Fig. 3.The process of correlation with non-integral chip delay.
As shown in Fig.3 the signal sa(t) and sb(t) are spread by the sequences a = [a1, a2, a3, a4] and b = [b1, b2, b3, b4] respectively. There exists chip delay τ between sa(t) and sb(t) due to multiple path transmission or asynchronous multi-user communication. Whenτ =qTc, q ∈Z+, Tc is the chip interval, we
get 4Tc
0 sa(t)sb(t)dt= (Tc−τ)(a1b2+a2b3+a3b4+a4b1) +τ(a1b3+a2b4+a3b1+a4b2)
= (Tc−τ)φEP(a,b; 1) +τ φEP(a,b; 2)
= (Tc−τ)[φ(a,b; 1) +φ(b,a; 3)] +τ[φ(a,b; 2) +φ(b,a; 2)] (10) As shown in Fig.3 and (10), correlation function with any non-integral chip delay equals to two correlation functions with integral chip delay. Therefore, the
correlation properties of CCs with non-integral chip delay is still ideal owning to its ideal correlation properties with any integral chip delay.
4 Comparison on Correlation Properties with of Traditional Spreading Codes
In this section, taking a family of CCCsC(4,4,16) as an example, the simulated correlation properties of CCs are shown to verify correctness of the proof work.
The congregated length ofC(4,4,16) is 64, therefore, the correlation properties of Gold sequences with length 63 and Walsh codes with length 64 are also simulated.
Fig. 4.Even periodic auto-correlation properties of different spreading codes.
Fig. 5.Even periodic cross-correlation properties of different spreading codes.
The auto- and cross-correlation properties of the three spread codes under different definition of correlation functions: even periodic, odd periodic and aperi- odic correlation functions are shown in Figs.4,5,6,7,8and9respectively. As can be seen from the simulated results, CCs are able to achieve ideal correlation prop- erties (the auto-correlation is a delta function and the cross-correlation is a zero function) under all the three definitions. Gold code just achieves approximate
Fig. 6.Odd periodic auto-correlation properties of different spreading codes.
Fig. 7.Odd periodic cross-correlation properties of different spreading codes.
Fig. 8.Aperiodic auto-correlation properties of different spreading codes.
ideal auto-correlation property with even periodic correlation definition and Walsh code just achieves approximate ideal cross-correlation property with even periodic correlation definition. Therefore, a CDMA system with Gold code as its spreading sequence performs better under MPI, while it with Walsh code performs better under MPI. However, opposite phase between adjacent bits is
Fig. 9.Aperiodic cross-correlation properties of different spreading codes.
usual. In this situation, the non-zero sidelobe in odd periodic auto-correlation property of Gold, as shown in Fig.6(a), will result in MPI, while the non-zero sidelobe in odd periodic cross-correlation property of Gold, as shown in Fig.7(b), will result in MAI.
5 Conclusions and Discussions
This paper proves the ideal correlation properties of CCs with non-integral chip delay under the definition of aperiodic correlation functions. The above com- parisons of CCs with traditional spreading codes on auto- and cross-correlation properties under different definitions of correlation functions verify the correct- ness of the proof work and show that a CC-CDMA system is able to achieve MPI- and MAI-free communication owning to the proved ideal aperiodic correlation properties.
However, due to the two-dimensional nature of CCs, the implementation of CC-CDMA system is a challenging work. In a direct sequence (DS) CC- CDMA system, each user will be allocated a particular CC from a code set as its signature code, and a user should spread its data withM element sequences of CC, respectively. In order to realize the spreading and de-spreading processes as definition of aperiodic correlation function, a CC-CDMA system must satisfies the following four conditions:
(1) M streams of spread signals of one user are required to be transmitted in M independent subchannels and separated at a receiver;
(2) each stream of spread signal should be de-spread using the right element sequence of the CC allocated to the user at a receiver;
(3) each stream of spread signal should be synchronized and therefore they have the same chip-delay;
(4) the de-spread signals with M element sequences should combined with equal gains.
