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Proceedings ArticleDOI

5G-microwave Tracking Performance Characterization

20 Sep 2019-pp 2285-2298
TL;DR: It turns out, the numerology counts towards the signal tracking performance, however, the nominal tracking capacity expressed by 5Gmicrowave signals at the highest sampling frequency is reduced due to the lack of full bandwidth useful signals.
Abstract: This paper evaluates the theoretical performance of signal tracking in a noisy single-path environment using 5G-microwave and LTE signals. Such OFDM signals suit navigation applications thanks to build-in symbol sequences which despite being designed for communication services since are known at the receiver can be exploited for pseudorange computation. By using multiple numerologies, 5G is putting into place an important degree of flexibility which was not explored before. It turns out, the numerology counts towards the signal tracking performance. However, the nominal tracking capacity expressed by 5G-microwave signals at the highest sampling frequency is reduced due to the lack of full bandwidth useful signals. Top-ranked LTE-CRS performance can hypothetically improve by aggregating multiple carrier components.

Summary (4 min read)

1 INTRODUCTION

  • Today, the world is crowded with communication devices and radio signals which, despite not being designed for navigation, still carry a certain degree of information for location purposes.
  • In the recent years, LTE signals have been regarded with interest for navigation.
  • Once the CIR is estimated, the time of arrival estimate can be obtained.
  • 5G sub-6 GHz signals have high central frequency (3.5 GHz) and large bandwidth (up to 100 MHz) compared to LTE signals (e.g. carrier frequency 2.8 GHz, bandwidth 20 MHz), therefore they offer potentially increased tracking performance, while they can be associated with a signal coverage that is comparable with LTE.
  • The signal architecture is described with focus on ranging signal components being compared and discussed.

2.1 OFDM signal structure

  • Orthogonal frequency division multiplexing is a multicarrier transmission scheme that divides the system bandwidth into several narrow equally spaced sub-bands, referred to as subcarriers.
  • Lastly, subcarriers have separate modulation schemes that can be adapted to the frequency channel variations in flexible manner, or even muted.
  • The encoding operation that maps individual blocks of data symbols to OFDM symbols is the inverse fast Fourier transform (IFFT).
  • Note that the FFT is an efficient processing unit.
  • As subcarrier spacing meets the inverse of symbol duration, an increase in the total number of subcarriers under the same bandwidth translates into a longer symbol duration and, therefore, a more robust multipath transmission.

Baseband channel model

  • Since the subcarriers are narrowband, the channel impulse response is assumed to be constant over the 𝑖-th transmitted symbol duration ∆𝑠′ .
  • 𝑁𝑡 is the number of samples per symbol including the cyclic prefix.
  • The equation above becomes much reduced under the assumption of timing and/or frequency perfectly synchronized, which holds if the residual errors 𝛾 and/or 𝜖 are nulls.

2.2 Correlation with an OFDM signal over the pilot subcarriers

  • In OFDM, reference data symbols known as pilots are transmitted at specific times and frequencies.
  • Usually, pilot subcarriers are spaced with regular interval across subcarriers, i.e., 1 subcarrier out of ∆𝑝𝑖 is a pilot subcarrier.
  • 𝑁𝑔 is the first pilot index for the 𝑖-th symbol;.
  • Note that the CIR estimate is the convolution of the actual CIR by a sinc function.

2.3 OFDM signal acquisition

  • Let us consider the propagation environment as an average white gaussian noise channel (AWGN).
  • Let us denote with 𝜎2 the variance of the filtered AWGN.
  • After the CIR estimation, the matching pursuit (MP) algorithm [5] can be performed to obtain the delay estimates of each multipath component.

2.4 OFDM signal tracking

  • The estimation accuracy of the signal delay can be improved using a delay-locked loop which includes a discrimination function and a loop filter.
  • It can be shown that the cross-correlation function between the received signal and the early (or late) replica is a shifted copy of the cross-correlation (11), with a positive (or negative) shift that matches the one used for the replica generation.
  • The normalization factor is the derivative of the s-curve in the linear region which is around the zero-crossing and it is used to make the slope of the discriminator function equal to one in the linear region.
  • The position computation has not yet been developed and it is out of the scope of the paper.

