOI•

ML Detection in Phase Noise Impaired SIMO Channels With Uplink Training

Antonios Pitarokoilis1, Emil Björnson1, Erik G. Larsson1•
Linköping University1
01 Jan 2016-IEEE Transactions on Communications (IEEE)-Vol. 64, Iss: 1, pp 223-235
TL;DR: The problem of maximum likelihood (ML) detection in training-assisted single-input multiple-output (SIMO) systems with phase noise impairments is studied for two different scenarios, i.e., the case when the channel is deterministic and known (constant channel) and the case of stochastic and unknown (fading channel).
Abstract: The problem of maximum likelihood (ML) detection in training-assisted single-input multiple-output (SIMO) systems with phase noise impairments is studied for two different scenarios, i.e., the case when the channel is deterministic and known (constant channel) and the case when the channel is stochastic and unknown (fading channel). Furthermore, two different operations with respect to the phase noise sources are considered, namely, the case of identical phase noise sources and the case of independent phase noise sources over the antennas. In all scenarios, the optimal detector is derived for a very general parameterization of the phase noise distribution. Furthermore, a high signal-to-noise-ratio (SNR) analysis is performed to show that symbol-error-rate (SER) floors appear in all cases. The SER floor in the case of identical phase noise sources (for both constant and fading channels) is independent of the number of antenna elements. In contrast, the SER floor in the case of independent phase noise sources is reduced when increasing the number of antenna elements (for both constant and fading channels). Finally, the system model is extended to multiple data channel uses and it is shown that the conclusion is valid for these setups, as well.

Summary (3 min read)

Jump to: [I. INTRODUCTION] – [II. SYSTEM MODEL] – [A. Constant Channel (CC)] – [B. Fading Channel (FC)] – [Proposition 1:] – [Proposition 2:] – [A. High SNR Analysis for the Synchronous Operation] – [The observation vector] – [V. NUMERICAL EXAMPLES] – [A. Extension to Longer Data Intervals] – [ŝt = arg max] and [VI. CONCLUSIONS]

I. INTRODUCTION

  • The demand on wireless data services is expected to increase significantly over the next decade.
  • Hence, the study of the impact of hardware impairments is of particular importance and relevance in Massive MIMO systems.
  • This happens when the variance of the phase noise innovations and the coherence interval of the channel fading are large [7, Section IV.C].
  • Finally, the authors of [11] observe that the phase noise number (i.e., the second term in the high-SNR capacity expansion) is higher in the case of independent phase noise sources.
  • Motivated by that, the authors rigorously derive the optimal detector in phase noise impaired SIMO systems with uplink training for various cases of interest.

II. SYSTEM MODEL

  • A single-antenna user communicates with a BS equipped with M antenna elements, which are impaired with phase noise.
  • Two different cases are treated with respect to the knowledge of the wireless channel.
  • Namely, in the first case, termed as constant channel (CC), the channel is assumed deterministic and known at the receiver [25] , [26] .
  • Hence, the transmitted symbol is observed in the presence of only additive noise and multiplicative phase noise.
  • The authors start with the description of the CC for simplicity and subsequently they describe the extension to the FC.

A. Constant Channel (CC)

  • The Fourier expansion in (3) can represent any pdf in [−π, π) that is continuous, differentiable, unimodal, even and has zero mean.
  • For oscillators equipped with a PLL, the phase noise increment is well modeled by a random variable from a von Mises (or, equivalently, Tikhonov) distribution [11] .
  • This models a practical distributed antenna deployment where the use of a separate oscillator per BS antenna is required.
  • Hybrid topologies are also possible, however, they are less interesting to analyze since their SER is expected to lie between the SER of the S and NS operations.
  • Hence, they are not considered in this work.

B. Fading Channel (FC)

  • During the second channel use, the signal received at the m-th BS antenna is given by EQUATION.
  • The fading coefficients h m remain constant over both channel uses.

Proposition 1:

  • The result follows trivially from Proposition 1 by taking the natural logarithm of (44), ln (p(x, y|s)), and dropping the terms that are independent of s.
  • The results in Corollary 1 hold for arbitrary constellations.
  • In the following the authors particularize Corollary 1 for the case of phase shift keying (N-PSK) constellations.

