In very shallow water, underwater acoustic (UWA) communication channel is influenced by environmental parameters such as multipath, scattering and background noise. Furthermore, the channel is time-varying and a degree of time varying depends on source and receiver motion, sea surface fluctuation, medium property fluctuation, and so on[1,2]. Therefore a received signal shows a delay spread and a Doppler spread. A long delay spread limits available coherent channel bandwidth B_c and increase frequency selectivity. A wide Doppler spread or short coherent time T_c limits a transmitted signaling interval. A delay spread and a Doppler spread are also interpreted as a frequency domain fading and a time domain fading, respectively.

To cope with adverse effects of both spreads on underwater acoustic communication system, frequency and time diversity techniques are adopted in fading multipath channels. These may be viewed as the transmission of the same information either at different frequencies or in different time slots. The separation of the diversity transmissions in frequency by B_c or in time by T_c is basically a form of redundant code in an attempt to break up the error burst and thus to obtain independent errors.

The performance of BFSK has been studied to quantify the bit-error-rate(BER) as a function of a delay spread and a transmission rate for a fixed carrier frequency[3,4].

The frequency diversity technique FH/FSK (fraquency hopping frequency shift keying) for high speed data transmission has adopted to reduce a carrier frequency dependent BER for a given delay spread[5]. The simulation results shows that the proposed FH/FSK can be applied as underwater acoustic communication system without a channel coding.

The time diversity technique such as a convolution code(CC) and Reed-Solomon(RS) code has been applied in underwater acoustic communication systems[6-8]. The error correcting capability of CC is found to be better than RS in frequency non-selective multipath channel but vice versa in frequency selective channel. However, these studies do not consider time variant multipath fading statistics which depends on frequency dependent multipath interference.

In this study, the characteristics of very shallow water multipath fading channel is analyzed and the performances of two different forward error correction (FEC) codes are compared based on multipath channel characteristics. The convolution code (CC) and ReedSolomon (RS) code are adopted.

Fig. 1(a) and 1(b) show typical multipath channels and received signals waveform. Both figures show a signal fading principle due to interference of multipath. In the channel of Fig. 1(a) which depicts a time invariant multipath channel, the received signal is measured as a time variant signal due to a long delay spread or a narrow channel bandwidth with a high speed transmission rate or a wide signal bandwidth. In the channel of Fig. 1(b) which depicts a time variant multipath channel, the received sinusoid signal is also measured as a time variant signal envelope due to a Doppler spread.

For the time invariant of multipath channel such as Fig.1(a), the time invariant channel impulse response h(t) given as

Here, α_n and τ_n are the nth path signal amplitude and delay time. If the coherent channel bandwidth B_c which is given as a function of the effective delay spread τ_eff, is less than the signal bandwidth B_s, a distortion occurs within the signal bandwidth and the signal waveform exhibits a fading as in Fig. 1(a). Therefore each information bearing base band signal has a different signal-to-noise ratio (SNR). The channel in this case is defined as a frequency selective.

In the case of Fig. 1(b), the time variant impulse response h(τ,t) of band pass communication system is given as[9]

The first and second terms show discrete and continuous multipath components, respectively. The α_n(t) is then the multipath signal time variant amplitude which depends on time variant boundary reflection coefficient, propagation path loss, and frequency dependent absorption loss, and τ_n(t) is the nth multipath time variant delay time. β(τ,t) is a continuous multipath time variant amplitude. Therefore received signal amplitude of band pass system will be faded and the statistics of fading signal envelope |h(τ,t)| such as Rayleigh or Rice distribution is related to multipath structure.

The autocorrelation function of h(τ,t) is defined as

where Δ_t is an observation time difference between two different time instanth h(τ,t). If the observation time difference Δ_t is set to be 0, then R_h(τ₁,τ₂;0) becomes a multipath intensity profile (MIP). Fourier transform of the autocorrelation function R_h(τ₁,τ₂;0) gives a channel coherence bandwidth B_c.

In time-varying underwater channel, the signal temporal coherence is used to describe the rate of the signal fluctuation depending on Doppler spread. The higher the signal fluctuation, the faster the temporal coherence decreases with time. Temporal coherence is defined by the correlation of the signals separated by a delay time, normalized by the power of the signal, as given by

where [p^∗()⊗p()]_max means the maximum value of the cross-correlation of the two time series or the convolution of the time-reversed signals (denoted by ^∗) with the other signal[10]. A slowly or fast fading channel is defined by large or small coherence time.

In communication channels, errors can occur independently at random, burst, or in a mixed manner. The forward error correction (FEC) codes scheme has been applied to combat these errors. Without an interleaving, a convolution code(CC) has been known to be effective for a random error correcting but Reed-Solomon to be more effective in correcting burst errors.

The CC is generally specified by three parameters (n, k, m), where n is the number of encoder output bits corresponding to the k information bits and k is the number of bits shifted into the encoder at one time. m is the constraint length or the number of input data bits that the current output is dependent upon. As shown in Fig. 1, the number of output bits (n=2) is twice that of input bits (k=1) and the constraint length is 3 corresponding to two shift registers plus one input.