3 LTE AND 5G SIGNALS DESCRIPTION FOR SIGNAL APPLIED STUDY

  • Third Generation Partnership Project (3GPP) specifications contribute with the global scale standardization process, which is regulated by the global telecommunication standardization sector (ITU-T) of the International Telecommunication Union (ITU).
  • The ITU International Mobile Telecommunication (IMT) system include evolving standard frameworks, such as IMTAdvanced and IMT-2020 for LTE and 5G industry, respectively.

3.1 LTE signal structure

  • The frame structure of the LTE signal is defined by the European Telecommunication Standards Institute (ETSI), a European standards organization (ESO) partner with 3GPP, in its technical specification document [9].
  • The signal structure for FDD is organized in frames, sub-frames and slots, where each frame (10 ms) is divided into 10 subframes and each subframe (1 ms) is divided into 2 slots (0.5 ms).
  • For normal CP, a resource block consists of 12 subcarriers interspaced with ∆𝑐=15 kHz, and 7 symbols.
  • The first symbol (5.21 µs) in the resource block is longer than the regular symbol duration (4.69 µs).
  • The resource grid for one subframe is showed in Figure 3.

Frequency bands

  • The European Communication Office (ECO) reported information on the licensing of mobile frequency bands for the European Conference of Postal and Telecommunications Administrations (CEPT) member countries [10].
  • Network operators provide mobile service through standardized 3GPP LTE bands [11].

Cell-specific reference signals

  • Cell-specific reference signals are designed for channel estimation, which permits channel equalization and data demodulation under channel distortion conditions.
  • These signals are generated by using pseudo-random generators.
  • The length of these signals which are transmitted in every subframe and over the whole operating bandwidth is proportional to the maximum allowed number of resource blocks.
  • In case of multiple antennas, one reference signal can be mapped in different antenna ports.
  • The way with which this is ruled is signal type wise.

Synchronization signals

  • The standard [9] defines two sets of signals, the primary synchronization signals, PSSs, linked to the physical-layer cell identity, and the secondary synchronization signals, SSSs, linked to the physical-layer cell identity group.
  • Five consecutive resource elements are left unused at both ends of the occupied band while the direct current (DC) component is forced with null.
  • The frequency allocation for PSS and SSS is showed in Figure 4.
  • The same PSS sequence is transmitted in the two slots; thus, the frame boundary cannot be detected without the half-frame uncertainty by using PSS only.
  • Thus, the knowledge of location of synchronization signals translates into the knowledge of duplexing scheme and it holds the other way around.

Physical broadcast channel

  • The physical broadcast channel (PBCH) is transmitted within the central six resource blocks.
  • This allows the user equipment during the synchronization process to decode PBCH and read master information block (MIB) to ultimately get system bandwidth, which is needed to detect cell-specific reference signals.

3.2 5G signal structure

  • The incoming 5G radio access technology aims at accommodating various equipment types and users, and extremely high data rate.
  • Furthermore, increasing subcarrier spacing, since implies reducing symbol duration, suits low latency communication applications.
  • For the purpose of this paper the authors will consider only the normal cyclic prefix.
  • Each resource block consists of 12 consecutive subcarriers over the frequency domain and one OFDM symbol over the time domain.
  • Inversely, the time occupancy of one resource block decreases as a function of the numerology.

Frequency range

  • In new radio, there are two separate frequency ranges respectively called FR1 and FR2.
  • Each frequency range includes a certain number of operating bands.
  • The frequency range FR2 is out of the scope of the paper, therefore the authors drop the description of the signal related to this frequency range.
  • In the FR1, the higher carrier frequencies are placed within the operating bands 77, 78 and 79, which all are designed for commercial deployments.

New radio system configuration

  • In new radio, the total number of subcarriers, the number of data subcarriers and the sampling frequency can be configurated using the values in Table 7, 8 for respectively numerology 0, 1.
  • The signals associated to numerology 2 are not covered in the context of this paper.
  • To operate the initial cell search, the primary synchronization signal, PSS, and secondary synchronization signal, SSS, as well as the physical broadcast channel, PBCH, are transmitted in the synchronization signal/PBCH (SS/PBCH) block or SS block (SSB) for simplicity.
  • Subcarriers number 0 through 47 and subcarrier number 192 through 239 in OFDM symbol number 2 are assigned to PBCH.
  • The subcarrier and symbol indexes used in the description are defined in relation to the SSB start.