Proposition 2:

  • For the S operation, the calculation of the optimal detectors requires the computation of inner products between vectors of size M. For the NS operation, the computational complexity scales also linearly with M. Hence, the complexity of the optimal detectors scales in all cases linearly with the number of BS antennas.
  • From (15) and ( 25), the ML detectors involve the calculation of infinite series, where the l-th term is a function of the modified Bessel functions, I l .
  • Since the series converge very fast, the truncation error can be made negligible.
  • The following lemma is useful to demonstrate this claim.

A. High SNR Analysis for the Synchronous Operation

  • Hence, distinguishing two symbols that have different amplitude is trivial at high-SNR.
  • Distinguishing two symbols that have different phase is much more challenging.
  • Constellation points that are at the same radius belong to the same sub-constellation and their pairwise error probability can be calculated in a manner similar to PSK constellations.
  • The authors proceed by deriving the asymptotic SER at high-SNR for PSK constellations.
  • For the CC-S case, let φ be zero mean random variable with pdf p Φ (φ) as in (3) , where the distribution is unimodal and symmetric around the mean, also known as Proposition 4.

The observation vector

  • The derivation of the optimal detection rule even in this regime appears to be mathematically intractable.
  • The suboptimal decision rule that the authors use is the minimum Euclidean distance from a scaled N-PSK, i.e., ŝ = arg min EQUATION ) where S is the N-PSK alphabet.
  • Hence, the SER floor for the FC-NS case can be made arbitrarily small as M → ∞.
  • Similar conclusions were also drawn in [11] for the uplink case.
  • Similar conclusions have already been drawn in prior work, such as [12] , where it is shown that in the NS operation the phase noise impairments at the BS average out but not the ones at the user terminals.

V. NUMERICAL EXAMPLES

  • In this section the authors present numerical examples that verify the validity of the analytical results presented in Sections III and IV.
  • As κ increases the distribution becomes more concentrated around the mean.
  • In the medium SNR regime (≈ 0 − 10 [dB]) the non-synchronous operation has a clear advantage over the synchronous operation.
  • The theoretical SER floor for the CC-S and FC-S cases is also given by the dotted line.
  • This implies that the additional randomness due to fading in the FC-NS case has a direct impact on the SER performance.

A. Extension to Longer Data Intervals

  • In practice more than one channel uses are spent for data transmission.
  • For this purpose, the authors consider a setup where the data interval is extended to T channel uses.
  • Hence, the approach can be summarized as follows.
  • If a suboptimal tractable detector for the NS operation performs better than a genieaided, i.e. better-than-optimal, tractable detector for the S operation, then the same will hold for the corresponding optimal detectors.
  • As noted, this detector is suboptimal but implementable.

ŝt = arg max

  • This detector performs better than the actual causal ML detector for the synchronous operation, since it has the additional knowledge of the true prior symbols and the evolution of the phase noise process up to t − 1.
  • This corresponds to the practical scenario of free-running oscillators.
  • It is clear that the suboptimal FC-NS detector performs better than the 'better-than-optimal' FC-S detector, which establishes the claim that the results of the previous sections are valid in more complex setups.

VI. CONCLUSIONS

  • The problem of ML detection in a training-assisted single-user SIMO channel with phase noise impairments and M BS antennas was studied.
  • For both assumptions on the channel gains two operations were investigated, i.e., the synchronous and non-synchronous operations.
  • Closed-form expressions of the optimal detectors were given for a general parameterization of the phase noise increments.
  • SER floors were observed for all cases under study.
  • For the synchronous operation the SER floors were independent of M for both the constant and fading channel case.

