Carrier synchronization is a crucial part of any wireless receiver, which is required due to frequency and phase offset. In case of transmission in a Time Division Multiple Access system the carrier synchronization has to be carried out for every burst separately. The DVB-RCS2 standard specifies a large variety of reference burst types with very limited known symbols. For each of these types a thorough exploration of different synchronization algorithms is required to find a trade-off between a good communication performance at very low Signal to Noise Ratio (SNR) and an efficient hardware implementation.

A state-of-the-art algorithm for carrier synchronization is based on the so called Fast Fourier Transformation (FFT). An inherit limitation for the precision of frequency estimation is given by the FFT point size. To counteract this limitation, the FFT point size must be increased. In this paper we extensively compare two possible interpolation techniques for FFT results in three FFT-based carrier synchronization methods. These are applied to various reference burst types specified in the DVB-RCS2 standard. The trade-offs of these combinations are identified with a special focus on hardware implementation efficiency. Furthermore, we present a flexible IP core which can process the three synchronization methods in an efficient way and analyze its implementation complexity and throughput on a Xilinx Kintex FPGA.

The transmission of data over a wireless channel results in frequency and phase offsets. The frequency offset is caused by the imperfections of the different oscillators in transmitter and receiver, which will always deviate from the nominal value. Furthermore, the Doppler effect of moving objects results in a frequency offset. The phase shift between transmitter and receiver occurs by the unknown distance between those. Therefore, carrier synchronization is required in wireless receivers. It performs the estimation of the unknown frequency offset and unknown phase offset and corrects the received signal according to the estimated values. In case of a scenario with different transmitters for a receiver, e.g., a Time Division Multiple Access (TDMA) system, the carrier synchronization has to be carried out separately for every burst.

Carrier synchronization on burst structured data transmission can be
exemplified on Second Generation Digital Video Broadcasting – Return Channel
Satellite (DVB-RCS2). A Joint Technical Committee (JTC) specified this as part
of an open standard initially in 2011 and recently revised it,
cf.

The DVB-RCS2 receiver knows the transmission burst types in advance, which is
used to implement dynamic operation. Those bursts types are constructed by
adding known symbols between the payload symbols. Using the in advance known
symbols allows the receiver to detect the burst and synchronize the carrier
phase and frequency offsets. There are three burst type formats defined by the
DVB-RCS2 standard, cf.

DVB-RCS2 burst formats with preamble symbols in red, pilot symbols in blue, postamble symbols in green and payload symbols without color.

The tolerable burst frequency offset is not defined by the DVB-RCS2 standard
but limited in agreement with gateway manufacturers. A representative set of
values is in range from 0.5 % to 3 % of a symbol rate, which is
specified by

To synchronize the received bursts there are different types of algorithms
applied which can be classified into two categories, i.e. Data-Aided (DA) and
Non-Data-Aided (NDA). Only known symbols, as introduced in
Fig.

Instead of adding further FFT points we investigate techniques for
interpolation of the FFT result to improve the estimated frequency offset. We
compare results of the standard approach of zero-padding against two advanced
interpolation techniques, cf.

In detail, this paper makes the following main contributions:

We show the trade-off between communication performance and implementation efficiency for three FFT-based carrier synchronization methods with interpolation. The communication performance is measured by the Frame Error Rate (FER) of channel decoding after carrier synchronization. Implementation efficiency is measured in terms of hardware resources and achievable throughput on a Xilinx Kintex FPGA.

Due to variation of number, amount and distribution of known symbols, different methods for carrier synchronization are required. A broad range of burst types is specified by the DVB-RCS2 standard including targeted communication performance. Two different interpolation techniques are investigated with NDA and two DA carrier synchronization schemes to efficiently achieve the targeted values.

In this section we describe the signal model and introduce the used DA and NDA carrier synchronization methods. Finally, the interpolation techniques are described in detail.

The transmitted symbols

Carrier synchronization algorithms are partitioned in three categories,
cf.

This paper focuses on the FFT-based algorithm introduced by

Furthermore, the communication performance is improved with two interpolation techniques. Considering the squares of the magnitudes of the maximum amplitude and their neighbor bins or alternatively considering the magnitude of the named bins.

The Data-Aided with all known symbols (DA-KS) method of the modified R&B is tailored to synchronize two types of burst type formats: first, bursts with large pilot period and, second, bursts with short pilot period and a limited number of pilot symbols. Here, the effect of phase ambiguity between two succeeding pilot blocks is removed. This is effective due to utilizing preamble and postamble symbols additionally to all pilot symbols for frequency and phase offset estimation.

For modulation removal on the received signal, data symbols of the received
burst are wiped out and the known symbols are multiplied by their conjugate
complex value

For burst type formats with short pilot spacing and sufficiently large number
of pilot symbols the algorithm of the previous section can be adapted to
reduce the FFT point size. The here introduced method utilizes pilot symbols,
i.e. Data-Aided with pilot symbols only (DA-PL). The modulation removal of
Eq. (

The modulation removal is given by

For the NDA carrier synchronization, the described algorithm of
Sect.

One way to improve estimated frequency offset and estimated phase offset is
called zero-padding. By this the modulation removed symbol sequence

Interpolation techniques are introduced to reduce the FFT point size and, thus, reducing complexity and increasing throughput. We compare two techniques to interpolate between the bin with maximum FFT output amplitude and its direct neighbors by using the magnitude or square magnitude of the complex FFT output.