Therefore, it’s challenging to design and implement a CC-CDMA system. The work [7] has present a comprehensive survey of existing literature in the area
of CC-CDMA system and it divided the existing CC-CDMA solutions into two categories: time division multiplex and frequency division multiplex CC-CDMA systems, according to the kinds of independent sub-channels. However, both of the two CC-CDMA system architecture have its problem on implementation complexity or spread and spectrum efficiency. Therefore, as for the future works, we will pursue to optimize the system deign of CC-CDMA systems.
References
1. Zhou, Y., Jiang, T., Huang, C., et al.: Peak-to-average power ratio reduction for OFDM/OQAM signals via alternative-signal method. IEEE Trans. Veh. Technol.
63(1), 494–499 (2014)
2. Nguyen, H.C., de Carvalho, E., Prasad, R.: Multi-user interference cancellation schemes for carrier frequency offset compensation in uplink OFDMA. IEEE Trans.
Wirel. Commun.13(3), 1164–1171 (2014)
3. Suehiro, N., Hatori, M.: N-shift cross-orthogonal sequences. IEEE Trans. Inf. Theory 34(1), 143–146 (1988)
4. Welch, L.: Lower bounds on the maximum cross correlation of signals (corresp.).
IEEE Trans. Inf. Theory20(3), 397–399 (1974)
5. Sarwate, D.V., Pursley, M.B.: Crosscorrelation properties of pseudorandom and related sequences. Proc. IEEE68(5), 593–619 (1980)
6. Sun, S.-Y., Chen, H.-H., Meng, W.: A survey of complementary coded wireless communications. IEEE Commun. Surv. Tutor.17(1), 52–69 (2015)
7. Sun, S., Han, S., Yu, Q., Meng, W., Li, C.: A survey of two kinds of complemen- tary coded CDMA wireless communications. In: 2014 IEEE Global Communications Conference, pp. 468–472 (2014)
A Novel Structure Digital Receiver
Zijian Zhang(&), Dongxuan He, and Yulei Nie
School of Information and Electronics, Beijing Institute of Technology, Beijing, China {2120150844,2120130765,nieyulei}@bit.edu.cn
Abstract. This paper studies a novel structure digital receiver to demodulate signal with large frequency offset. When the carrier frequency offset is large, the matchedfilter willfilter out part of the in-band signal, resulting in decrease of SNR and deterioration of BER. Different from traditional receiver structure, the novel receiver put a coarse frequency correction module before the matched filter, which will reduce the negative influence of matchedfilter under large frequency offset. Simulation results show that the new structure displays similar performance to the traditional structure under small frequency offset and great performance improvement when the frequency offset is large.
Keywords: Frequency offsetMatchedfilter
1 Introduction
The commonly used digital receiver structure is shown in Fig.1. The baseband signal obtained after the digital down conversion and sampling rate conversion will pass through the matchedfilter, the timing module, the frequency synchronization module, phase synchronization module and the decoding module. After decoding we can get the bit stream [1]. Sometimes the received signal comes from different transmitters, so the feedback structure in reference [1,2] can’t be used. The structure shown in Fig.1has broader applicability.
Matchedfiltering operation has two roles, thefirst is to ensure that the timing data has no inter symbol interference (ISI). The second is to make the SNR at the timing point has the largest value.
Sampling rate
conversion Matched filter synchronizationFrame Digital down
conversion
Decoding Carrier
tracking
Frequency and Phase offset
correction
Timing synchronization A/D
input
Bit stream output
Fig. 1. The commonly used digital receiver structure
©ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2018 X. Gu et al. (Eds.): MLICOM 2017, Part II, LNICST 227, pp. 71–78, 2018.
https://doi.org/10.1007/978-3-319-73447-7_9
The signal transmitter and receiver’s crystal instability and other factors will cause the existence of the carrier frequency offset and phase offset. The purpose of the frequency offset correction module and the phase correction module is to estimate the frequency offset and phase offset on the signal and then compensate it respectively.
Based on whether the pilot sequence is used, frequency offset estimation algorithm can be divided into DA (data aided) and NDA (non-data aided) estimation algorithm, which is the same in phase offset estimation.
