Digital Signal Processing

Scientific & Technical

“Digital Signal Processing” No. 4-2015

In the issue:

- OFDM system for communication

- high rate communication system
- multithreshold decoding
- MIMO communication system
- LDPC codes
- filter banks and OFDM
- analysis of quantization noises
- novel FPGA verification tool

- FPGA implementation techniques
- multiprocessor clusters
- GNU Radio system

Frequency and timing synchronization algorithm for OFDM systems for communication over multipath channels
Bakker A.V., The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: CAZAC Sequence, OFDM, PN Sequence, time synchronization, frequency offset.

The article deals with novel synchronization algorithm based on constant amplitude zero auto correlation (CAZAC) sequence for orthogonal frequency division multiplexing (OFDM) systems.

OFDM has been of major interest for both wire line-based and wireless applications due to its high data rate transmission capability and its robustness to multipath delay spread. However, OFDM systems are much more sensitive to synchronization errors than single carrier systems, since synchronization errors might destroy the orthogonality among all subcarriers and, therefore, introduce inter-carrier interference and inter-symbol interference [1].

Several approaches have been proposed for estimating the time and frequency offset either jointly or individually. Most frequency and timing estimation methods exploit the periodic nature of the time-domain signal by using a cyclic prefix (CP) [6], or by designing the training symbol (TS) having repeated parts [2-5]. In CP based method, cyclic prefix is used to correlate with the last part of data symbol, while in TS based method, training symbols is used for symbol synchronization in the receiver. In contrast with CP, it involves overhead for transmitting training symbols, but it does not suffer from the effect of the multipath channel [5]. This paper covers the TS based method for estimating the time and frequency offset.

For correct timing and frequency estimation of OFDM symbol, different TS based methods have been proposed. The well-known frequency and time synchronization technique is proposed by Schmidl and Cox [2]. It uses a training symbol containing two same halves to estimate the symbol timing and, then, computes the phase difference between the two halves to estimate the fractional frequency offset. However, due to the existence of the CP, the metric has a plateau which makes the time synchronization fallible. To eliminate the plateau, Minn [3] has proposed identical preambles in time domain with opposite signs and Park [4] designed a new repeated-conjugated-symmetric sequence which makes the metric has a sharp peak for synchronization. However, due to CP and the special structure of the sequence, the metric has side lobes which can disturb the synchronization.

But on the other hand, it has been observed that peak of the timing metric (Park, Minn) degrades at low SNR and sometimes it reaches below the threshold value. Hence to rectify this problem we propose a preamble scheme that has pseudo noise (PN) sequence of values 1 and -1, which performs better at low SNR. An PN based preamble design is proposed by Wang [9], where four repeated CAZAC sequence weighted by a PN sequence are used.

In this paper, we propose a improved algorithm based on repeated CAZAC sequence weighted by a PN sequence for synchronization.

Firstly, it uses the CAZAC sequence weighted by a PN sequence to obtain a new timing metric, which eliminates the side lobes [8]. The good self-correlation quality of the CAZAC and PN sequence introduces a sharp peak in timing metric, more accurate for time synchronization. Secondly, the fractional frequency offset can be estimated by computing the phase difference between the two same halves of the sequence. The fast Fourier transform of CAZAC sequence is still a CAZAC sequence. Based on this quality, we can get the integer frequency offset by computing the offset of the CAZAC sequence in frequency domain.

Computer simulation results show that the proposed algorithm has a larger frequency estimation range and achieves superior performance to the existing methods in both AWGN and multipath fading channel.


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2. Schmidl T.M., Cox D.C. Robust Frequency and Timing Synchronization for OFDM. IEEE Trans. Communications, vol.45, no.l2, pp. 1613-1621, 1997.

3. Hlaing Minn, Vijay K. Bhargava, Khaled Ben Letaief. A Robust Timing and Frequency Synchronization for OFDM Systems, IEEE Transactions on Wireless communications, vol. 2, no. 4, pp. 822-838, 2003.

4. B. Park and H. Cheon , C. G. Kang, and D. S. Hong. A Novel Timing Estimation Method for OFDM systems, IEEE Commun. Lett., vol. 7, pp. 239 – 241, May 2003

5. Classen, F. and Myer, H. Frequency synchronization algorithm for OFDM systems suitable for communication over frequency selective fading channels. IEEE VTC’94, pp. 1655–1659, 1994.

6. J. J. van de Beek, M. Sandell, and P.O. Bojesson, ML estimation of time and frequency offset in OFDM systems, IEEE Transactions on Signal Processing, vol. 45, no. 7, pp. 1800-1805, 1997.

