Performance Comparison of Overlap FDE Techniques In Underwater Communication Sohaib Kiani1, Sobia Baig2, Shoaib Ali1, Shahid Ali1
1Centres of Excellence in Science and Applied Technologies (CESAT), Islamabad, Pakistan 2 GIK Institute of Engineering Sciences and TechnologyTopi, Swabi, Pakistan
[email protected],
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[email protected] Abstract—The underwater channel being a multipath channel undergoes frequency selective fading. Equalization techniques both in time domain and frequency domain are used to suppress the effects of reverberations at the receiver. However, time domain techniques have higher complexity. Frequency domain Equalization involves the use of cyclic prefix in between the guard intervals. This makes the channel matrix circular for which simple frequency domain equalization techniques could be used. For Wavelet Packet based multi carrier modulated system FDE cannot be applied due to the absence of guard intervals. Therefore overlap FDE has been used for multicarrier modulation systems. Equalization weights are calculated using the Zero forcing and MMSE algorithms. In this paper the performance of two algorithms has been compared for multicarrier modulation systems for underwater acoustic communication channel. Index Terms—Multi-Carrier Modulation, Code Division Multiple Access, Frequency Domain Equalization, MMSE, Zero Forcing, Underwater acoustic communication.
I. INTRODUCTION Underwater Acoustic Channel suffers from multipath fading due to time varying nature of the channel. Due to which the multipath nature of the channel acoustic signals travel in oceanic waveguides resulting in reverberations at the receiver. Research is being carried out for developing high data rate underwater acoustic communication over long distances using Multi Carrier Modulation (MCM) techniques [11]. MCM systems take the advantage of reducing Intersymbol interference by using several sub band carriers. However due to frequency selective nature of the channel, equalization techniques are required to mitigate multipath channel impairment. Applications of MCM include communication between autonomous underwater vehicles and underwater acoustic networks. In conventional MCM system Fourier basis are used. A major drawback of using Fast Fourier Transform (FFT) is the reduction of spectral efficiency due to cyclic prefix (CP) insertion, in order to mitigate Inter Symbol Interference (ISI) due to multipath channel. Moreover, rectangular shape window in time domain gives high side lobes subcarriers, which makes system sensitive to Inter Carrier Interference (ICI) and frequency offset error. To overcome these problems Wavelet based MCM technique has been proposed in literature for OFDM and MC-CDMA [1]. Wavelet Packet
(WP) based system ensures high spectral containment in its subcarriers, thus gives very low side lobes. WP based systems are spectrally efficient because no CP is needed to avoid ISI [2]. Several other objectives motivate the current research on WPM [3]. Conventional DFT based MCM systems give high performance due to frequency diversity through Minimum Mean Square Error (MMSE) Frequency Domain Equalization (FDE) technique [4]. Simple FDE technique cannot be used for Wavelet Packet based MCM due to the absence of CP. Already proposed Rake combiner for Wavelet Packet MCCDMA give high performance by achieving time diversity but it is not suitable for downlink transmitter [1]. This is due to the fact that Rake Combiner increase hardware cost. Moreover, its number of branches increases with the number of multipath in the channel [5]. To overcome these problems Overlap FDE technique is proposed for WP OFDM and WP-MC-CDMA, ensuring high system performance through frequency diversity. In the absence of Guard Interval (GI) containing CP, ISI is present around the start of symbol block. The residual ISI after FDE is given by the circular convolution of FDE impulse response as shown in Fig. 1 and symbol block, which gives ISI at both corners of symbol block [6]. In overlap FDE FFT window size has been increased to integral multiples of number of subcarriers (Nc) and after equalization only central part would be captured for demodulation. WP-MC-CDMA Bit Error Rate (BER) performance increases with an increase in Spreading Factor (SF) due to