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ML Detection in Phase Noise Impaired SIMO
Channels with Uplink Trainin
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Antonios Pitarokoilis, Emil Björnson and Erik G. Larsson
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Linköping University Post Print
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Antonios Pitarokoilis, Emil Björnson and Erik G. Larsson, ML Detection in Phase Noise
Impaired SIMO Channels with Uplink Trainin, 2015, IEEE Transactions on Communications,
http://dx.doi.org/10.1109/TCOMM.2015.2498163
Postprint available at: Linköping University Electronic Press
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-122617
1
ML Detection in Phase Noise Impaired SIMO
Channels with Uplink Training
Antonios Pitarokoilis, Student Member, IEEE, Emil Bj
¨
ornson, Member, IEEE,
and Erik G. Larsson, Senior Member, IEEE
Abstract
The problem of maximum likelihood (ML) detection in training-assisted single-input multiple-output
(SIMO) systems with phase noise impairments is studied for two different scenarios, i.e. the case when
the channel is deterministic and known (constant channel) and the case when the channel is stochastic
and unknown (fading channel). Further, two different operations with respect to the phase noise sources
are considered, namely, the case of identical phase noise sources and the case of independent phase
noise sources over the antennas. In all scenarios the optimal detector is derived for a very general
parameterization of the phase noise distribution. Further, a high signal-to-noise-ratio (SNR) analysis is
performed to show that symbol-error-rate (SER) floors appear in all cases. The SER floor in the case of
identical phase noise sources (for both constant and fading channels) is independent of the number of
antenna elements. In contrast, the SER floor in the case of independent phase noise sources is reduced
when increasing the number of antenna elements (for both constant and fading channels). Finally, the
system model is extended to multiple data channel uses and it is shown that the conclusions are valid
for these setups, as well.
Index Terms
Phase Noise, Communication Systems, MIMO Systems.
This work was supported by the Swedish Foundation for Strategic Research (SSF) and ELLIIT. The authors are with the
Division of Communication Systems, Dept. of Electrical Engineering (ISY), Link¨oping University, 581 83 Link¨oping, Sweden.
This work was presented in part at IEEE ICC 2015, London, UK, June 2015.
2
I. INTRODUCTION
The demand on wireless data services is expected to increase significantly over the next
decade. Hence, next generation wireless networks must provide substantially larger data rates.
Recently, it has been shown that massive multiple-input multiple-output (Massive MIMO) can
provide substantial gains in spectral efficiency and radiated energy efficiency [1]–[3]. In Massive
MIMO, K non-cooperative users are served by a base station (BS) with M BS antennas over
the same time and frequency resources. When M is significantly larger than K (e.g., one order
of magnitude) linear transmit and receive processing techniques are close to optimal and the
minimum required radiated power can be reduced as a function of M when a fixed information
rate is desired [4], [5].
In Massive MIMO, the BS uses estimated channel impulse responses to coherently combine the
received uplink signals. The quality of the estimated channel state information (CSI) has direct
impact on the performance of Massive MIMO systems. Hardware impairments further degrade
the acquired channel knowledge. In addition, the deployment of Massive MIMO systems requires
the use of inexpensive hardware, so that the monetary cost remains low. Such equipment is likely
to have limited accuracy. Hence, the study of the impact of hardware impairments is of particular
importance and relevance in Massive MIMO systems. Recently, this area has attracted significant
research interest [6].
An unavoidable hardware impairment in wireless communications is phase noise. Phase noise
is introduced in communications systems during the upconversion of the baseband signal to
passband and vice versa due to imperfections in the circuitry of local oscillators. Ideally, the
local oscillators should produce a sinusoidal wave that is perfectly stable in terms of amplitude,
frequency and phase. In the frequency domain that would correspond to a Dirac impulse located
at the carrier frequency. However, the phase of the generated carrier of realizable oscillators
typically fluctuates. This is manifested by a spectral widening around the carrier frequency
3
in the power spectral density of the local oscillator output. Phase noise can cause significant
degradation in scenarios where it varies faster than the channel fading. This happens when the
variance of the phase noise innovations and the coherence interval of the channel fading are
large [7, Section IV.C]. Some scenarios where the phase noise degradation dominates over the
degradation due to channel variation are fixed indoor communication and Line-of-Sight (LoS)
communication, such as WiFi at millimeter-wave frequencies and wireless broadband-to-home
services, respectively. Further, phase noise causes a random rotation of the information signal,
i.e. it is a multiplicative distortion. This makes the analysis and mitigation of the phase noise
considerably more involved in comparison to additive distortions, such as quantization noise and
generic non-linearities. In fact, it appears that Massive MIMO systems are less robust to phase
noise than hardware impairments modeled as additive distortions [7].
The problem of calculating the capacity of phase noise impaired systems is particularly
challenging. Closed-form expressions are not available even for the simplest cases. In [8] the
author derives the first two terms of the high signal-to-noise–ratio (SNR) expansion of the
capacity of a phase noise impaired non-fading single-input single-output (SISO) system for any
phase noise process that is ergodic, stationary, and has finite differential entropy rate. In [9]
the first two terms of the high-SNR capacity expansion for the block memoryless phase noise
channel are derived. In [10] a high-SNR capacity upper bound for the Wiener phase noise
MIMO channel is derived. Recently, the authors in [11] report approximate upper and lower
bounds on the high-SNR capacity for the multiple-input single-output (MISO) and single-input
multiple-output (SIMO) phase noise channels and compare the cases where separate and common
oscillators are used. Lower bounds on the sum-capacity of multi-user Massive MIMO systems
with linear reception and phase noise impairments are recently reported in [7], [12] and [13].
The problem of data detection in non-fading channels with phase noise impairments has been
extensively studied in the literature. In [14] the optimal binary detector for partially coherent
channels is derived. Detectors that are optimal in the high-SNR regime are derived in [15]. In [16]
4
the problem of optimal symbol-by-symbol (SBS) detection in SISO systems is investigated when
the carrier phase is unknown and it is shown that the computational complexity is prohibitive
in the general case. A suboptimal but implementable algorithm is derived when the unknown
carrier phase stays constant for a block of consecutive symbols and its performance is compared
to the case of exact carrier phase information. In [17] a simulation-based phase noise model
is used and the existence EVM floors for SISO systems is shown. The authors of [18] derive
algorithms for SISO phase noise channels without fading based on factor graphs and the sum-
product algorithm. An extension of this work for single-user MIMO systems is given in [19],
where an estimate of the channel is inserted into the likelihood function as if this estimate
were equal to the true channel–resulting in a mismatched detector. A set of soft metrics for the
single-user non-fading phase noise channel under various assumptions is derived in [20] and
their performance is compared. In [21] an algorithm for joint data detection and phase noise
estimation is derived for single-user MIMO systems and its performance is compared to a derived
Cram´er-Rao bound.
Even though the problem of phase noise in communication systems is extensively studied,
there are still many open questions. In particular, the effect of phase noise on beamforming is
not fully understood yet. In [22] the authors study the effect of phase noise in the error vector
magnitude (EVM) of an antenna array. They show through analysis and measurements that the
EVM at the direction of the main lobe is reduced when independent phase noise sources are
used. In [12] achievable rates for the uplink transmission of Massive MIMO systems with time-
reversal maximum-ratio-combining in frequency-selective channels are derived for the case of
identical and independent phase noise sources. It is observed that the use of independent phase
noise sources at the BS results in an increased achievable rate. This result is also supported by a
toy example, where the actual capacity can be easily computed and shows that the capacity with
independent phase noise sources is larger that the capacity with a single phase noise source.
A similar result is reported in [7], where the authors show that the phase noise variance can
Citations
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Journal Article•DOI•
A Survey of Physical-Layer Authentication in Wireless Communications