For DA algorithm, The KAY algorithm [3], LR algorithm [4], Fitz algorithm [5] are commonly used. The KAY algorithm has larger frequency offset estimation range but lower accuracy compared to the LR algorithm. Therefore, in practical applications, we couldfirst use the KAY algorithm to do a coarse frequency offset correction, and then use the LR algorithm to do afine frequency offset correction. The signal after these two frequency corrections will only have a small residual frequency offset [6].
ML algorithm is commonly used in phase correction, after the phase compensation, there will be a small residual phase offset on the signal.
Usually a carrier tracking is performed to further reduce the residual frequency offset and residual phase offset, and tracking the carrier frequency and phase’s changes, the PLL (phase-locked loop) is commonly used for tracking, the output of the PLL is the data symbols.
After decoding, the data symbols are transformed to bit stream.
With the increase of the carrier frequency offset, the receiver’s performance will drop. To solve this problem, they use a feedback structure for more accurate digital down conversion in DVB-S2 [1], but if the received signal comes from different transmitters, this method can’t be used. In this paper, a novel structure is proposed to solve the problem.
2 Performance Degradation Due to Frequency Offset
In this part, we discuss why the receiver’s bit error rate increase significantly due to the large frequency offset.
Through the investigation of the receiver modules, it’s found that when the carrier frequency offset is large, the matchedfilter will cause a great deterioration of the SNR.
This phenomenon can be visually observed in the frequency domain, as shown in Fig.2, when the signal has no carrier frequency offset, all the signalsfiltered out by matchedfilter are out band noise, but when carrier frequency offset exists, part of the signal spectrum will appear outside the band of the matchedfilter, thefiltering oper- ation willfilter out this part of signal spectrum, which will cause a significant deteri- oration of the SNR.
The Fig.3further demonstrates the phenomenon.
The ES=N0value isfixed to 18 dB before matchfiltering. The SNR of the matched filter’s output decreases gradually as the increase of normalized frequency offset, which will cause the rising of the system’s BER.
We can also explain the problem through another perspective, for the sake of simplicity, we choose ideal low passfilter to be pulse-shapingfilter and matchedfilter
(In practical applications we use root-raised cosinefilter). If the total transfer function of baseband system satisfies the Nyquistfirst criterion:
X
i
Hðwþ2p
Ts ị ẳTs j j w p
TS; ð1ị
the optimum sampling points have no ISI (inter symbol interfere). When there is no frequency offset, the transfer function is:
Fig. 2. Frequency domain of signal and matched filter. The red part represents the matched filter, the black part represents the signal. (Colorfigure online)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
16.4 16.6 16.8 17 17.2 17.4 17.6 17.8 18 18.2 18.4
Normalized frequency offset
SNR (dB)
Fig. 3. The SNR of the matchfilter’s output
Hðwị ẳ TS j j w TpS
0 otherwise
; ð2ị
which satisfies Nyquist first criterion. However, when carrier frequency exists, the transfer function is:
Hðwị ẳ TS Tpp\w\TpS
Tp[Ts
0 otherwise
; ð3ị
Nyquist first criterion can’t be satisfied anymore, thus producing the ISI and degrading the performance.
3 New Digital Receiver Structure
In order to solve the problem described above, this paper presents a new digital receiver structure. The core idea of this structure is to eliminate the SNR deterioration caused by the matchedfilter. For this purpose, we will compensate the carrier frequency offset as much as possible before matchfiltering, then matchfilter the compensated signal.
The digital receiver structure is shown in Fig.4:
The baseband signal after digital down conversion and sample rate conversion will pass through a low passfilter (LPF), whose bandwidth is sufficiently larger than the signal bandwidth to ensure that the signal with frequency offset can still lie in the pass band of the low passfilter, which ensures that the spectrum of the signal will not be filtered by the low-pass filter and out-of-band noise is filtered as much as possible.
Commonly, the passband bandwidth can be set as the sum of the signal bandwidth and the maximal frequency offset.
The KAY algorithm is used to calculate the carrier frequency offsetfirst due to its large estimates range. Before the frequency offset estimation, we use the OM timing algorithm to get the optimum sample point which is needed by the KAY algorithm.
Since we use a LPF instead of matchedfilter, the best sample point is less accurate and has more noise, but it is enough for coarse frequency offset estimation.