Fig. 1. Impulse Response for Zero-Forcing Frequency Domain Equalization
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high frequency diversity gain through Overlap MMSE-FDE technique [5]. In this paper, in order to calculate the FDE weights, Zero Forcing (ZF) and MMSE have been used and their BER performance comparison would be given with reference to Spreading Factor (SF). ZF technique completely removes ISI, which gives no Inter Code Interference due to frequency selectivity of the channel. However frequency diversity gain in this case is zero [7]. In MMSE technique Inter Code Interference is still present but its gives better performance due to frequency diversity gain. The organization of this paper is as follows. Section II is about WP based MCM transmitter. In section III Overlap FDE technique would be explained. Section IV would give description about received signal and its equalization. Simulation results would be shown and compared in section V. Section VI would be the conclusion of this paper. II. WAVELET MCM TRANSMITTER The transmitter structure for WP-MC CDMA system is shown in Fig. 2. In this transmitter design a block of N user symbols are first converted from serial to parallel through (S/P) to decrease symbol rate by a factor of 1/N. Then the parallel blocks of symbols are spread individually by the same spreading code assigned to the user. The spread chips are then serially converted through (P/S) and then modulated to different subcarriers Nc through an Inverse Discrete Wavelet Packet Transform (IDWPT) block. This modulation mapping is equivalent to the Inverse Fast Fourier Transform (IFFT) block in the conventional sinusoid waveform based multicarrier system. Frequency domain diversity is achieved by transmitting same symbol on multiple carriers. The exact structure of the IDWPT depends on the selected wavelet packet tree. In order to achieve better performance in different situations, different wavelet packet tree structures can be used, as discussed by [6] and [8]. In order to cancel the effect of time-dispersive multipath channel, WP-MC-CDMA requires a simple equalization technique. Cyclic Prefixing in conventional MC-CDMA ensures the formation of a circulant channel matrix, which enables the application of simple FDE. Overlap FDE is proposed based on zero forcing (ZF) and Minimum Mean Square Error (MMSE) algorithm for equalization of WP-MCCDMA systems.
Fig. 2. Wavelet Packet MCM Transmitter
blocks are taken, due to which the residual IBI would be present around the corners of 2Nc-point FFT block. To suppress IBI, central Nc sample points are extracted from the equalized output in order to recover the desired signal as shown in Figure 2. The signal is transmitted over L-path frequency selective fading channel. The complex valued path gain and time delay of L-propagation path are denoted by hl and τl respectively. The received signal is converted into frequency domain for Overlap FDE. For Performing FDE, the desired signal block needs to be expressed as a circular convolution between the channel impulse response and the transmitted signal block. Since CP cannot be inserted, the IBI appears. So 2Nc-point FFT is applied to decompose the received signal block for the reception of the mth WOFDM signal. rm(t) is given as [8], L −1
rm (t ) = ∑ ht ym ((t − l ) mod 2 N c ) + ρ m (t ) + nm (t ) (1) l =0
where ym(t) is the transmitted signal block of 2Nc samples.
ρm (t ) is the IBI, and ηm (t ) is additive white Gaussian noise
(AWGN) with zero mean and variance 2 N o / To with N0 being single sided power spectrum density. ym(t) is given as [8] ⎧ 1 ⎛ Nc ⎞ , t = 0 ~ Nc − 1 ⎪ sm −1 ⎜ t + ⎟ 2 ⎠ 2 ⎝ ⎪ ⎪⎪ N 3 ⎛ N ⎞ ym (t ) = ⎨ sm ⎜ t − c ⎟ , t = c ~ Nc − 1 2 2 2 ⎝ ⎠ ⎪ ⎪ 3 ⎛ 3 ⎞ ⎪ sm +1 ⎜ t − N c ⎟ , t = N c ~ 2 N c − 1 2 ⎝ 2 ⎠ ⎩⎪