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Ning Xie1, Zhuoyuan Li1, Haijun Tan1•
Shenzhen University1
01 Jan 2021-IEEE Communications Surveys and Tutorials
TL;DR: A detailed survey of features and techniques that can be used in the Physical-Layer Authentication schemes, and divides the existing PLA schemes into two categories: passive and active schemes.
Abstract: Authentication is an important issue in wireless communications because the open nature of the wireless medium provides more security vulnerabilities. Recently, Physical-Layer Authentication (PLA) attracts many research interests because it provides information-theory security and low complexity. Although many researchers focus on the PLA and exploit its potential in enhancing wireless security, the literature is surprisingly sparse with no comprehensive overview of the state-of-the-art PLA and the key fundamentals involved. Thus, this article provides a detailed survey of features and techniques that can be used in the PLA. We categorize the existing PLA schemes into two categories: passive and active schemes. In the passive schemes, a receiver authenticates the transmitter based on the physical-layer features of the received signals. We further divide the passive schemes into two sub-categories: device-based features and channel-based features. In the active schemes, a transmitter generates a tag based on a secret key and embeds it into a source message. Then, a receiver authenticates the transmitter based on the tag whether it exists in the received signal. We further divide active schemes into two sub-categories: non-covert schemes and covert schemes. Moreover, we also provide some future research directions.

76 citations

Cites background from "ML Detection in Phase Noise Impaire..."

  • ...In other words, the amplitude of phase noise is determined by the imperfections of local oscillators [66]....

    [...]

Journal Article•DOI•
RF Impairments in Wireless Transceivers: Phase Noise, CFO, and IQ Imbalance – A Survey