7. S. D. Choi, J. M. Choi, J. H. Lee. An initial timing offset estimation method for OFDM systems in Êayleigh fading channel, IEEE 64th Vehicular Technology Conference, pp. 1–5, September 2006.

8. D.C. Chu. Polyphase codes with good periodic correlation properties, IEEE Trans. Inform. Theory, vol. IT-18, pp. 531–532, July 1972.

9. H. Wang, L. Zhu, Y. Shi, T. Xing, and Y. Wang. A novel synchronization algorithm for OFDM systems with weighted CAZAC sequence. J. Comput. Inf. Syst. 8(6), pp. 2275–2283, 2012.

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Using of multithreshold decoding for error correction in wireless channels
G.V. Ovechkin, e-mail:
D.A. Shevlyakov
, e-mail:

The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: : communication systems, error-correction coding, self-orthogonal codes, multithreshold decoding, coding gain, communication channel, precoding, MIMO, OFDM.


The article deals with multithreshold decoders (MTD) for self-orthogonal codes. It's known the MTD provides near optimum bit-error rate performance over gaussian channels for good self-orthogonal codes with linear implementation complexity. In the article the performance of MTD over fading channels is investigated.

The lower bounds for multithreshold decoders bit error probability in uncorrelated Rayleigh and Rician channels are presented. These bounds are useful for BPSK or QPSK modulation and hard-decision demodulator. The simulation results presented in the article show these bounds are tight enough in field of suboptimal MTD's performance. Additionally the MTD's performance over correlated Rayleigh and Rician channels are investigated. The recommendations for improving the performance of MTD about several dB in such channels are given.

Improving reliability of data transmission over fading channels with intersymbol interference is able with using of OFDM and MIMO technologies. Known results for MTD application in such conditions show the MTD provides the performance comparable with other error-correction methods. In the article precoding is used for additional performance improvement. The precoding are used is based on using of good space-time channels for data transmission. These channels are selected with using of the channel state information known perfectly to the transmitter. The simulation results show the MTD with precoding provides significant performance improvement in such channels in comparison with using MTD without precoding.

Analysis of presented results shows the MTD provided near optimal performance over gaussian channels is able to correct errors effectively in much worse channel conditions. The provided coding gain is many times more than coding gain over gaussian channel.

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2. Zolotarjov V.V., Zubarev Ju.B., Ovechkin G.V. Mnogoporogovye dekodery i optimizacionnaja teorija kodirovanija (Multithreshold decoding and optimizing coding theory). M.: Gorjachaja linija–Telekom, 2012. 238 p.

3. Zolotarjov V.V., Ovechkin G.V. Povyshenie nadezhnosti peredachi i hranenija dannyh s ispol'zovaniem mnogoporogovyh metodov dekodirovanija pomehoustojchivyh kodov (Improving data transmission and storage relaibility with multithreshold decoders for error-correction codes) // Cifrovaja obrabotka signalov (Digital signal processing), 2012, no. 1, pp. 16–21.

4. Zolotarjov V.V., Nazirov R.R., Chulkov I.V., Ovechkin G.V. Algoritmy MPD (MTD algorithms) // Rossijskij kosmos. 2009. no. 1. pp. 60–63.

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8. Ovechkin G.V., Shevljakov D.A. Jeffektivnost' primenenija mnogoporogovyh dekoderov s prostranstvenno-vremennym kodirovaniem (Performance of using multithreshold decoders with space-time coding) // Matematicheskoe i programmnoe obespechenie vychislitel'nyh sistem: Mezhvuzovskij sboknik nauchnyh trudov. Ryazan, RSREU, 2013. pp. 115–121.

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Correlation properties of MIMO communication channel coefficients with maneuvering object

Yu.N. Parshin., e-mail:
V.I. Kudryashov., e-mail:
Ryazan State Radio Engineering University (RSREU)

Keywords: MIMO channel, channel coefficients matrix, maneuvering object, measurement error, correlation analysis.

Currently is observed a rapid growth of use of maneuvering objects for receiving and transmitting information. In this case requires a high channel capacity. To increase data rate in terms of fading and multipath in communication systems with maneuvering objects use MIMO technology. Such a data channel provides high capacity by space–time encoding and decoding using multiple antennas at the transmitting and receiving side.

One problem with application of MIMO channels for communication with maneuvering objects is large channel matrix variability in time when object is moving. Previously performed an analysis of channel matrix measurement errors influence on MIMO communication channel capacity. It is established that movement of object causes additional dynamic channel matrix estimation error. It is therefore important to determine the behavior of MIMO data transmission system channel coefficients in a variety of typical conditions.