We use the frequency offset calculated by the KAY algorithm to compensate the output signal of the low-passfilter. This operation aims to move the spectral center of the signal to zero frequency as much as possible. And then we use the compensated
Fig. 4. The new digital receiver structure
signal to do the match filtering, which will not filter out the spectrum of the signal anymore, thus further enhancing the SNR.
After match filtering, we do timing operation and carrier recovery with higher precision to get the data symbols. We use the OM timing algorithm to do the timing operation, the LR algorithm to do the frequency offset compensation with higher accuracy and ML algorithm to compensate the phase offset. Finally we get the bit stream.
The Fig.5shows the SNR curve of the matchfilter’s output.
The ES=N0value of the system’s input isfixed to 18 dB and the normalized carrier frequency offset changes. In thisfigure the ordinary line represents the SNR in the old structure receiver and the line with diamond marks represents the SNR in the new structure receiver. Compared with the old structure, we can see the SNR in the new structure has been greatly improved, and the receiver with new structure can work under a larger carrier frequency offset. Thus the performance of the new structure digital receiver can be significantly improved.
4 Simulation Results
The simulation results compare the performance of the two different structures of digital receiver. Test signal is 16QAM. Each frame contains the unique word portion and the data portion. The channel is an additive white Gaussian noise channel.
When the normalized frequency offset between the transceivers isfixed to 0.07 [7], ES=N0is set to 18 dB, the output constellation of the two kinds of digital receivers is
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
16.4 16.6 16.8 17 17.2 17.4 17.6 17.8 18 18.2 18.4
Normalized frequency offset
SNR (dB)
Fig. 5. The SNR of the matchfilter’s output
shown in Fig.6. It can be seen in the case of relatively small frequency offset, con- stellation quality improves slightly.
The Fig.7shows the bit error rate curve of the two receivers. For convenience, we use the hard decision method [8] to demodulate the constellation. The ordinary line indicates the bit error rate curve of the old structure receiver, and the line with diamond marks represents the bit error rate curve of the new structure receiver. It can be seen that the performance of the two receivers is almost the same when the normalized frequency offset is small.
When the normalized frequency offset between the transceivers is increased to 0.15 while ES=N0is still 18 dB, the constellation of the two receivers is shown in Fig.8. It
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Quadrature
In-Phase Constellation of the old structure
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Quadrature
In-Phase Constellation of the new structure
Fig. 6. The constellation of the two receivers.
9 10 11 12 13 14 15 16 17 18 19
10-4 10-3 10-2 10-1 100
Es/N0 (dB)
BER
BER of the old structure receiver BER of the new structure receiver
Fig. 7. The BER of the two receivers.
can be seen that in the case of large frequency offset, the traditional structure receiver can’t work normally, but the new structure receiver still shows perfect performance.
The Fig.9 shows the bit error rate curves of these two different receivers. The ordinary line represents the bit error rate curve of the old structure receiver, and the line with diamond marks represents the bit error rate curve of the new structure receiver.
We can see that when the frequency offset is relatively large, the new structure receiver’s bit error rate has been significantly improved.
-0.5 0 0.5
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
Quadrature
In-Phase Constellation of the old structure
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Quadrature
In-Phase Constellation of the new structure
Fig. 8. The constellation of the two receivers.
9 10 11 12 13 14 15 16 17 18 19
10-4 10-3 10-2 10-1 100
Es/N0 (dB)
BER
BER of the old structure receiver BER of the new structure receiver
Fig. 9. The BER of the two receivers.
5 Conclusion
The new structure receiver shows similar performance to the old one when the fre- quency offset is small enough. But when the frequency offset increases, the match filtering operation will cause the damage to the signal spectrum and reduce the SNR, so that the bit error rate will increase. In this paper, a new structure of digital receiver is proposed. The front end uses a low-passfilter and a frequency compensation module to reduce the frequency offset, and then uses matchfiltering to improve the SNR, followed by carrier synchronization with higher accuracy. This new structure digital receiver can work normally under large frequency offset. When the normalized frequency offset is larger than 0.07, the performance will be better compared to the traditional digital receiver, while the cost is very little. The new structure receiver has a high value of engineering use.