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Amirhossein Mohammadian1, Chintha Tellambura1•
University of Alberta1
02 Aug 2021-IEEE Access
TL;DR: In this article, the authors present RF-impairment signal models and discuss their impacts, including phase noise (PN), carrier frequency offset (CFO), and in-phase (I) and quadrature-phase imbalance.
Abstract: Wireless transceivers for mass-market applications must be cost effective. We may achieve this goal by deploying non-ideal low-cost radio frequency (RF) analog components. However, their imperfections may result in RF impairments, including phase noise (PN), carrier frequency offset (CFO), and in-phase (I) and quadrature-phase (Q) imbalance. These impairments introduce in-band and out-of-band interference terms and degrade the performance of wireless systems. In this survey, we present RF-impairment signal models and discuss their impacts. Moreover, we review RF-impairment estimation and compensation in single-carrier (SC) and multicarrier systems, especially orthogonal frequency division multiplexing (OFDM). Furthermore, we discuss the effects of the RF impairments in already-established wireless technologies, e.g., multiple-input multiple-output (MIMO), massive MIMO, full-duplex, and millimeter-wave communications and review existing estimation and compensation algorithms. Finally, future research directions investigate the RF impairments in emerging technologies, including cell-free massive MIMO communications, non-orthogonal multicarrier systems, non-orthogonal multiple access (NOMA), ambient backscatter communications, and intelligent reflecting surface (IRS)-assisted communications. Furthermore, we discuss artificial intelligence (AI) approaches for developing estimation and compensation algorithms for RF impairments.

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Alexandros-Apostolos A. Boulogeorgos, Αλέξανδρος Απόστολος Μπουλογεώργος
01 Jan 2016-viXra
TL;DR: Η μελέτη και σχεδίαση των ση χρηστώn σε εφαρματικής που απαιτοos�́ν υψηλό ρυθμ
Abstract: During the last decades, wireless communications have evolved from a scarce technology, used by professionals for niche applications to a rapidly advancing research field. Ever increasing proliferation of smart devices, the introduction of new emerging multimedia applications, together with an exponential rise in wireless data (multimedia) demand and usage are already creating a significant burden on existing wireless systems. Future wireless networks, with improved data rates, capacity, latency, and quality of service (QoS) requirements, are expected to be the panacea of most of the current wireless systems’ problems. Interference management is critical towards this goal, whereas transceiver design and implementation are expected to play an important role. This thesis investigates the influence of interference in wireless systems, revisits promising network- and user-side interference management solutions, as well as studies the impact of interference, caused by hardware imperfections, on the performance of the wireless link and propose countermeasures. The thesis is divided into two parts. In the first part of the thesis, different types of interference and modern interference management solutions, which are expected to be used in the future wireless networks, are reviewed. Moreover, the influence of fading and interference, due to the existence of multiple possible users operating simultaneously in the same carrier frequency, on the spectrum sensing capability of a low-complexity energy detector (ED) is investigated. Analytical tools for the performance evaluation of this problem, i.e., the false alarm and detection probabilities, are derived, while the problem of appropriately selecting the energy detection threshold and the spectrum sensing duration, in order to satisfy a specific requirement, is discussed. The results reveal the detrimental effect of interference and the importance of taking into consideration the wireless environment when evaluating the ED spectrum sensing performance and selecting the ED threshold. Finally, the offered analytical framework can be applied in cognitive radio systems, which are included in several wireless standards, and are expected to be employed in ultra-dense wireless environments. The second part of this thesis investigates the impact of transceivers radio frequency (RF) front-end imperfections on the performance of the wireless system. RF imperfections generally result to signal distortion in single-carrier communications, while, in multi-carrier communications, they additionally cause interference. In both cases, RF imperfections may cause significant degradation to the quality of the wireless link, which becomes more severe as the data rates increases. Motivated by this, after briefly illustrating the influence of different types of RF imperfections, namely in-phase and quadrature imbalance (IQI), phase noise, and amplifiers non-linearities, the analytical framework for the evaluation and quantification of the effect of IQI on wireless communications in the context of cascaded fading channels, is derived. To this end, closed-form expressions for the outage probability over N∗Nakagami-m channels for both the cases of single- and multi-carrier communications, when at least one communication node suffers from IQI, are provided. To justify the importance and practical usefulness of the analysis, the offered expressions along with several deduced corresponding special cases are employed in the context of vehicle-to-vehicle communications. This study gives critical insight for the performance degradation in wireless communications, due to RF imperfections, and indicates the need for designing proper RF imperfections compensation techniques. Next, the impact of IQI and partial successive interference suppression (SIS) in the spectrum sensing of full duplex CR systems, for both the cases of single- and multi-carrier ED, is studied. In this context, closed-form expressions are derived for the false alarm and detection probabilities, in the general case, where partial SIS and joint transmitter and receiver IQI are considered. The derived expressions can be used in order to properly select the energy detection threshold that maximizes the ED spectrum sensing capabilities. 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Furthermore, the impact of uncompensated IQI on orthogonal frequency division multiple access (OFDMA) systems, in which a power allocation (PA) policy is employed in order to maximize each user’s capacity, is demonstrated. To overcome, the user’s capacity loss, due to IQI, a novel, low-complexity PA strategy is presented, which, by taking into account the levels of IQI of the served users, notably enhance each user’s achievable capacity. Finally, a novel low-complexity scheme, which improves the performance of single-antenna multi-carrier communication systems, suffering from IQI at the receiver, is proposed. The proposed scheme, which we refer to as I/Q imbalance self-interference coordination (IQSC), not only mitigate the detrimental effect of IQI, but, through appropriate signal processing, also coordinates the self-interference terms produced by IQI, in order to achieve second-order frequency diversity. 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43 citations