Simulation setup

  • The one side equivalent loop filter bandwidth was set to 20 Hz, the loop update spacing was set to the time separation between pilot symbols, as in Table 2, 3, 10, and the correlator spacing was set to 1 sample; the signal structure parameters.
  • They have been validated by real signals for LTE, not for 5G.

Comparative results

  • Figure 8 shows the standard deviation of the delay error estimate as a function of the signal to noise ratio for different mobile radio signals.
  • The simulated signals are listed in Table 11.
  • For paired numerologies, the standard deviation of delay error estimate for 5G-PBCH is 2.6 times smaller than the standard deviation of delay for 5G-xSS From N0 to N1 the standard deviation of the delay estimate is reduced by a factor of 2, due to the increase of the subcarrier spacing .
  • For reference signal that consists of constant number of pilot subcarriers (all other signals) the channel bandwidth does not influence the noise variance of the discriminator function.
  • Therefore, the performance indicator 𝐹𝑠𝛽 = 𝐹𝑠𝑁𝑝∆𝑝 ′ 𝑁𝑐⁄ = ∆𝑓𝑁𝑝∆𝑝 ′ (21) is independent from the channel bandwidth.

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5G-microwave Tracking Performance Characterization
Auryn Pink Soderini, Paul Thevenon, Christophe Macabiau, Laurent
Borgagni, John Fischer
To cite this version:
Auryn Pink Soderini, Paul Thevenon, Christophe Macabiau, Laurent Borgagni, John Fischer. 5G-
microwave Tracking Performance Characterization. ION GNSS+ 2019, 32nd International Technical
Meeting of the Satellite Division of The Institute of Navigation, Sep 2019, Miami, United States.
pp.2285-2298, �10.33012/2019.17016�. �hal-02555023�

5G-microwave Tracking Performance
Characterization
Auryn P. Soderini, Paul Thevenon, Christophe Macabiau, Ecole Nationale de l'Aviation Civile
Laurent Borgagni, John Fischer, Orolia
BIOGRAPHIES
Auryn Soderini is a Ph.D. student in the Department of Science and Air Navigation Engineering at the French National School
of Civil Aviation, Toulouse, France. He received his M.Sc. degrees from Tampere University of Technology, Finland, in 2016.
His current research interests focus on signal processing for positioning and navigation in mobile networks.
Dr. Paul Thevenon obtained a Ph.D. in the signal processing laboratory of ENAC. From 2010 to 2013, he was employed by
CNES to supervise GNSS research activities. Since 2013, he is employed by ENAC as an Assistant Professor. His current
activities are GNSS signal processing, integrity monitoring and hybridization.
Christophe Macabiau graduated as an electronic engineer in 1992 from the ENAC (Ecole National de l'Aviation Civile) in
Toulouse, France. He received his Ph.D. in 1997. Since 1994 he has been working on the application of satellite navigation
techniques to civil aviation and has been in charge of the TELECOM Lab of the ENAC since 2000.
Laurent Borgagni is a Research and Development Director and John Fischer is an Advanced Research and Development Vice
President at Orolia, a world leader in GPS-based time and frequency equipment.
ABSTRACT
This paper evaluates the theoretical performance of signal tracking in a noisy single-path environment using 5G-microwave
and LTE signals. Such OFDM signals suit navigation applications thanks to build-in symbol sequences which despite being
designed for communication services since are known at the receiver can be exploited for pseudorange computation. By using
multiple numerologies, 5G is putting into place an important degree of flexibility which was not explored before. It turns out,
the numerology counts towards the signal tracking performance. However, the nominal tracking capacity expressed by 5G-
microwave signals at the highest sampling frequency is reduced due to the lack of full bandwidth useful signals. Top-ranked
LTE-CRS performance can hypothetically improve by aggregating multiple carrier components.
1 INTRODUCTION
Today, the world is crowded with communication devices and radio signals which, despite not being designed for navigation,
still carry a certain degree of information for location purposes. The propagation environment and related system dynamics can
be regarded as navigation reference sources. Such signals that rely on an existing infrastructure are notably appropriate to shape
cost-effective navigation solutions.
Worldwide mobile wireless networks are most densely deployed in urban areas. Here, buildings, trees and other elements
such as interference and spoofing can reduce the performance of navigation systems exclusively based on GNSS. Therefore, a
resilient navigation solution based on current long terms evolution (LTE) signals and future fifth generation (5G) signals is
targeted. A communication receiver with built-in functions such as time synchronization and channel estimation measuring
received signal time delay can further be completed by additional functions to meet demanding positioning accuracy
requirements. Extracting time delay information is seen as the natural way to address localization opportunistically, although
other ways using different metrics such as angle of arrival, not primarily focused in this paper, may be pursued.
In the recent years, LTE signals have been regarded with interest for navigation. Some interesting features that make these
signals attractive are the high bandwidth employed, which can be 20 MHz at the most, and their high received power in urban
situations. Among the signals that can be used for opportunity navigation, synchronization signals (xSSs), namely primary
synchronization signals (PSSs) and secondary synchronization signals (SSSs), and cell-specific reference signals (CRSs) have
been regarded notably. These signals, namely ranging signals (RSs), can be used to estimate the channel impulse response
(CIR) by which time of arrival (TOA) can be extrapolated. The CIR estimate is obtained by correlating xSS (CRS), extracted
from the time frame synchronized received signal, with the local replica ideally matching xSS (CRS). Once the CIR is
estimated, the time of arrival estimate can be obtained. The higher bandwidth of CRS signals (i.e. complex symbols scattered

