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Circuits and Systems for Receiving, Transmitting and Signal Processing
Устройства и системы передачи, приёма и обработки сигналов
Research article
DOI: https://doi.org/10.18721/JCSTCS.15102 UDC 621.391.8
SYMMETRICAL ITERATIVE ALGORITHM FOR CANCELLING INTER-CHANNEL INTERFERENCE OF SEFDM SIGNALS
S.A. Suhotskiy1, S.V. Zavjalov2 e, A.S. Ovsyannikova3, I.I. Lavrenyuk4
1,2,3,4 Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russian Federation
e zavyalov_sv@spbstu.ru
Abstract. This article deals with spectrally efficient frequency-division multiplexing signals (SEFDM). Authors considered symmetrical and asymmetrical iterative algorithms to prevent BER performance degradation. These algorithms reduce inter-channel interference (ICI) between the subcarriers, which leads to better value of BER performance. The authors analyzed complexity and results of the algorithms, and determined the best conditions for a symmetrical algorithm with different number of subcarriers and different frequency multiplexing coefficient.
Keywords: SEFDM, demodulation, algorithm, BER performance, feedback on decision
Acknowledgements: The reported study was funded by RFBR according to the research project No. 20-37-90007\20
Citation: Suhotskiy S.A., Zavjalov S.V., Ovsyannikova A.S., Lavrenyuk I.I. Symmetrical iterative algorithm for cancelling inter-channel interference of SEFDM signals. Computing, Telecommunications and Control, 2022, Vol. 15, No. 1, Pp. 19-28. DOI: 10.18721/JCSTCS.15102
This is an open access article under the CC BY-NC 4.0 license (https://creativecommons.org/ licenses/by-nc/4.0/).
© Suhotskiy S.A., Zavjalov S.V., Ovsyannikova A.S., Lavrenyuk I.I., 2022. Published by Peter the Great St. Petersburg Polytechnic University
Научная статья
DOI: https://doi.org/10.18721/JCSTCS.15102 УДК 621.391.8
СИММЕТРИЧНЫЙ ИТЕРАЦИОННЫЙ АЛГОРИТМ КОМПЕНСАЦИИ МЕЖКАНАЛЬНЫХ ПОМЕХ SEFDM-СИГНАЛОВ
С.А. Сухоцкий1, С.В. Завьялов2 е, А.С. Овсянникова3, И.И. Лавренюк4
1,2,з,4 Санкт-Петербургский политехнический университет Петра Великого,
Санкт-Петербург, Российская Федерация
е zavyalov_sv@spbstu.ru
Аннотация. Рассмотрены спектрально-эффективные сигналы c частотным мультиплексированием (SEFDM-сигналы). Представлен анализ симметричных и асимметричных итерационных алгоритмов для улучшения помехоустойчивости приёма. Предложенный подход к построению алгоритмов позволяет уменьшать межканальные помехи (ICI) между сигналами на поднесущих частотах, что приводит к улучшению помехоустойчивости приёма. Выполнен анализ сложности алгоритмов и определены наилучшие условия для применения симметричного алгоритма при разном количестве поднесущих и разном коэффициенте частотного мультиплексирования.
Ключевые слова: SEFDM, демодуляция, алгоритм, помехоустойчивость, обратная связь
Финансирование: Данное исследование проведено при финансовой поддержке РФФИ в рамках исследовательского проекта № 20-37-90007\20
Для цитирования: Suhotskiy S.A., Zavjalov S.V., Ovsyannikova A.S., Lavrenyuk I.I. Symmetrical iterative algorithm for cancelling inter-channel interference of SEFDM signals // Computing, Telecommunications and Control. 2022. Т. 15, № 1. С. 19-28. DOI: 10.18721/JCSTCS.15102
Статья открытого доступа, распространяемая по лицензии CC BY-NC 4.0 (https://creative-commons.org/licenses/by-nc/4.0/).
Introduction
Ideas of spectrally efficient frequency-division multiplexing (SEFDM) is used in Beyond 5G [1, 2] systems and as the foundation for 6G technology standard [3, 4]. SEFDM can provide many times more data than 5G [1]. The other way of using SEFDM is optical channels [5]. Based on Orthogonal frequency-division multiplexing (OFDM) we can achieve higher spectral efficiency by reducing separation between subcarriers frequencies [6]. Spectral efficiency can be expressed as R/AF, where R — symbol rate and AF — occupied frequency bandwidth [7]. Unfortunately, SEFDM has a big disadvantage of inter-channel interference (ICI) between signals on subcarriers that leads to incorrect demodulation and bit error rate (BER) performance degradation [8]. It is shown that energy losses for SEFDM compared to OFDM at BER = 10-3 can achieve 5—15 dB depending on scenarios [9]. There are different demodulation algorithms solving this problem: algorithm with feedback on decision [7, 10], Viterbi algorithm [11], maximum likelihood sequence estimations (MLSE) algorithm [7, 12]. MLSE algorithm is rarely used in real communication systems due to excessive complexity of implementation. Viterbi algorithm is simpler than MLSE but Viterbi algorithm still requires top hardware platforms. So algorithms with cancelling inter-channel interference can provide low energy losses and low requirements for hardware. Usually algorithms with cancelling inter-channel interference are considered with interference of one signal on nearby frequency subcarrier. This article deals with development algorithms through considering more interference signals on different frequencies with estimation of operation complexity.