III. OVERLAP FDE For FDE, received signal has to be first converted into frequency domain and then each frequency component is multiplied with its corresponding equalizer weights. In the case of WP-MC-CDMA channel matrix is not circular as there is no CP, so there would be Inter Block Interference (IBI) present only around the beginning of the received signal block. The residual IBI after MMSE-FDE is given by the circular convolution between IBI and MMSE-FDE filter impulse response [6]. Impulse response of Zero Forcing (ZF) FDE is shown in Figure 1. After FDE IBI would be localized near both ends of Nc-point FFT block [6]. To eliminate the residual IBI, Overlap FDE is used. In Overlap FDE 2Nc-point FFT
(2)
As shown in Fig. 3 2Nc-point FFT is applied to decompose the received signal rm(t) into 2Nc frequency components [6], ⎛ 1 2 N −1 t ⎞ Rm ( q ) = ∑ rm (t ) exp ⎜ − j 2π q 2 N ⎟ (3) 2 N c t =0 c ⎠ ⎝ c
= H ( q )Ym ( q ) + Π m ( q ) where
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Fig. 3. Wavelet Packet MCM Receiver with overlap Frequency Domain Equalization
H (q) =
2 N c −1
l
t =0
1 Ym (q ) = 2 Nc
2 N c −1
τl ⎞
⎝
c
∑ t =0
2 N c −1
1 2 Nc
2 N c −1
∑ t =0
⎛ t ⎞ ρ m (t ) exp ⎜ − j 2π q ⎟ 2 Nc ⎠ ⎝
∑η t =0
⎟ ⎠
⎛ t ⎞ ym (t ) exp ⎜ − j 2π q ⎟ 2Nc ⎠ ⎝
1 N m (q) = 2Nc Π m (q) =
⎛
∑ h exp ⎜ − j 2π k 2 N
m
(4)
⎛ t ⎞ (t ) exp ⎜ − j 2π q ⎟ 2 Nc ⎠ ⎝
The received signal in frequency domain Rm(q) is multiplied by the FDE weight w(q) as
ˆ (q) + Nˆ (q) (5) Rˆm (q) = ω (q) Rm (q) = Hˆ (q)Ym (q) + Π m m where FDE weights are calculated through zero forcing (ZF) and MMSE [10],
TABLE I SIMULATION PARAMETERS Parameters WP-OFDM WP-MC-CDMA Modulation Scheme QPSK Sampling Frequency Fs 256 KHz No. of SubCarriers Nc 256 Guard Interval Ng Guard Interval Length Tg Spreading Factor 1 16 Coding Sequence Pseudo Random 16-path Frequency Selective Fading Channel with AWGN Equalization Technique Overlap FDE Overlap FDE FDE Block Size 512 512 FDE Weights ZF,MMSE Channel Estimation Ideal
⎧ H * (q ) ⎪ 2 H (q ) ⎪ ω (q ) = ⎨ H * (q ) ⎪ 2 ⎪ H ( q ) + ( E / N ) −1 s o ⎩
ZF
(6) MMSE
After FDE, 2Nc-point IFFT is applied to to obtain the time domain signal for demodulation. rˆm ( t ) =
2 N c −1
∑
q=0
⎛ t ⎞ Rˆ m ( q ) exp ⎜ j 2π q ⎟ N 2 ⎝ c ⎠
(7)
IV. SIMULATION RESULTS Comparison between ZF and MMSE techniques is shown in Fig 4. Both techniques have been applied to WP-OFDM using Overlap FDE. Results shows slight performance degrade of 2 dB in ZF case as compare to MMSE at 5E-3, due to the fact that ZF enhance AWGN noise. Error floor comes for ZF technique at 17db and for MMSE at 19 dB Eb/No. BER comparison between ZF and MMSE scheme for using WP-MC-CDMA and QPSK is shown in Fig. 5. It can be observed from simulation results that MMSE based system outperforms by 13 dB as compared to ZF based system at 1E3 BER. MMSE-FDE can give large frequency diversity, however it provide high ICI due to high frequency selectivity
Fig. 4. BER performance for WP OFDM using ZF and MMSE for Equalization
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[10] Fumiyuki Adachi, Deepshikha Garg, Shinsuke Takaoka, and Kazauki Takeda "Orthogonal Multi-Carrier DS-CDMA with Frequency Domain Equalization", IEICE Transaction Communications, April 2008 [11] Xiaodong Zhang; Guangguo Bi, "Design of OFDM Systems for High Speed Unerwater Communication", Personal Indoor and Mobile Radio Communications, 12th IEEE International Conference on Computational Science and Engineering, 2009.
Fig. 5. BER performance for MC CDMA using ZF and MMSE for Equalization
[9]. ZF-FDE produces no ICI but give no frequency diversity either. V. CONCLUSION In the proposed scheme frequency diversity in Wavelet Packet based MCM systems is exploited using overlap FDE. In Wavelet Packet based system waveforms are well localized in time and frequency which makes them more robust against ISI and ICI. Wavelet Packet also gives better performance for MCM systems as compare to DFT based systems. Overlap FDE for Wavelet systems has low complexity as compared to TDE. From simulation results it is also observed that MMSE always perform better than ZF. Moreover, performance of MMSE based equalization techniques increases as the spreading factor is increased. Channel estimation proposed is considered to be ideal and can be done for time varying channel. REFERENCES [1]
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