over the whole occupied bandwidth) translates into a better accuracy of TOA estimate as compared to that can be achieved by
the smaller bandwidth xSS signals (i.e., continuous complex symbols allocated in 1 MHz of frequency resources). One such
TOA estimate is rough, hence used to start the delay tracking. In this stage, known as delay-locked loop (DLL), 3 different
correlator outputs, calculating the correlation function at 3 different instants, are combined into a discriminator to obtain the
update value of the delay estimate. The noise variance of the discriminator function decreases as a function of the carrier to
noise density ratio [1], [2], [3]. The impact of multipath on the ranging error decreases as a function of the signal bandwidth
[1]. Hence, CRSs are top-ranked signals for opportunity navigation based on LTE.
Several papers discussed the structure of LTE signals and therein ranging signals, and characterized the tracking performance
for such signals. However, to the best of our knowledge, there were rare publications addressing the tracking performance of
near future 5G-microwave signals.
The commercial deployment of 5G systems is planned for the year 2020 through microwave deployment e.g., frequencies in
the sub-6 GHz spectrum. As 5G microwaves will be deployed in one year, the current number of undefined elements with
respect to the system initial phase is expected to be very small. Consequently, the degree of system exploration for positioning
is expected to be good enough. 5G sub-6 GHz signals have high central frequency (3.5 GHz) and large bandwidth (up to 100
MHz) compared to LTE signals (e.g. carrier frequency 2.8 GHz, bandwidth 20 MHz), therefore they offer potentially increased
tracking performance, while they can be associated with a signal coverage that is comparable with LTE.
This paper discusses the signal characteristics and evaluates the expected tracking performance for LTE and 5G sub-6 GHz,
comparatively
The general structure of the document is as follows. The first section of the paper is an introduction. The second section is a
description of the acquisition and tracking of signals in orthogonal frequency division multiplexing (OFDM) systems to derive
pseudorange measurements. The discriminator function model of the delay tracking loop and its error variance due to noise are
discussed. The third section is a description of LTE and 5G-microwave signals. The signal architecture is described with focus
on ranging signal components being compared and discussed. In the fourth section, the signal tracking performance is
demonstrated for the two communication systems, and for the different ranging signals and system configurations. Finally, the
conclusions are drawn, and future work is identified.
2 OFDM SIGNAL TRACKING FOR PSEUDORANGE MEASUREMENT
2.1 OFDM signal structure
Orthogonal frequency division multiplexing is a multicarrier transmission scheme that divides the system bandwidth into
several narrow equally spaced sub-bands, referred to as subcarriers. These subcarriers are characterized by the following
principal properties. Firstly, subcarriers are orthogonal sequences. It means that the spectral maximum of each subcarrier occurs
at the zero-crossing frequency of the remaining subcarriers in the series. Therefore, each subcarrier spectrum can partially
overlap to each other without causing interference. This permits to use the spectrum resources efficiently. However, under the
non-ideal synchronization statement, synchronization errors reduce the orthogonality among subcarriers and produce inter-
carrier interference (ICI). Thus, spectrum efficiency comes at the expense of synchronization error sensitivity, which constrains
the subcarrier spacing design relative to system requirements. Secondly, subcarriers are narrowband. As such, they individually
experience a nearly flat channel transfer function even if the overall channel is frequency selective. More precisely, this
condition is fulfilled when the spectrum amplitude variations of the channel are small enough compared to the subcarrier
bandwidth. In this respect, channel equalization and subsequent symbol detection in the receiver become easy, which is a key
feature for transmission occurring in propagation channels affected by heavy multipaths. Lastly, subcarriers have separate
modulation schemes that can be adapted to the frequency channel variations in flexible manner, or even muted.
In multipath propagation environments, inter-symbol interference (ISI) might occur when the transmitted symbol duration is
small compared to the maximum multipath delay. Such interference introduces channel distortion that degrades the subcarriers
orthogonality due to the time spread of contiguous transmitted symbols. To cope with this phenomenon the duration of each
transmitted symbol is artificially extended in the transmitter by a guard interval, also known as cyclic prefix (CP). Precisely,
the cyclic prefix is a copy of the terminal portion of the symbol appended at the symbol front, which allows to increase the
overall symbol duration with no need to reduce the subcarrier spacing, and which makes the symbol demodulation robust to
symbol start synchronization error. This higher degree of freedom obviously comes at the expense of data rate.
OFDM signals are designed to accommodate data symbols, specifically complex symbols, onto a two-dimensional time-
frequency physical layer. The digital waveform is nothing but a sequence of individually encoded blocks of data symbols,
referred to as OFDM symbols. The encoding operation that maps individual blocks of data symbols to OFDM symbols is the
inverse fast Fourier transform (IFFT). Likewise, the fast Fourier transform (FFT) decodes OFDM symbols to data symbol
blocks. Note that the FFT is an efficient processing unit. Thus, it supports a relatively high number of input samples at once
for which the processing computation is low enough for typical system requirements. The number of parallel samples at both