The purpose is to analyze of MIMO communication system channel coefficients correlation with maneuvering objects indispensable to development of optimal algorithms for channel matrix estimating for different models of maneuvering object motion.

To evaluate the correlation function of MIMO communication system channel coefficients performed computer simulations. The model is based on a one–ring geometric model of signal scattering, as well as various motion models.

Calculated correlation functions of channel coefficients for different motion models of object. If the movement of object is deterministic, for example, describes a Dubins model or more simple polynomial models and phase of from elementary scatterers can be assumed to be constant at predetermined time interval, then behavior of channel coefficients is also deterministic. Sources of channel coefficients random perturbations are the initial phase of the elementary scatterers, which change their value at each experiment. This model is valid if movement of object for relevant time is very small, and angle of sight of elementary scatterers varies so little that does not lead to significant change of scattering coefficient.

It is shown that channel coefficients correlation function is maintained at 90% for a sufficient period of time for evaluation and extrapolation of channel matrix.


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ACE spectrum influence on channel coding gain of known LDPC codes

A.A. Ovinnikov, The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: error floor, irregular low density parity check (LDPC) codes, progressive-edge-growth (PEG) algorithm, girth, approximate cycle extrinsic message degree (ACE).

The construction of finite-length irregular LDPC codes with low error floors is currently an attractive research problem. In particular, for the binary erasure channel (BEC), the problem is to find the elements of selected irregular LDPC code ensembles with the size of their minimum stopping set being maximized. Due to the lack of analytical solutions to this problem, a simple but powerful heuristic design algorithm, the approximate cycle extrinsic message degree (ACE) constrained design algorithm, has recently been proposed. Building upon the ACE metric associated with a cycle in a code graph, we use the ACE spectrum of LDPC codes as a useful tool for evaluation of codes from selected irregular LDPC code ensembles. We justify the ACE spectrum approach through examples and simulation results.

The paper presents comparative characteristics of the effectiveness of codes with low-density parity-check in the channel with white noise. Study includes codes from standards 802.11n and 802.16e, and the number of codes obtained by known synthesis algorithms (Mak, PEG). The results of comparing their characteristics are as follows:
1. Low threshold level for irregular codes considered ensembles observed in the case where the minimum value of ACE metrics η0, η1, η2 are at least three for a coding rate R = 0.5. In this case it plays the role of the cumulative value of metrics for different lengths of cycles. In particular, for PEG code parameters N = 1296, g0 = 6, R = 0.5 min ACE metric value for a cycle with a length equal to the girth of the graph is 27, that is the maximum value for all used codes. However, it does not significantly reduce the error floor effect, because remaining reference spectrum S(ηi), i ≠ 0 take the value of zero or one.
2. Increase the girth of the graph does not lead to a decrease in the level of error floor, which is typical of PEG with code lengths N = 1056, 1296 and 1344.
3. Error floor reduction is achieved due to two factors: increase of ACE metric values for cycles with different length and to reduce the total number of short cycles in the Tanner graph.

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Filter banks and OFDM in broadband data transmission multicarrier systems
Vityazev V.V., e-mail:
Nikishkin P.B., e-mail:
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

filter banks, OFDM, data transmission, broadband, combine approach, spectral efficiency, adaptation, noise reduction.

The considered signals analysis/synthesis methods are based on digital band-pass filter (DBF) banks. This methods are applied for transmultiplexer construction in telecommunication systems.

Multirate digital signal processing was developing rapidly. Filter banks based signals analysis/synthesis systems started to be used in speech, sound and image coding.

As a new stage of evolution DBF banks are used in broadband data transmission multicarrier systems. This can be considered as an alternative to OFDM technology.

Broadband data transmission multicarrier system are exposed to fading, Doppler bias and frequency extension. A lot of attention is paid to searches for ways of spectral efficiency loss compensation in multicarrier systems. The use of DBF banks can be one of possible solutions for the problem.

Next approach is proposed in the article. The whole frequency range of the broadband channel is divided into separate sub-ranges. OFDM signal is formed inside every frequency sub-range. These signals are then composed into one group signal.

Advantages and disadvantages of the approach are discussed.

An alternative approach filter banks construction can be based on comb filters.

FBMC (filter banks multicarrier) technology and broadband data transmission multicarrier systems implementation provide the best solution in terms of spectral and energy efficiency.