Journal Article•DOI•
Physical Layer Authentication Jointly Utilizing Channel and Phase Noise in MIMO Systems

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Pinchang Zhang, Yulong Shen1, Xiaohong Jiang2, Bin Wu3•
Xidian University1, Future University Hakodate2, Tianjin University3
17 Jan 2020-IEEE Transactions on Communications
TL;DR: It is demonstrated that the proposed scheme makes it possible for us to flexibly control authentication performance by adjusting thresholds (for channel gain, phase noise, and decision, respectively) to achieve a required authentication performance in specific MIMO applications.
Abstract: In this paper, we propose a physical layer authentication scheme in heterogeneous coexist multiple-input-multiple-output (MIMO) systems. This scheme utilizes two physical layer features in terms of location-specific channel gains and transmitter-specific phase noise caused by imperfect oscillators to identify transmitters. Three properties of the proposed scheme: covertness, robustness, and security, are analyzed in detail. By using a maximum-likelihood estimator (MLE) and extended Kalman filter (EKF), we estimate channel gains and phase noise, and formulate variances of estimation errors. We also quantize the temporal variations of channel gains and phase noise through the developed quantizers. Based on quantization results and theories of hypothesis testing and stochastic process, we then derive the closed-form expressions for false alarm and detection probabilities with the consideration of quantization errors. Simulations are carried out to validate the theoretical results of the two probabilities. Based on theoretical models, we further demonstrate that the proposed scheme makes it possible for us to flexibly control authentication performance by adjusting thresholds (for channel gain, phase noise, and decision, respectively) to achieve a required authentication performance in specific MIMO applications.

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Cites background from "ML Detection in Phase Noise Impaire..."

  • ...Due to the impairments of local oscillators, phase noise is generated during the up-conversion of baseband signal to bandpass and vice versa [14]....

    [...]

  • ...B = 2πc B Ts, where both c [m] X and c [n] B are constants and represent the one-sided 3-dB bandwidth of the Lorentzian spectrum of the oscillators at the m transmit and n receive antennas, respectively [14], [15], [27]....

    [...]

  • ...Phase noise is generated at both transmitter and receiver sides during the up-conversion of baseband signal to bandpass and vice versa due to the impairments of local oscillator [14], [15], [27]....

    [...]

  • ...According to [14]–[16], phase noise innovation variances are closely relevant to physical properties of oscillators, i....

    [...]

  • ...According to [14]–[16], phase noise is determined by the quality of the oscillators being used at the transmitter and receiver....

    [...]

Journal Article•DOI•
A Simple Phase Noise Suppression Scheme for Massive MIMO Uplink Systems

[...]

Yi-Fan Wang1, Ju-Hong Lee1•
National Taiwan University1
01 Jun 2017-IEEE Transactions on Vehicular Technology
TL;DR: Simulation results show that when the required SNR is satisfied, the output SNR of the proposed scheme can approach the upper bound, except for very large PN variances.
Abstract: In wireless communications, massive multiple-input multiple-output (MIMO) uplink systems in which the base station is equipped with a large number of antennas can provide significant spectral and energy efficiency by means of simple signal processing. Therefore, massive MIMO uplink systems are an attractive technology for next-generation wireless systems and for green communications. However, phase noise (PN) introduced by the impairment of oscillators can cause a severe performance loss in wireless communication systems. Solving the PN problem for massive MIMO uplink systems is challenging as it is a multivariate joint PN estimation and data detection problem. The optimal solution is difficult to derive and may lead to high complexity. In this paper, we propose a low-complexity PN suppression scheme based on the zero-forcing detector to solve this problem. By using the ideal PN free output signal-to-noise ratio (SNR) as a performance upper bound, simulation results show that when the required SNR is satisfied, the output SNR of the proposed scheme can approach the upper bound, except for very large PN variances. Moreover, the complexity of the proposed scheme is low because the proposed scheme can update the current PN estimation and data detection by the previous ones via a simple iterative process.