© Сухоцкий С.А., Завьялов С.В., Овсянникова А.С., Лавренюк И.И., 2022. Издатель: Санкт-Петербургский политехнический университет Петра Великого
The structure of transmitter and receiver of SEFDM signal
The transmitted discrete SEFDM signals can be expressed by the following expression [13]:
N/2-1 , . kn
'— 2 jan—
sn =Z Cke N, n = 0,1,..., L -1. (1)
k=-N/ 2
In this equation N is a number of subcarriers, {Ck } is vector of modulated symbols, where k is a current number of subcarrier, a = AfT is a factor of compressed bandwidth, Af is the frequency distance between signals on subcarriers, T is transfer time of one OFDM symbol, n = 0, 1, ..., L — 1, L is the number of time samples in one SEFDM symbol [13—15].
Structure scheme of SEFDM transmitter is presented on Fig. 1a [13]. The first step to generate signal is creating modulation symbols from input bits using modulation with Mapper block. For our study, we chose quadrature phase-shift keying (QPSK). Therefore, this type of modulation transmits 2 bits per subcarrier. Next, the generation requires to put a vector of symbols in serial/parallel block and add (NFFT — N) zeros, where NppT is a number of samples in fast Fourier transform and N is the number of subcarriers to see the out-of-band emission on the spectrum. The result enters the inverse fast Fourier transform (IFFT) block with NppT size, where symbols become time samples. The next part is ignoring (1 — a)NppT samples to reduce duration of signal and then serial/parallel block.
Output signal from previous block has to be transformed with digit-to-analog converter, filters and power amplifiers. The last part of transmitting scheme is antenna.
b)
Fig. 1. Structure scheme of transmitter and receiver
Structure scheme of SEFDM signals receiver is presented in Fig. 1b. The mixture of SEFDM signal and AWGN is received by antenna with low noise amplifier, filters and analog-to-digit converter. Result samples of signal enter the S/P block with adding zeros afterwards to decompress spectrum from AF^™,, = , to AF„„,, and follow to FFT block. Following data come in the "Algorithm for
SEFDM OFDM OFDM ° °
cancelling inter-channel interference" block to improve BER performance. Fixed evaluations of symbols transform into bits in Demapper.
Iterative algorithm for cancelling inter-channel interference
After the FFT block, interference samples of each subcarrier iteratively can be saved in Block storage
as k , where ith subcarrier affects 1th subcarrier. k can be called coefficients of mutual interference from
y J '1
different subcarriers (Fig. 2).
For example, normalized value of interference for signals at current subcarrier and at neighboring i = ±1 subcarrier is equal to 0.64 with a = 0.5, if a = 0.1 interference value increases to 0.98.
The idea of the algorithm is iterative subtraction from considered subcarrier of every interference sample of any other subcarrier. This way, the expression for received samples can be written as Eq. (2).
For the convenience we reassigned received modulated symbols as {C* , symbols after the first iteration of algorithm — C'.
C* -IkjC* = C'. (2)
j=i
The idea of this algorithm is similar with algorithm for one-frequency Faster-than-Nyquist signals, proposed in [16]. Note, that this algorithm is not similar with algorithms based on feedback on decision and has some common solutions with error-correcting coding.
Eq. (2) is supposed to subtract ICI only from one of the sides, the left one. This type of feedback on decision algorithm can be called asymmetrical. By analogy, algorithms with feedback on decision with subtraction from both sides can be called symmetrical. For Eq. (2) we can express structure scheme of the first iteration of our algorithm (Fig. 3). Note, that symbols C' can be transmitted to demapper to form output bits or to the second iteration of algorithm.
First received sample from IFFT block C* goes through without any changes and improving. Second received sample C2 gets subtracted with product of k12 and C1. That leads to removal ICI from the first subcarrier. These two operations can be united in "Block 1.2". Here and further delay line for pro-
u \ -e—u=Q.5 —6—c=0.1
I ;
K 1 J , 1 :v\ax
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 i
Fig. 2. Inter-channel interference on nearby subcarriers
Fig. 3. Structure scheme of algorithm (first iteration)
cessing time is injected in block of subtraction. For C3* process repeats but amount of operations doubles. In this way we continue till the CN sample.