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Analysis of quantization noises in multirate structures of narrowband FIR-filters.
Vityazev V.V., e-mail:
Gorushkin R.S., e-mail:
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: multirate signal processing, narrowband FIR-filter, quantanization noise, decimation, interpolation, modeling.

This article is devoted to the analysis problem of quantization noises in multirate strucutures of narrowband filters with finite inpulse response (FIR-filters). The goal of this research is to minimize influence of such noises increasing the number of transformation stages and decreasing orders of series connected decimation and interpolation filters.

In order to confirm theoretical conclusions we modeled a noise model for single- and twostage structures of a narrowband FIR-filter.

In accordance with the conducted theoretical and experimental researches on decimation noises influence on multirate structures of narrowband FIR-filters decimation noises dispersion increases proportionally to the decimation coefficient and depends on the magnitude–frequency characteristics sidelobes level in the stopband and the narrowband coefficient. An increase in the transformation stages quantity in the narrowband system allows to decrease the decimation coefficient of the first-stage decimation filter and dispersion component of decimation noises outlet multistage realization. Considering that dispersion of decimation noises components outlet the system of all later stages is lower than at the first stage, we can make a general conclusion that decimation noises influence may be decreased by an increase in the transformation stages quantity.

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FPGA implementation techniques for multi-channel adaptive FIR filters of active noise control systems
I.V. Ushenina, Penza State Technological University (PenzSTU), Russia, Penza

active noise control, multi-channel adaptive filtering, processing block.

This paper considers the FPGA implementation techniques for the multi-channel adaptive FXLMS FIR filters. Adaptive FIR filters with filtered-reference least mean square (FXLMS) algorithm is widely used in active noise control systems.

At first, the applications of active noise control which require the high-performance multi-channel adaptive filters are revealed.

Then, the author compares the possible architectures of multi-channel adaptive FXLMS filter. These architectures can be based on one of two main approaches: pipelining the filter’s taps or creating the array of independent processing blocks. Within the scope of the first approach, the author analyses such filter architectures as systolic, transposed, and «adder tree». In spite of high performance potentially provided, pipelined filter architecture was recognized as unsuitable for FPGA implementation of multi-channel FXLMS filter. It is because of restricted quantity of sources inside of the FPGA DSP slices in which the filter’s taps would be realized.

Under the second approach, there are some possibilities to realize the processing blocks’ array and interaction between them. In the paper, KxJ (where K is the quantity of loudspeakers, J is the number of reference microphones) array of processing blocks is considered.

Each kj-th processing block consists of two DSP slices working in parallel, as well as two memory blocks containing the filters’ coefficients and partial results of calculations. During the sample interval, one of the DSP slices filters the reference signal; the other one recalculates the coefficients of kj-th adaptive filter.

For the proposed filter’s architecture, some details of its implementation are considered. The memory volume and DSP slices quantity requirements are substantiated. For a single processing block, the dependency of its performance on the sizes of memory blocks is analyzed.

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9. (27.08.2015)

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Multiprocessor clusters based on signal processors with static super-scalar architecture
Å.À. Bukvàråv, e-mail:
A.A. Kuzin, e-mail:
E.N. Pribludova, e-mail:

À.G. Ryndyk , e-mail:
Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Russia, Nizhny Novgorod

Keywords: digital processing, signal processor, multiprocessor clusters, integrated module

In this paper two structures of multiprocessor clusters on basis of signal processors with static super-scalar architecture are presented. Some design features are considered, configuration and appearance of the multiprocessor cluster are shown and characteristics of cluster are provided.

Generally, calculating cluster is collection of calculating units, connected by some communication network. Each computing unit has the random access memory and works under control of the operating system. The most widespread is uniform clusters use where all units are absolutely identical on the architecture and productivity. Feature of a cluster is component application of serial production.

For problems of digital signal processing use as units of a cluster of specialized high-performance processors is represented perspective. As a rule, DSP processors have the built-in memory, and communications between processors in a cluster are provided with the built-in means of processors.

Development of a multiprocessor cluster on the basis of DSP processors is a private problem of the integrated DSP module design with possibility of productivity scaling.

The chosen option of the integrated module configuration in the form of basic (the bearing board) with the submodules (attics) installed on it assumes installation from one to five multiprocessor clusters that provides change of productivity over a wide range.

The submodule represents functionally and structurally finished four-processor cluster. Besides, the submodule has special signal distribution of high-speed LINK-ports on sockets for the purpose of trace simplification of a basic board.

The developed multiprocessor clusters are intended for use into integrated module in stationary and mobile systems of high-performance digital signal processing.


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