A novel combined algorithms for 32-QAM carrier recovery

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1 A novel combined algorithms for 32-QAM carrier recovery M. Musso*, M. Gandetto*, G. Gera**, S. Canepa*, R. Singh* and C. S. Regazzoni* * Department of Biophysical and Electronic Engineering, University of Genova, Genova, taly ** National nter-university Consortium for Telecommunications, Genova, taly {musso,gandetto,gera,reetu,carlo}@dibe.unige.it, Abstract n this paper a novel method to realize the synchronization process in case of 32-QAM will be presented. The system is based on the times-n carrier recovery and doesn t depend on data decision. Starting from the Par and Ahn method which tracs, after a non linearity, the carrier recovery only for the in-phase symbols of a 16-QAM modulation, the proposed method combines a Phase Loc Loop and a Costas loop to use also in-quadrature symbols to solve the problem of tracing process. Moreover the algorithm has been extended to a 32 QAM modulation and it has been tested with received symbols corrupted by phase noise and thermal noise. Numerical results are presented to support the effectiveness of the proposed algorithm. Key words: Receiver Technology, Carrier recovery, Synchronisation, 32-QAM system 1. NTRODUCTON Nowadays the grown of communications has brought to a great development of digital systems, such as high quality video and multimedia broadcasting, where M- level quadrature modulations are widely used [3][4] [10][11]. The Quadrature Amplitude Modulation (QAM) has become common in bandwidth efficient digital communication systems; in particular 16-state rectangular shaped QAM (16 QAM) and higher-level QAM modulation (32, 64, 128 and 256) have been adopted in many high-capacity digital radio lins and in voice-band data transmission [8][9][12]. For these types of modulations, one of the most important problems is carrier recovery [5] to allow a coherent demodulation. The accuracy required for the receiver is high and increases with the number of level M. n fact errors in synchronisation degrade the performances because they rotate the position of the received symbol in the in phase and in quadrature plane bringing it closer to the decision boundaries associated with another symbol. Therefore, due to its crucial role, the synchronisation problem is the subject of a considerable development and research [6]. One of the most classical approach to the synchronisation problem is to consider this as formed by two different tass. The first one is to regenerate the spectral line by using nonlinear transformations. The second tas is to loc the frequency by using a Phase Loc Loop (PLL) or other similar devices. On the contrary to the decision-directed carrier recovery, in these types of systems the solution is given independently by the data decision. 2. CARRER RECOVERY Modulation is a process of systematic modification of one or more parameters of a sinusoidal signal (carrier signal) by another signal (modulating signal). The modified signal is called modulated signal The parameters of a sine wave are the amplitude, the frequency and the phase and all of them can be modified to carry information; if the amplitude is modified the modulation is called amplitude modulation (e.g. AM and DSB among the analog modulations and OOK and ASK among the digital); if the modification is applied to the frequency or phase, the modulation is called angular modulation (e.g.. FM e PM among the analog modulations and FSK and PSK among the digital). There are also modulations where the modification concerns both the amplitude and the phase e.g. the QAM (Quadrature-Amplitude Modulation), that are widely used in radio bridge applications because of their good spectral efficiency.. Usually the generation of modulated signals is quite easy; the same is not true for the receiving side where it is necessary to rebuild the parameters very precisely the parameters utilized during transmission [13]. Generally speaing, we can subdivide the receivers in two categories: coherent receivers and non-coherent receivers.. Non-coherent receivers don t need the nowledge of the frequency and the phase of the carrier However in the case of angular modulations in not possible to use a non-coherent detector because the information is carried by the frequency and phase. Because of that, a correct coherent demodulation needs a precise synchronization between the oscillator of the receiver and the one of the transmitter.