The RS code (n, k, t) is a non-binary cyclic code and known to be capable of correcting errors which appear in burst. n, k, and t are the block code length, message length, and error correcting symbols, respectively. n-k and t=(n-k)/2 are the measure of redundancy in the block and the number of correctable symbols, respectively.

In this study, QPSK/CC (2,1,3) and QPSK/RS (7,3,2), which give similar redundancies of 2 and 2.2, are applied to compare error correction performance.

Fig.2 shows schematic diagram of sea experimental configuration in very shallow multipath channel environment. The experiments were conducted in the bay of the Geo-je Island. The experimental parameters are shown in Table 1. The depth is about 15.7 m, the effective height of sea surface is about 0.1 to 0.3 m and bottom sediment is mud. The distance between the source (ITC 1001) and receiver (B&K 8106) are set to be about 100 and 400 m for a range difference effect. Transmitter and receiver are positioned asymmetrically in a middle layer to get a large time delay difference between multi-paths as possible. The depth of source and receiver are 10 and 7 m, respectively.

Fig. 3(a) is sound velocity profile (SVP) analyzed by the conductivity, temperature, and depth. In Fig. 3(b), the numerical value of each eigenray means grazing angle with respect to sea surface plane and only the first five arrivals which could show high signal amplitude are shown.

Fig. 4 shows a transmission frame structure for 1 second, which is composed of a synchronization signal and information signal. The pseudo noise (PN) signal of modulated by 16 kHz (128 bit) is used for frame synchronization. The bandwidth of PN signal is 13 to 19 kHz. Before data transmission in each source to receiver range, 30s of PN signal is transmitted to measure the channel impulse response, temporal coherence and fading statistics of channel.

Fig. 5(a) and 5(b) show multipath intensity profiles for 100 and 400 m, respectively. By using the relation between multipath intensity profile or delay spread and channel coherent bandwidth, -3 dB coherent bandwidths of 100, and 400 m are found to be 60 and 200 Hz, respectively.

Fig. 6(a) and 6(b) shows power spectrum of received PN signal. There are dips and maxima which show destructive and constructive interference frequencies in PN signal bandwidth.

Fig. 7 shows fading statistics of 100 and 400 m at carrier frequency of 16 kHz with 100 Hz bandwidth. The fading statistics of 100 and 400 m follow Rayleigh and Rice distribution, respectively. By considering the dips in Fig. 6(a) for 100 m range, since a destructive interference appears at 16 kHz and so there is not any dominant component in this frequency band, the first term in eqn. (2) is ignored and the channel statistics will be Rayleigh distribution. However, in Fig. 6(b) for 400 m range, since 16 kHz locates in a constructive interference range and so the first term in eqn. (2) can not be ignored, the channel statistics will be Rice distribution.

Fig. 8 shows temporal coherence distributions for 100 and 400m ranges using eqn. (4).

The temporal coherence of 100 m drops to 0.88 in about 0.5 s but the temporal coherence of 400 m shows about 0.96. It is clear that Doppler spread of both ranges are less than 1 Hz by the formula given in previous study.

Temporal coherence variation with time seems to mimic well the surface fluctuation. The variation magnitude of 100 m range is larger than that of 400 m since relative motion of sea surface at 100 m range is greater than that of 400 m range.

Table 2 shows the results for performances of RS and CC at 100 m range and three different symbol rates (100, 200 and 400 symbol per second (sps)). Signal bandwidth of each symbol rate is larger than channel coherent bandwidth of 60 Hz. Probability density is Rayleigh distribution as shown in Fig. 7(a). All the BERs of RS is less than that of CC.

Table 3 shows results for performances of RS and CC at 400 m range. The channel coherent bandwidth and probability density are 200 Hz and Rice distribution, respectively. Only the signal bandwidth of 100 sps is less than channel coherent bandwidth of 200 Hz. In this case the BER of CC is less than that of RS. This result confirms that authors’ previous water tank experiment result which shows that error correcting capability of RS is worse than CC in frequency non- selective channel but RS is better than CC in frequency selective channel[8].

Comparing BERs of Table 2 for 100 m and Table 3 for 400 m range, All the BERs at the same transmission conditions of former are larger than those of latter. This is due to the fact that the SNR of 100 m is less than that of 400 m range, since the fading statistics of 100 and 400 m are approximated as Rayleigh and Rice distribution, respectively.

Error correction codes of CC and RS are adopted in very shallow water channel and their performances are evaluated based on the multipath channel characteristics. At two different source-receiver ranges of 100 and 400 m, their coherent bandwidths, multipath interference magnitudes as a function of frequency, fading statistics and temporal coherence are analyzed. The sea experiment results show that RS code has better performance than CC in frequency selective channel. In frequency non-selective channel, CC performance is better than that of RS. Both CC and RS shows better performance in Rice fading than Rayleigh fading channel.

In conclusion, RS code is found to be a better choice than CC since errors occur as bursts in very shallow water frequency selective fading channel. Since fading statistics depends on both range and frequency its effect on UWA communication system remains in future work.