References
1. Casini, E., Gaudenzi, R.D., Ginesi, A.: DVB-S2 modem algorithms design and performance over typical satellite channels. Int. J. Satell. Commun. Netw.22(3), 281–318 (2004) 2. Cioni, S., Corazza, G.E., Vanelli-Coralli, A.: Antenna diversity for DVB-S2 mobile services
in railway environments. Int. J. Satell. Commun. Netw.25(5), 443–458 (2010)
3. Kay, S.: A fast and accurate single frequency estimator. IEEE Trans. Acoust. Speech Signal Process.37(12), 1987–1990 (1989)
4. Luise, M., Reggiannini, R.: Carrier frequency recovery in all-digital modems for burst-mode transmissions. IEEE Trans. Commun.43(2/3/4), 1169–1178 (1995)
5. Fitz, M.P.: Planarfiltered techniques for burst mode carrier synchronization. In: 1991 Global Telecommunications Conference, GLOBECOM 1991. Countdown to the New Millennium.
Featuring a Mini-Theme on: Personal Communications Services, vol. 1, pp. 365–369. IEEE (1992)
6. Mengali, U., D’Andrea, A.N.: Synchronization Techniques for Digital Receivers. Plenum Press, New York (1997)
7. Albertazzi, G., Cioni, S., Corazza, G.E., et al.: On the adaptive DVB-S2 physical layer: design and performance. IEEE Wirel. Commun.12(6), 62–68 (2005)
8. Baldi, M.: Low-density parity-check codes. QC-LDPC Code-Based Cryptography. SECE, pp. 5–21. Springer, Cham (2014).https://doi.org/10.1007/978-3-319-02556-8_2
Analysis of Passive Intermodulation Effect on OFDM Frame Synchronization
Yi Wang, Xiangyuan Bu(&), Xiaozheng Gao, and Lu Tian School of Information Science and Electronics, Beijing Institute of Technology,
No. 5 of South Zhong-guan-cun Avenue, Beijing 100081, China wangyi9301@gmail.com, bxy@bit.edu.cn,
gxz6789@163.com,tianlu218@gmail.com
Abstract. Passive intermodulation can lead to a decrease in the performance of frame synchronization for the orthogonal-frequency-division multiplexing (OFDM) systems. In this paper, the Schmidl&Cox algorithm of frame syn- chronization is simplified by difference calculation to avoid overly complicated analysis. The statistical properties of time metric function in the presence of passive intermodulation interference are obtained by Gaussian distributionfit- ting. The closed form of false and missing detection probabilities are derived to evaluate the frame synchronization performance. Finally, simulations are con- ducted to demonstrate the validity of the analysis results.
Keywords: Passive intermodulationFrame synchronization
Orthogonal-frequency-division multiplexing (OFDM)Statistical properties
1 Introduction
As the demand of propagation rate rises, multicarrier modulation has been used in wireless communication systems. The orthogonal-frequency-division multiplexing (OFDM) system is one of the most successful implementations of multicarrier mod- ulation. But when the system transmits the multiple carriers, the carriers which pass through the passive device can generate the combination products of the multi- frequencies due to nonlinearity [1]. Thus the passive intermodulation (PIM) products are formed. PIM has become a threat for these multicarrier systems, especially for the OFDM system with high transmitting power [2,3].
PIM can lead to a degradation of the sensitive receivers when falling into the receiving band. The degradation in the performance of the communication systems can be quantified by bit error rate (BER) and synchronization probabilities. The PIM effects on the BER of M-PSK modulations were investigated in [4]. However, there is no complete model to characterize the PIM effect on synchronization. The OFDM frame synchronization is tofind the start position of every frame in OFDM systems. The classical Schmidl&Cox synchronization algorithm was proposed for OFDM system by Schmidl and Cox in 1997 [5]. Based on the Schmidl&Cox algorithm, the influence of narrowband interference on timing synchronization was investigated by Marey and Steendam [6]. However, the broadband characteristic of PIM interference brings dif- ficulty to the analysis on frame synchronization [7,8].
©ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2018 X. Gu et al. (Eds.): MLICOM 2017, Part II, LNICST 227, pp. 79–86, 2018.
https://doi.org/10.1007/978-3-319-73447-7_10