2 This process is nown as carrier recovery, has been solved through different techniques and is still subject of study to continue improving the performances of the systems and to allow communications even when the channel is severely degraded Carrier Recovery problems Due to the fact that the information is present in the frequency or in the phase, in case of angular modulations the non prefect synchronization of the local oscillators cause several problems. To majour clarity in the following figures a 16- QAM is shown, however similar consideration could be made on a 32-QAM. The 16-QAM signal is: s t = a p( t 2D) cos(2πf t + φ ) + () b p( t 2D) sin(2πf t) a, b = ± 1, ± 3 where D represents the bit time p(t) a rectangular signal duration D seconds a and b represent the amplitudes of the transmitted symbol in phase and in quadrature Uncorrected frequency offset between the transmitter and the receiver causes continuous rotation of the constellation at the receiver, as shown in Figure 1. Figure 1 Frequency offset effects c c (1) nstead phase noise causes displacement of the received constellation points along circular arcs centred at the nominal constellation point locations. n presence of a phase offset of π /5 rad and a AWGN (Additive White Gaussian Noise) channel with signal to noise ratio of 10 db the following situation (Figure 2) is possible. Therefore also with a small phase offset the symbols can be moved in a different decision region and an increase of the error probability is present. Figure 2 Phase offset in an AWGN channel 3. PROPOSED METHOD n this paper an innovative method, that doesn t depend on data decision, is presented to realise the synchronisation process in case of 32-QAM. t is focused on the well nown times-four (x 4) method [6] already used with QPSK and 4-QAM and it is a further improvement of the Par & Ahn method [1] that had been developed for 16-QAM. n [1] the carrier can be recovered by means of a 4 th -power pre-processing device whose output feeds a PLL circuit. Symbols in a 16-QAM constellation can be considered on three circles. After a suitable normalisation, according to Par & Ahn method, the problem of carrier recovery for a 16 QAM becomes the problem of carrier recovery for a 12-PSK (Figure 3a). By using the 4 th -power device, each symbol in the first and 3 rd circle is transformed into two symbols with only a in phase component (A, C in Figure 3a, with phase equal to 180 ). On the other hand symbols belonging to the second circle after 4th power transformation still have both a phase and quadrature component, so they are useless for carrier recovery. By means of an envelope detector and a window detector, symbols which don t belong to the phase axis (Figure 3a) are detected and their presence drives a trac and hold bloc, that switches off the PLL and holds the last carrier value. f symbols A and C are detected, the PLL is activated and the tracing process begins. The drawbac is that, without a suitable training sequence periodically inserted in the signal, the receiver can be unable to recover the carrier, because all symbols corresponding to group B and B cannot be used for synchronisation. n order to have better performances and solve the previous problem two PLLs in parallel has been proposed [2]. The first one wors in the same manner of the [1], but instead of discarding symbols B and B their phase is changed by a fixed amount and the second PLL is activated. n such a way all symbols can be used

3 and training sequences are no longer needed for carrier recovery. These solutions are valid for a 16-QAM modulation, but a further improvement is needed when modulations with more levels are used. n this paper we consider a carrier recovery scheme for a 32-QAM modulation. The system is modified from the one presented in [2] which is not suitable for this case: in fact symbols don t belong to three different circles (as for 16-QAM), but to five different circles and therefore after the 4 th power processing seven groups of symbols are identified (Figure 3b). Figure QAM (a) and 32 QAM (b) symbols after the 4 th power pre-processing. The proposed method is reported in [2]: the received signal is used by two branches; the first one where it is processed by a 4 th -power pre-processing device and sent to one PLL and a Costas loop. As reported above and shown in Fig 1b applying 4th-power pre-processing to a 32 QAM a group with only in-phase component (A and C) and six antipodal symbols (B, B, D, D, E and E ) are obtained. This result has to be taen into account in second branch which generates the control of the two tracing devices. The envelope detector and the window detector identify which of seven groups the received signal belongs to, then in relation to the detected symbol the second order PLL (for symbols A and C) or the Costas Loop (for symbols B, B, D, D, E and E ) is activated. Behind what has been stated, the window detector generates three signals: the first one drives the two loops, enabling or disabling their inputs, depending on the value output from the envelope detector. f a symbol from the first or the third circle is received (symbols A and C in Fig. 1b), then the PLL will be enabled and the Costas Loop disabled; on the contrary, if the symbol