side of the IFFT must be of the form
with system parameter. This number that matches the samples within the symbol
excluding the cyclic prefix, also matches the size of the FFT used for encoding and decoding the data symbols.
Note that the signal bandwidth is defined by the sampling frequency
or inverse of sampling interval
. Thus, the sampling
frequency divided by the total number of subcarriers returns the subcarriers spacing 
, which is the frequency resolution of
subchannels. Likewise, the sampling interval multiplied by the total number of subcarriers returns the duration of the OFDM
symbol 
(without cyclic prefix). As subcarrier spacing meets the inverse of symbol duration, an increase in the total number
of subcarriers under the same bandwidth translates into a longer symbol duration and, therefore, a more robust multipath
transmission. The main OFDM parameters are summarized in Table 1.
Baseband channel model
The digital form of the channel impulse response can be written as







󰆓
(1)
where is the symbol index, is the discrete time reference,

is a complex scale factor, denotes the Dirac delta function
and is the number of multipaths;
and

󰆒
are respectively the delay of the direct component and the delay of the multipath
relative to the direct component both normalized by the sampling interval
. Since the subcarriers are narrowband, the channel
impulse response is assumed to be constant over the -th transmitted symbol duration 
󰆓
.
The FFT of (1), written as




󰇛


󰆓
󰇜
is referred channel frequency response.
Table 1. OFDM parameters. Abbreviation: OFDM, orthogonal frequency division multiplexing
Notation
Unit
Equivalence
Description
-
-
Number of data subcarriers per OFDM symbol
-
-
Number of guard subcarriers per OFDM symbol
-
Total number of subcarriers per OFDM symbol