18 citations

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Patrick Billingsley
01 Jan 1979
TL;DR: In this paper, the convergence of distributions is considered in the context of conditional probability, i.e., random variables and expected values, and the probability of a given distribution converging to a certain value.
Abstract: Probability. Measure. Integration. Random Variables and Expected Values. Convergence of Distributions. Derivatives and Conditional Probability. Stochastic Processes. Appendix. Notes on the Problems. Bibliography. List of Symbols. Index.

6,334 citations

Journal Article•DOI•
Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas

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Thomas L. Marzetta1•
Bell Labs1
01 Nov 2010-IEEE Transactions on Wireless Communications
TL;DR: A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval and a complete multi-cellular analysis yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve.
Abstract: A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval. Time-division duplex operation combined with reverse-link pilots enables the base station to estimate the reciprocal forward- and reverse-link channels. The conjugate-transpose of the channel estimates are used as a linear precoder and combiner respectively on the forward and reverse links. Propagation, unknown to both terminals and base station, comprises fast fading, log-normal shadow fading, and geometric attenuation. In the limit of an infinite number of antennas a complete multi-cellular analysis, which accounts for inter-cellular interference and the overhead and errors associated with channel-state information, yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve. In particular the effects of uncorrelated noise and fast fading vanish, throughput and the number of terminals are independent of the size of the cells, spectral efficiency is independent of bandwidth, and the required transmitted energy per bit vanishes. The only remaining impairment is inter-cellular interference caused by re-use of the pilot sequences in other cells (pilot contamination) which does not vanish with unlimited number of antennas.

6,248 citations

"ML Detection in Phase Noise Impaire..." refers background in this paper

  • ...Recently, it has been shown that massive multiple-input multiple-output (Massive MIMO) can provide substantial gains in spectral efficiency and radiated energy efficiency [1]–[3]....

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Journal Article•DOI•
Massive MIMO for next generation wireless systems

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Erik G. Larsson1, Ove Edfors2, Fredrik Tufvesson2, Thomas L. Marzetta3•
Linköping University1, Lund University2, Bell Labs3
19 Feb 2014-IEEE Communications Magazine
TL;DR: While massive MIMO renders many traditional research problems irrelevant, it uncovers entirely new problems that urgently need attention: the challenge of making many low-cost low-precision components that work effectively together, acquisition and synchronization for newly joined terminals, the exploitation of extra degrees of freedom provided by the excess of service antennas, reducing internal power consumption to achieve total energy efficiency reductions, and finding new deployment scenarios.
Abstract: Multi-user MIMO offers big advantages over conventional point-to-point MIMO: it works with cheap single-antenna terminals, a rich scattering environment is not required, and resource allocation is simplified because every active terminal utilizes all of the time-frequency bins. However, multi-user MIMO, as originally envisioned, with roughly equal numbers of service antennas and terminals and frequency-division duplex operation, is not a scalable technology. Massive MIMO (also known as large-scale antenna systems, very large MIMO, hyper MIMO, full-dimension MIMO, and ARGOS) makes a clean break with current practice through the use of a large excess of service antennas over active terminals and time-division duplex operation. Extra antennas help by focusing energy into ever smaller regions of space to bring huge improvements in throughput and radiated energy efficiency. Other benefits of massive MIMO include extensive use of inexpensive low-power components, reduced latency, simplification of the MAC layer, and robustness against intentional jamming. The anticipated throughput depends on the propagation environment providing asymptotically orthogonal channels to the terminals, but so far experiments have not disclosed any limitations in this regard. While massive MIMO renders many traditional research problems irrelevant, it uncovers entirely new problems that urgently need attention: the challenge of making many low-cost low-precision components that work effectively together, acquisition and synchronization for newly joined terminals, the exploitation of extra degrees of freedom provided by the excess of service antennas, reducing internal power consumption to achieve total energy efficiency reductions, and finding new deployment scenarios. This article presents an overview of the massive MIMO concept and contemporary research on the topic.

6,184 citations

"ML Detection in Phase Noise Impaire..." refers background in this paper

  • ...Ratio of modified Bessel functions Iμ(x) I1(x) and the bound from Lemma 1 for μ = [2, 3, 4] as a function of x ....