received belongs to the second, fourth or fifth circle (symbols B, B, D, D, E and E in Figure 3b), the PLL will be disabled and the Costas Loop enabled. When a loop is not enabled, the input of each VCO is a mean calculated over the last two bit periods of the phase error coming from the loop filter, in order to eep memory of the carrier state. The other two signals from the window detector are used to select the right offset for the in-phase component, indicated as 2, 4 and 5 in Figure 4. n order to use the capability of this Loop to trac antipodal symbols Algorithm description The proposed system activates the two loops one at time according to the outcome of the envelope of the received signal. The loop that is active is in trac mode whereas the other one is in open loop mode. For example when the input estimate symbol has only the in-phase component, the window detector set at 1 the trac swich signal; in this manner the PLL is activated and the Costas wors in open loop ( Driven mode). On the other hand when a intermediate symbol is recognised an external offset is introduced; this is made to mae an in-phase component equal to zero; after this step the Costas is activate and the system continues to trac the phase variation starting by the output of the PLL, meanwhile the PLL is in Driven mode. The two loops are able to communicate withg each other therefore they maintain the complete system update on the instantaneous phase variations. To obtain the necessary offset having symbols with only in-quadrature component the analysis of the received signal is made. n fact, this offset is equal to inphase component of the intermediate circumference after the normalisation and the 4 th power processing. For major clarity in the first part an example with a 16- QAM is shown. n this case the symbols can be expressed as: B' '' = cos 4 i ± sin 4 q 3 where i and q are the versors on the phasor plane. Therefore the cancellation of in-phase component can be made by subtracting a signal as cos 4 cos( 4 ω c t) and in this manner a bipolar signal is obtained. n a 32-QAM case in-phase and quadrature components can tae the values ± 1, ± 3, ± 5. As already shown the removal of amplitude modulation and the following rising to the power of four of the received signal, lead to the constellation of figure 3b. Therefore D and E components in the phasor plane (Figure 3b) are two new couples of points that have inphase and quadrature components non negligible. The proposed system maes use of the Costas Loop property of allowing the tracing on bipolar symbols in the 32 QAM case and needs to insert a different offset depending on the estimated circumference. For this reason the window detector will generate three signals, one that behaves lie a switch between PLL and Costas Loop, the other two will enable the right offset that must be applied to the input signal.

4 Offsets are indicated as gain 2, 4 and 5 and their values are respectively: 2 = cos 4 = 0,28 4 = cos 4 = 0,7 5 and 3 5 = cos 4 = 0,55. 5 Finally a second amplitude normalization is necessary to solve the problems due to the different amplitudes of phasors. n this regard the Costas Loop will have at its input a sinusoidal signal of constant amplitude. The acquisition phase is critical for the proposed system and is handled differently with respect of the tracing phase. To mae the PLL and Costas loop able to trac the carrier, it is necessary to introduce a synchronization word that is nown to the system at the beginning of the transmission and then every reset of the receiver.. This word is composed by six symbols, three symbol A followed by three symbols B. First of all the PLL is activated. This is due to the necessity of the Costas loop to have a carrier synchronized in frequency and phase before to inserting the offset. The main advantage of this approach is in its simple architecture. The idea which leads the proposed algorithm is to select a different loop in relation to the received symbols allowing firstly the receiver to exploit the best performances of each Loop and moreover use of all the symbols and not only part of them, as reported in [2]. This last capability avoids the need of training sequence increasing the number of bit for the payload. Figure 4. The proposed method 4. RESULTS The proposed algorithm has been tested and evaluated by using a Matlab Simulin model. The considered system is characterised by a carrier of 70 MHz with a mean Doppler shift of 50 KHz and bit rate of 3.4 Mbit/s. The received symbols have been considered as corrupted by an Additive White Gaussian Noise (AWGN) combined with a Phase Noise. Carrier recovery together with frequency offset and envelope decision error by the window detector inevitably move the BER curve (obtained from simulations) away from the theoretical curve obtained using equation (2) for the 32 QAM [2]: 1 Eb P = be 2Q (2) 4 N 0 n Figure 5, instead is shown a comparison between the theoretical curve and the curve obtained from simulations of the proposed system for the 32 QAM. Figure 5 Error probability vs Eb/N 0 comparison between 32-QAM and theoretical values n this case too the simulated curve diverges from the theoretical and shows a threshold of 13dB, below which the training sequences are needed.