Due to the discrete nature of FFT each output bin represents a frequency range
and Eq. (

The FFT output with index

For correction of the frequency offset a virtual bin

The phase offset estimation is not considered by

An alternative approach is an interpolation based on the energy of the complex
FFT output bins which is introduced by

For the phase offset estimation, using this interpolation technique, a virtual
FFT-output is calculated by

This section presents the simulation model and gives an overview of the DVB-RCS2 burst types with linear modulation and their communication performance.

The DVB-RCS2 receiver is explored in the presence of frequency and phase offsets through extensive Monte Carlo simulations. Depending on the burst type, different DA and NDA carrier synchronization methods are feasible. An overview with focus on the achievable FFT point size reduction by adding the interpolation techniques is shown in this chapter.

The simulation model considered in this paper is shown in
Fig.

DVB-RCS2 simulation chain.

This paper assumes a uniformly distributed frequency offset up to 1.5 % of
the symbol rate. For bit-precise simulation of the carrier synchronization the
real and imaginary part of the received symbols are simulated with

To achieve the communication performance specified by

Max-Log-Map algorithm with

The polynomials, interleaver parameter and puncturing pattern according to DVB-RCS2 standard

For this paper we considered

Parameters of presented DVB-RCS2 burst types.

We present a representative subset of use cases in this paper. The introduced
burst types, which differ in terms of their length, code rate, modulation
type, number and distribution of known symbols, are shown in Table

We demonstrate and compare the impact of the in Sect.

As reference, for each demonstrated burst type, we show the results of the
simulation chain, see Fig.

Burst type

The benefit of using interpolation techniques for the phase and frequency
offset estimation is shown in Fig.

Burst type

Burst type 8: Preamble, pilot symbols and postamble assisted burst format; Performance of DA-KS vs. DA-PL synchronization at short burst length with two interpolation techniques.

Comparing both interpolation techniques shows for a few cases an impact on the
communication performance as demonstrated in Fig.

Burst type

Burst type

Burst type

Burst type

For long bursts types, exemplified on burst type

In contrast to the previous burst types, burst type

Burst type

Burst type

Figure

In this selection of exemplary results we were able to show communication
performance for different lengths, modulation types and distribution of known
symbols on various burst types defined in Table

In this section, we present hardware implementation results of our carrier synchronization with the investigated interpolation techniques. Each of these architectures is synthesized for different FFT point sizes, which we compare at fixed communication performance based on the resulting hardware complexity.

In order to compare hardware implementation efficiency, i.e. resources and
throughput, our designs were implemented in synthesizable VHDL that is mapped
onto a Xilinx Kintex FPGA. To optimize the implementation we use Xilinx highly
optimized Intellectual Property (IP) cores. For the FFT computation we
selected the pipelined streaming I/O architecture of the Xilinx FFT IP core,
cf.

Carrier synchronization architecture block diagram.

We have implemented three hardware architecture types that differ in the
respective interpolation method. The block diagram of the general
architecture is shown in Fig.

The architecture, introduced in Fig.

Post P&R Results of the Architecture of a DVB-RCS2 Carrier Synchronization Module.

DVB-RCS2 carrier synchronization throughput comparison for different synchronization methods with and without interpolation.

We used Xilinx Vivado 2018.3 suite for synthesis and place and route (P&R).
The target platform is Xilinx Kintex family with speedgrade

The utilized FPGA resources consist of Flip-Flops (FF), Lookup Tables (LUT),
Block Random Access Memories (BRAM) and Digital Signal Processing (DSP) units,
as shown in Table

The two compared interpolation techniques require about the same amount of all
resources with a rather small difference of a few blocks. Compared to pure
zero-padding, it is evident that for either of the two interpolation
techniques additional blocks are utilized, i.e. about

To make a fair comparison, we fix the communication performance for all three
approaches. In Table

Overall, the throughput of either interpolation technique is the same due to
the same FFT size at fixed communication performance close to the reference
communication performance. Furthermore, the required resources shown in
Table

We have investigated the effect of two interpolation techniques on three different FFT-based carrier synchronization methods regarding communication performance and hardware implementation efficiency. For all three synchronization methods, we observed better communication performance at the same FFT point size by adding the interpolation techniques. In some cases characterized by a very low zero-padding factor, the magnitude interpolation technique showed better communication performance than the energy interpolation technique. To achieve the same communication performance as a standard synchronization method without interpolation, the interpolation-based techniques required half the FFT point size or less. Thus, using interpolation techniques leads to an improvement in throughput by a factor of two to four while the increase in hardware resources was upper bounded by less than 20 %. This leads to an improved hardware implementation efficiency at a fixed communication performance by at least 67 % by using interpolation.

The source code is represented by the formulas in this paper and can be reproduced. The applied source code is based on proprietary libraries, which are not publicly available.

All relevant models and results of the research are contained in the manuscript. The results can be reproduced with the presented formulas.

OG and UW contributed equally on the conceptualization, methodology, software, hardware, validation, formal analysis, investigation, writing, visualization, review and editing. NW contributed on the supervision, review and editing.

The authors declare that they have no conflict of interest.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the special issue “Kleinheubacher Berichte 2020”.

This paper was edited by Jens Anders and reviewed by Daniel Krüger and one anonymous referee.