[Hz]
-
Pilot spacing
-
-
Number of pilot subcarriers in the OFDM symbol
[s]
-
Sampling interval
[Hz]

Sampling frequency


󰆒
[Hz]
-



󰆒


Subcarrier spacing
Normalized pilot spacing
[Hz]

Transmission bandwidth
[Hz]

Protection bandwidth
[Hz]

Signal bandwidth
-
-
Number of samples within the cyclic prefix
-
Number of samples per symbol including the cyclic prefix

[s]


OFDM useful symbol duration

󰆓
[s]

󰆓


OFDM symbol duration
Baseband demodulated data model
The received data symbols at the FFT output after timing and frequency synchronizations, and cyclic prefix removal, can be
written as












󰇛󰇜
(3)
Before FFT, Equation (3) is a circular convolution between the channel impulse response and each transmitted symbol, and it
includes both time and frequency residual errors. The notation in (3) can be summarized as
is the symbol index
is the subcarrier index
is a random initial phase
is the residual carrier frequency offset normalized by 
is the residual time offset normalized by
is the number of samples per symbol including the cyclic prefix
is the number of subcarrier per symbol
is the channel impulse response digital representation
is the encoded baseband data at the IFFT output
with the symbol sample index; is the normalized delay of the direct component at the time of
synchronizing; ; is the estimate
The equation above becomes much reduced under the assumption of timing and/or frequency perfectly synchronized, which
holds if the residual errors and/or are nulls.
2.2 Correlation with an OFDM signal over the pilot subcarriers
In OFDM, reference data symbols known as pilots are transmitted at specific times and frequencies. In this context, bearing
the signal structure in mind, we will use the terms time and symbol as well as frequency and subcarrier interchangeably. Given
a pilot frequency index space , the transmitted pilots are modelled as




(4)
where

are the transmitted data symbols and
is the subcarrier index set for the pilots in the i-th symbol.
Usually, pilot subcarriers are spaced with regular interval across subcarriers, i.e., 1 subcarrier out of 
is a pilot subcarrier.
In this case, as in LTE and 5G signals, it can be written,


(5)
where 
and
are the pilot spacing and the total number of pilots for the -th symbol, and
is the first
pilot index for the -th symbol;
,
is the total number of subcarriers. Note that
and
are common to all symbols.
The inclusion of pilots within a block of decoded data symbols is illustrated with an example in Figure 1.
Figure 1. OFDM signal structure and pilot inclusion

References
More filters
Journal ArticleDOI
TL;DR: In this paper, the joint maximum likelihood (ML) symbol-time and carrier-frequency offset estimator is presented for orthogonal frequency-division multiplexing (OFDM) systems.
Abstract: We present the joint maximum likelihood (ML) symbol-time and carrier-frequency offset estimator in orthogonal frequency-division multiplexing (OFDM) systems. Redundant information contained within the cyclic prefix enables this estimation without additional pilots. Simulations show that the frequency estimator may be used in a tracking mode and the time estimator in an acquisition mode.

2,232 citations

Journal ArticleDOI
TL;DR: The investigations demonstrate that the SAGE algorithm is a powerful high-resolution tool that can be successfully applied for parameter extraction from extensive channel measurement data, especially for the purpose of channel modeling.
Abstract: This study investigates the application potential of the SAGE (space-alternating generalized expectation-maximization) algorithm to jointly estimate the relative delay, incidence azimuth, Doppler frequency, and complex amplitude of impinging waves in mobile radio environments The performance, ie, high-resolution ability, accuracy, and convergence rate of the scheme, is assessed in synthetic and real macro- and pico-cellular channels The results indicate that the scheme overcomes the resolution limitation inherent to classical techniques like the Fourier or beam-forming methods In particular, it is shown that waves which exhibit an arbitrarily small difference in azimuth can be easily separated as long as their delays or Doppler frequencies differ by a fraction of the intrinsic resolution of the measurement equipment Two waves are claimed to be separated when the mean-squared estimation errors (MSEEs) of the estimates of their parameters are close to the corresponding Cramer-Rao lower bounds (CRLBs) derived in a scenario where only a single wave is impinging The adverb easily means that the MSEEs rapidly approach the CLRBs, ie, within less than 20 iteration cycles Convergence of the log-likelihood sequence is achieved after approximately ten iteration cycles when the scheme is applied in real channels In this use, the estimated dominant waves can be related to a scatterer/reflector in the propagation environment The investigations demonstrate that the SAGE algorithm is a powerful high-resolution tool that can be successfully applied for parameter extraction from extensive channel measurement data, especially for the purpose of channel modeling

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Additional excerpts

  • ...Note that different algorithms performing acquisition delay estimate there exist in literature [6] [7]....

