Performance Evaluation of the ComplexCoefficient Adaptive Equalizer Using the Hilbert Transform
 Author: Park KyuChil, Yoon Jong Rak
 Publish: Journal of information and communication convergence engineering Volume 14, Issue2, p78~83, 30 June 2016

ABSTRACT
In underwater acoustic communication, the transmitted signals are severely influenced by the reflections from both the sea surface and the sea bottom. As very large reflection signals from these boundaries cause an intersymbol interference (ISI) effect, the communication quality worsens. A channel estimationbased equalizer is usually adopted to compensate for the reflected signals under the acoustic communication channel. In this study, a feedforward equalizer (FFE) with the least mean squares (LMS) algorithm was applied to a quadrature phaseshift keying (QPSK) transmission system. Two different types of equalizers were adopted in the QPSK system, namely a realcoefficient equalizer and a complexcoefficient equalizer. The performance of the complexcoefficient equalizer was better than that of two realcoefficient equalizers. Therefore, a Hilbert transform was applied to the realcoefficient binary phaseshift keying (BPSK) system to obtain a complexcoefficient BPSK system. Consequently, we obtained better results than those of a realcoefficient equalizer.

KEYWORD
Feedforward equalizer , Intersymbol interference , Least mean squares algorithm , Quadrature phaseshift keying , Underwater acoustic communication

I. INTRODUCTION
Because of the reflections from the boundaries in underwater acoustic communication, the communication channel used is known to exhibit a frequencyselective fading channel with a multipath delay spread [13]. The performance of the underwater acoustic communication system degrades because of the intersymbol interference (ISI) [4,5] caused by the signals reflected from the sea surface and the sea bottom. A channel estimationbased equalizer is usually adopted to compensate for the ISI effect [5,6].
In this study, a feedforward equalizer (FFE) with the least mean squares (LMS) algorithm is applied to the quadrature phaseshift keying (QPSK) transmission system in order to cancel out the ISI effect [7,8]. Two types of equalizers are introduced, namely a realcoefficient equalizer and a complexcoefficient equalizer. We also introduced a binary phaseshift keying (BPSK) system with two real and a complexcoefficient equalizers. For the imaginary part such as the quadrature (Q) channel of the QPSK system, a Hilbert transform was used in the BPSK system [9,10].
The rest of this paper is organized as follows: in Section II, a comparison of two types of equalizers is presented. In Section III, simulation configurations are introduced. Section IV presents the concept of the complexcoefficient BPSK system. In Section V, the simulation results and the experimental results of the proposed methods are discussed. A summary of the performance of the proposed method is presented in Section VI.
II. COMPARISON OF TWO TYPES OF EQUALIZERS
In general, there are two binary state channels, namely the inphase (
I ) channel and the quadrature (Q ) channel, in a QPSK modulation and demodulation system, as shown Fig. 1(a). The transmitted signalx (t ) on the receiver is separated and demodulated into the output signalsy_{I} (t ) andy_{Q} (t ) by using a cosine signal or a sine signal with the same carrier frequency as that used on the modulation system. Then, the output signals are converted into fourstate {1 +j , 1 –j , –1 +j , –1 –j } data from each outputy_{I} (t ) andy_{Q} (t ).When an equalizer for the compensation of the channel distortion is applied to the output signals, two types of systems are considered. The first type of system includes two separated realcoefficient equalizers for each output
y_{I} (t ) andy_{Q} (t ), as shown in Fig. 1(b). This system can be considered a separated two BPSK system. The other is a complexcoefficient equalizer for the merged output signaly (t ) =y_{I} (t ) +jy_{Q} (t ), shown in Fig. 1(c).III. SIMULATION CONFIGURATIONS
Fig. 2 shows a layout of the experimental geometry at the bay of the Gwangan Beach located on the east side of Busan city, Korea. The range between the transmitter and the receiver is set to be 50, 100, 200, and 500 m. The depths of the transmitter and the receiver are set to be 7 m and 20 m, respectively. As the temperature and the sound speed of the vertical depth were almost flat, an image method [11] was used for the implementation of the underwater acoustic communication channel, and the related channel impulse responses are shown in Fig. 3.
We assumed that the channel response had five impulse signals: direct signal, surfacereflected signal, bottomreflected signal, surfacebottomreflected signal, and bottomsurfacereflected signal. The sampling frequency and the carrier frequency are set to be 160 kHz and 20 kHz, respectively. The transmission rates are set to be 500, 1000, 2000, and 4000 symbols per second (sps). The transmitted image is a standard Lena image that consists of 50 × 50 pixels with an 8bit resolution (20,000 bits).
Fig. 4 shows the block diagram of the FFE with the LMS algorithm. Here,
m (n ),y (n ),z (n ),e (n ), and denote binary data in the modulation system, the channel output, the equalizer output, the error signal, and the decision output, respectively. The LMS algorithm is used for the determination of the coefficient on the equalizer to compensate for the ISI. The FFE consists of a transversal finite impulse response filter with 30 taps. The filter output, the estimation error, and the tapweight adaptation are represented as discussed in [5].where
H , *, andμ denote the Hermitian form, the complex conjugate, and the step size parameter, respectively.IV. CONCEPT OF COMPLEX BPSK SYSTEM
In this section, we introduce a complex BPSK system based on the concept of the QPSK system. The BPSK system has the same structure as the
I channel of the QPSK system and has two states {1, –1}. To obtain theQ channel signal, a Hilbert transform was adopted. The Hilbert transform can be represented as follows [9,10]:It was obtained using the imaginary signal
y_{Q} (t ) with a 90° phase shift from the original real signaly_{I} (t ). The imaginary part of the binary data in the modulation systemm (n ) was also calculated for obtaining estimation error in Eq. (2). The BPSK modulation and demodulation system with a realcoefficient equalizer and a complexcoefficient equalizer is shown in Fig. 5.V. RESULTS AND DISCUSSIONS
First, the simulation results of two different equalizers of the QPSK system are presented. The bit error rates (BERs) according to the transmission rate and the range are presented in Fig. 6 and Table 1, respectively.
In Fig. 6, (a) shows the result obtained without the use of an equalizer; (b) the result obtained using two realcoefficient equalizers; and (c) the result obtained using a complexcoefficient equalizer. The same number of iterations for the training of the coefficient on the FFE is set for each simulation. From the obtained results, we concluded that the complexcoefficient LMS equalizer shows a better performance than the two separated realcoefficient LMS equalizers. The filter’s output signal
z (n ), error signale (n ), and tapweight vectorw (n ) have a crosscoupling system between them, as shown in Eqs. (1)–(3). This implies that a complex LMS algorithm is equivalent to a set of four real LMS algorithms because of the crosscoupling system between the filter output signal, the error signal, and the tapweight vector. From Fig. 6, we can infer that the results obtained in the case of the low sps and the long range were better than those obtained in the case of the high sps and the short range.Second, Fig. 7 and Table 2 show the simulation results of two different equalizers in the BPSK system. In Fig. 7, (a) shows the result obtaining without using the equalizer; (b) the result obtained using a realcoefficient equalizer; and (c) the result obtained using a complexcoefficient equalizer. The same number of iterations for the training of the coefficient on the FFE is set for all the simulations. Further, the results obtained using the complexcoefficient LMS equalizer were better than those obtained using the realcoefficient LMS equalizer in the BPSK system.
Finally, Fig. 8 shows the results of the equalization of the experimental data, carried out in a shallow ocean. The experimental conditions are the same those as shown in Fig. 1. The distance between the transmitter and the receiver was 10 m, and the bit rate was chosen to be 50 sps. In Fig. 8, (a) shows an original Lena image, (b) presents the result obtained without using an equalizer (BER=0.224), (c) and (d) illustrate the results with two realcoefficient equalizers (BER=0.181) and a complexcoefficient equalizer (BER= 0.123), respectively. Therefore, we can conclude that the complexcoefficient equalizer performs better than the two realcoefficient equalizers.
VI. CONCLUSIONS
In this study, an FFE with the LMS algorithm was applied to the QPSK system, and two realcoefficient equalizers and a complexcoefficient equalizer were adopted; their results were compared. The performance of a complexcoefficient equalizer was better than that of the two realcoefficient equalizers. On the basis of the results of the QPSK system, a Hilbert transform was applied to the realcoefficient BPSK system in order to obtain the complexcoefficient BPSK system. Further, the performance of a complexcoefficient equalizer was better than that of the two realcoefficient equalizers in the BPSK system.