5 n the following figures (Figure 6 and Figure 7) the tracing carried out by Costas when PLL is disabled and viceversa, in relation to the received symbol is show. n particular two different situations are presented: the first one with only AWGN and the second one with AWGN and phase noise. Different input signals have been considered. As expected the performances are better with an high signal to noise ratio, but also in case of SNR=5dB the correct tracing is obtained. n Figure 7 the phase noise is inserted: the increase from 2 to 8 causes a delay of the right recovery, but in 5 microseconds the system has recovered the carrier. Figure 6 Recovered carrier of signal corrupted by AWGN. Figure 7 Recovered carrier of signal corrupted by AWGN and phase noise. 5. CONCLUSON n this paper an innovative solution of carrier recovery based on the parallel use of a Phase Loc loop and a Costas Loop has been shown. n comparison with the standard systems, the proposed method is able to recover the carrier without the necessity to transmit training sequences. The system has been tested on a 32-QAM because this technique has been adopted in many high-capacity digital radio lins and in voice-band data transmission. Simulative results have been shown a behaviour similar to the theoretical, but with the necessity of E b /N 0 3dB higher. Future developments will analyse the performances in case of multipath presence and the use of higher-level QAM modulations (64, 128 and 256). REFERENCES [1] Y. Par; J. Ahn, A new carrier recovery method for 16- QAM signal, Personal Wireless Communications, 1997 EEE nternational Conference Dec. 1997, pp [2] C. Sacchi, M. Musso, G. Gera, C. Regazzoni, et Al. An Efficient Carrier Recovery Scheme for High-Bit-Rate W- Band Satellite Communication Systems, EEE Aerospace conference, Mar , Big Sy, Mt [3] H. Gharavi, Pilot-Assisted 16-Level QAM for Wireless Video, EEE Trans. on Circ. and Syst. for Video Technology, V. 12, N 2, Feb pp [4] V. Theodoraopoulos, et Al, A Dual Priority M-QAM Transmission System for High Quality Video over Mobile Channels, First nternational Conference on Distributed Framewors for Multimedia Applications (DFMA 05) February 6-9, Besançon, France. [5] H. Sari, S. Moridi, New Phase and Frequency Detectors for Carrier Recovery in PSK and QAM Systems, EEE Trans. on Communications, VOL. 36. NO. 9, Sept pp [6] A. J. Rustao et Al, Using Times-Four Carrier Recovery in M-QAM Digital Radio Receivers, EEE JSAC, Vol 5, N. 3, Apr 1987 pp [7] H. Sari, S. Moridi, New Phase and Frequency Detectors for Carrier Recovery in PSK and QAM Systems, EEE Transactions on Comm., Vol. 36, No 9, September [8] K. Kim, H. Choi, Design of Carrier Recovery Algorithm for High-Order QAM with Large Frequency Acquisition Range, EEE [9] Chun-Nan Ke, Cheng-Yi Huang, Chih-Peng Fan, An Adaptive Carrier Synchronizer for M-QAM Cable Receiver, EEE Transactions on Consumer Electronics, Vol. 49, No. 4, November [10] M. Luise, R. Reggianini: Carrier frequency recovers in all-digital modems for burst-mode transmissions EEE Trans. On Commun., Vol. COM-43, pp , March [11] U. Mengali, M. Morelli, Data-aided frequency estimation for burst digital transmission, EEE Trans. On Commun., Vol. COM-45, pp.23-25, Jan [12] M.P. Fitz Further Results in the fast estimation of a single frequency, EEE Trans. On Comm., Vol. COM- 42, pp , March [13] J. G. Proais, Digital Communications, McGraw-Hill nc., New Yor, NY, 1995 (Third Edition).

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