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  • ...Recently, it has been shown that massive multiple-input multiple-output (Massive MIMO) can provide substantial gains in spectral efficiency and radiated energy efficiency [1]–[3]....

    [...]

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Frequently Asked Questions (14)
Q1. What contributions have the authors mentioned in the paper "Ml detection in phase noise impaired simo channels with uplink trainin" ?

The problem of maximum likelihood ( ML ) detection in training-assisted single-input multiple-output ( SIMO ) systems with phase noise impairments is studied for two different scenarios, i. e. the case when the channel is deterministic and known ( constant channel ) and the case when the channel is stochastic and unknown ( fading channel ). Further, two different operations with respect to the phase noise sources are considered, namely, the case of identical phase noise sources and the case of independent phase noise sources over the antennas. Further, a high signal-to-noise-ratio ( SNR ) analysis is performed to show that symbol-error-rate ( SER ) floors appear in all cases. 

For free-running oscillators phase noise is often modeled as a discrete-time Wiener process, where the increments are i.i.d. wrapped Gaussian increments [30]. 

The authors note that due to the symmetry of the von Mises distribution around its mean and the uniform priors on the input symbols, the conditioning on any particular input symbol does not affect the result. 

The likelihood function of the observed phases ψ ∆ = [ψ1, . . . , ψM ] T , given the transmitted phase arg(s), can be expressed aspΨ|S(ψ|s) = M∏m=1pΨm|s(ψm|s) = eκ∑M m=1 cos(ψm−arg(s))(2πI0(κ)) 

To get a mathematically tractable expression, the authors consider that the increments φm are independent VM(0, κ) random variables for m = 1, . . . ,M . 

During the first channel use, the received complex baseband symbol, xm, at the m-th BSantenna is given by7 xm = √ ρgme jθm + wm, m = 1, . . . ,M, (1)where wm is the m-th component of the additive white Gaussian noise (AWGN) vector, w, distributed as a circularly symmetric complex Gaussian random vector, CN (0, IM), θm is the unknown initial phase reference uniformly distributed in the interval [−π, π). 

From (15) and (25), the ML detectors involve the calculation of infinite series, where the l-th term is a function of the modified Bessel functions, Il(·). 

Mand the corresponding ML decision rule for symbols selected from some alphabet S is given byŝ = argmax s∈S pΨ|S(ψ|s) = argmax s∈SM∑m=1cos (ψm − arg(s)) . 

(32)Corollary 5: From (32) the authors observe that there is a non-zero SER floor for the CC-S case, which depends only on the statistics of the phase noise increment and the PSK constellation density, N , but is independent of the number of receive antennas, M .Remark 1: The preceding analysis is also true for FC-S by defining x̃ ∆= h and ỹ ∆= hejφs. 

Then the SER floor at the high-SNR for equiprobable N-PSK symbols is given byPr {ǫ} ∆= 1− ∫ π N− π NpΦ(φ)dφ = 1− α0 N− ∞∑l=12αl πl sin ( l π N ) . 

The BS uses the received vectors x and y jointly, to derive the optimum estimate, ŝ, of the transmitted information symbol, s, i.e.,ŝ ∆ = argmax s∈S p(x,y|s). 

(33)Proposition 5: The decision metric, µn, for the symbol ej 2πn N from an N-PSK constellationbased on (33) is given byµn ∆ =M∑m=1(cos(ψm − 2πnN) − cos (ψm) ) = M∑m=1sin (πnN) sin ( ψm − πnN). (34)17If the authors denote by ǫ the error event, i.e., the case where the detected symbol ŝ is different from the transmitted symbol s, then the SER for equiprobable input symbols is given byPr {ǫ} = Pr { N−1⋃n=1{µn > 

The detector for the S operation is given by Corollary 3.Corollary 3: For a discrete constellation, S, the ML symbol, ŝ, for the S operation isŝ = argmax s∈S LSs = argmax s∈S B + ln(β0 + 2 ∞∑l=1βl cos (lζ)). 

Proposition 2: The pdf of the received vectors (x,y) given a symbol s for the S operationis given byp(x,y|s) = A (β0 + 2∞∑l=1βl cos (lζ))(20)where for the CC-S case the authors have A as in (10),βl = αlIl(2 √ ρ|s∗gTy|) 

Trending Questions (1)
What is the full form of CIS channel information system channel induced system channel information system incorporated system?

Finally, the system model is extended to multiple data channel uses and it is shown that the conclusion is valid for these setups, as well.

See answers from 17 other papers