[Fig. 1.] Block diagrams of the QPSK communication system: (a) QPSK modulation system, (b) QPSK demodulation system with two realcoefficient equalizers, and (c) QPSK demodulation system with a complexcoefficient equalizer.

[Fig. 2.] Schematic layout of the experiment: (a) experimental configuration and (b) temperature and sound speed profiles.

[Fig. 3.] Channel impulse responses according to distances: (a) 50 m, (b) 100 m, (c) 200 m, and (d) 500 m.

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[Fig. 4.] FFE with LMS algorithm.

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[Fig. 5.] BPSK communication system: (a) BPSK modulation system, (b) BPSK demodulation system with a realcoefficient equalizer, and (c) BPSK demodulation system with a complexcoefficient equalizer.

[Fig. 6.] Comparison of results obtained using two different types of equalizers: (a) no equalizer, (b) with two realcoefficient equalizers, and (c) with a complexcoefficient equalizer.

[Table 1.] Comparison of results obtained using the QPSK system with two different types of equalizers

[Fig. 7.] Comparison of results using two different types of equalizers: (a) no equalizer, (b) using a realcoefficient equalizer, and (c) using a complexcoefficient equalizer.

[Table 2.] Comparison of results obtained using the BPSK system with two different types of equalizers

[Fig. 8.] Experimental results: (a) original, (b) without the equalizer, (c) with realcoefficient equalizers, and (d) with a complexcoefficient equalizer.