We can use the second iteration of the algorithm for better results as shown in Fig. 4. Second iteration is the reverse version of the first. C'N goes through without any changes. C'N-1 gets subtracted with kN(N — and C'N . Step by step, ICI is reduced in every symbol. In addition, we can write off the equation for every symbol:
N
C/-I kjCJ = C. (3)
j=/+1
This way, if we use only the first iteration (Fig. 5), then we use asymmetrical algorithm with NpB left subcarriers, NpB = 0. If we use the first and the second iteration, then we use symmetrical algorithm with NpB = NpB + NpB right. Fig. 5 serves for better understanding of NpB positions and the structure of interference.
Modeling and results
Modeling was made in programming and numeric computing platform MATLAB.
After Demapper, we can calculate BER and find out how reduction of frequency space between subcarriers influences BER. For the BER performance, we need to use Eb/N0 parameter, where Eb is
Fig. 4. Structure scheme of algorithm (2nd iteration)
Fig. 5. Simplified scheme of N positions
the energy bit and N0 is spectral density of average power of noise [7]. At least 106 information bits are transmitted to calculate each value of BER.
Fig. 6a demonstrates this situation for various a, N = 256. At this graph we can see different curves matching different a. "Theory, QPSK (a = 1)" is the theoretical BER performance of OFDM signals (a = 1) with QPSK modulation of signals on each subcarriers. As we can see, modulation of case a = 1 perfectly matches with "Theory, QPSK (a = 1)".
Let us compare BER performance of standard demodulation and demodulation with asymmetrical algorithm on one subcarrier (NpB left = 1) (Fig. 6b). Both of them transmit 64 bits with N = 32. As we can see, the asymmetrical algorithm gives us small coding gain at these values of Eb/N0.
For better values of BER performance, we can increase amount of NFB step by step on every side and watch dependence of energy losses of our algorithm in comparison with the theory (Fig. 7) (value of BER is constant and equals 10-2). An analysis confirms the idea presented above about ICI tending to zero with N. tending to infinity. As we can see in Fig. 7, energy loss tends to limit with increasing NFB because furthest subcarriers have lower values of coefficients of mutual interference than nearby subcarriers. That is the reason why the idea of using NFB = N is very resource-intensive and moreover meaningless.
This way we can find the limit for NFB for every N, when BER performance doesn't change anymore. For example, we can consider a situation when signal is transmitted with N = 128 subcarriers (Fig. 7a), Eb/N0 is constant and equal to 10 dB. From this plot we can understand that for a = 0.7 the limit that can be taken is NFB = 4, for a = 0.75 - 6, for a = 0.8 - 8, for a = 0.85 - 11, for a = 0.9 - 14. Furthermore, we will see that the limit for NFB almost does not change with increasing N.
Conclusion
The article presents the idea of a symmetrical iterative algorithm for cancelling inter-channel interference of SEFDM signals from both sides of considered subcarrier by iterative analysis of every received subcarrier and interference of each of the neighboring ones. This work demonstrated existence of a limit for the number of subcarriers used for feedback when energy loss cannot be reduced any more, which can be used for optimizing settings and saving computing resources. As for numerical results (Fig. 8), the developed algorithm with found limit NFB in comparison with algorithm on one subcarrier gives
Fig. 6. BER performance: a — SEFDM signal with various a (N = 256); b — comparison of standard demodulation algorithm and asymmetrical FB demodulation algorithm (N = 32, NpB hft = 1)
Fig. 7. a — Dependence of energy loss versus a at various N (BER = 10-2);
FB
b — dependence of BER performance versus NFB = NFB + NFB right (Eh/Nn = 10 dB)
Fig. 8. Comparison of standard demodulation algorithm, asymmetrical feedback algorithm on one subcarrier (NFB hft = 1) and symmetrical feedback algorithm
coding gain in value of 2 dB in case of a = 0.9, N = 128 and BER = 10-2. For case the case of a = 0.8, coding gain is about 15 dB. For a = 0.7, energy coding cannot be detected as the algorithm BER curve is too high on one subcarrier that does not exceed the value of BER = 10-2. For the lowest a, the coding gain will be increasing even further.
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INFORMATION ABOUT AUTHORS / СВЕДЕНИЯ ОБ АВТОРАХ
Svyatoslav A. Suhotskiy Сухоцкий Святослав Александрович
E-mail: suhotskij2.sa@edu.spbstu.ru
Sergey V. Zavjalov Завьялов Сергей Викторович
E-mail: zavyalov_sv@spbstu.ru
Anna S. Ovsyannikova Овсянникова Анна Сергеевна
E-mail: ovsyannikova_as@spbstu.ru
Ilya I. Lavrenyuk Лавренюк Илья Игоревич
E-mail: lavrenyuk_i@spbstu.ru
Submitted: 18.04.2022; Approved: 23.05.2022; Accepted: 30.05.2022. Поступила: 18.04.2022; Одобрена: 23.05.2022; Принята: 30.05.2022.