    [...]

Journal ArticleDOI
TL;DR: It is shown how an estimate of the channel may be obtained using a matching pursuit (MP) algorithm and this estimate is compared to thresholded variants of the least squares channel estimate.
Abstract: Channels with a sparse impulse response arise in a number of communication applications. Exploiting the sparsity of the channel, we show how an estimate of the channel may be obtained using a matching pursuit (MP) algorithm. This estimate is compared to thresholded variants of the least squares (LS) channel estimate. Among these sparse channel estimates, the MP estimate is computationally much simpler to implement and a shorter training sequence is required to form an accurate channel estimate leading to greater information throughput.

686 citations


Additional excerpts

  • ...After the CIR estimation, the matching pursuit (MP) algorithm [5] can be performed to obtain the delay estimates of each multipath component....

    [...]

Journal Article
TL;DR: Though ESPRIT is discussed in the context of direction-of-arrival estimation, it can be applied to a wide variety of problems including spectral estimation and has several advantages over earlier techniques such as MUSIC including improved performance, reduced computational load, freedom from array characterization/calibration, and reduced sensitivity to array perturbations.
Abstract: A new approach to the general problem of signal parameter estimation is described. Though the technique ESPRIT is discussed in the context of direction-of arrival estimation, it can be applied to a wide variety of problems including spectral estimation. ESPRIT exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational in variance structure (e.g., pairwise matched and co-directional antenna element doublets) and has several advantages over earlier techniques such as MUSIC including improved performance, reduced computational load, freedom from array characterization calibration, and reduced sensitivity to array perturbations. Results of computer simulations carried out to evaluate the new algorithm arc presented.

274 citations


Additional excerpts

  • ...Note that different algorithms performing acquisition delay estimate there exist in literature [6] [7]....

    [...]

Journal ArticleDOI
TL;DR: Analytical expressions for performance of code- tracking loops using early-late discriminators, under small-error conditions are provided, showing that code-tracking accuracy depends on more than merely signal-to-noise ratio and early-Late spacing - the shape of signal and interference spectra are important, as is the receiver precorrelation bandwidth.
Abstract: Code tracking is an important attribute of receivers for Global Positioning System (GPS) and other global navigation satellite systems (GNSS). This paper and its sequel provide analytical expressions for performance of code-tracking loops using early-late discriminators, under small-error conditions. Expressions are provided for output signal-to-noise-plus-interference ratio (SNIR) and code-tracking error for arbitrary signal spectra, and Gaussian noise and interference having arbitrary spectral shapes. This first paper addresses coherent early-late processing (ELP) for given receiver precorrelation bandwidth and given early-late spacing, also providing a tight lower bound on code-tracking error independent of discriminator design. Theoretical expressions are derived, showing that code-tracking accuracy depends on more than merely signal-to-noise ratio and early-late spacing - the shape of signal and interference spectra are important, as is the receiver precorrelation bandwidth.

158 citations


Additional excerpts

  • ...The tracking loop filter can reduce the variance of the delay error at the discriminator output by a factor of 2BlTL [8], with Bl the one-side equivalent loop filter bandwidth expressed in Hertz and Tl the loop update expressed in seconds....

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Frequently Asked Questions (2)
Q1. What are the contributions in "5g-microwave tracking performance characterization" ?

This paper evaluates the theoretical performance of signal tracking in a noisy single-path environment using 5G-microwave and LTE signals. 

The validation of tracking based on PBCH signals needs to be addressed in the future work. Finally, the increase of the bandwidth due to the aggregation of multiple carrier components needs to be addressed in the future work.