Abstract
Signal to noise ratios (SNRs) are universal metrics for the performance analysis of communication systems. In underwater acoustic orthogonal frequency division multiplexing (OFDM) systems, compared with the time domain input SNR (ISNR), the pilot SNR (PSNR) and effective SNR (ESNR) are demonstrated to be more effective in system performance indication, especially the ESNR. In this paper, for a typical underwater acoustic OFDM system with orthogonal matching pursuit (OMP) based sparse channel estimation, we derive formulas with a closed form for evaluating the ESNR, which avoids the requirement of successful data decoding in conventional ESNR calculation. The derivation is also extended to PSNR easily. We find out that the ESNR is mainly determined by five parameters: the number of deterministic pilots, the number of dominant paths, the inter-carrier interference (ICI), the total channel power and the ISNR; while the PSNR is only determined by the ICI, the total channel power and the ISNR. Simulations and experimental data decoding are carried out to validate the correctness of the theoretical analysis in this paper.
Highlights
Underwater acoustic communication channels are characterized by factors such as: low propagation speed of sound in water, limited bandwidth, plentiful sound reflections and refractions, nonnegligible relative movements between the transmitter and receiver, etc
SIMULATION RESULTS To validate the derivations and analysis in the previous section, simulations of a typical underwater acoustic cyclic prefix (CP)-orthogonal frequency division multiplexing (OFDM) system are carried out, in which equispaced pilots are adopted without loss of generality. 3 channel settings corresponding to the cases of no Doppler effect with fewer and larger number of paths, independent and random Doppler scales in different paths are considered, in order to comprehensively test the performances in different channel conditions
In this paper, the two popular signal to noise ratio (SNR) metrics in OFDM systems, effective SNR (ESNR) and pilot SNR (PSNR) are analyzed based on orthogonal matching pursuit (OMP) channel estimation for a typical underwater acoustic OFDM system
Summary
Underwater acoustic communication channels are characterized by factors such as: low propagation speed of sound in water, limited bandwidth, plentiful sound reflections and refractions, nonnegligible relative movements between the transmitter and receiver, etc. For a multiple-input multipleoutput (MIMO) single carrier underwater acoustic communication system, the bit error rate (BER) along with MSE of the estimated symbols are adopted to measure the performance of the system with different Turbo equalization schemes [10]. In addition to the straightforward time domain input SNR (ISNR), the pilot SNR (PSNR) defined in the frequency domain (after fast Fourier transform (FFT) demodulation) is introduced in [11] Since it is defined as the ratio between the signal power measured on pilot subcarriers and the power on null subcarriers, it captures the ICI in OFDM systems, and it can reflect the level of the Doppler effect. In [14], the ESNR is adopted to represent the long-term statistical information of the channel, and serve as the performance metric in the proposed adaptive orthogonal frequency division multiple access (OFDMA) system for downlink underwater acoustic communications. Notation: An upper- (lower-) case bold letter denotes a matrix (column vector); a[m] denotes the mth element of vector a; A[m, n] denotes the (m, n)th element of matrix A; a{S} denotes the subvector of a containing a’s elements with indices in set S; A{S1,S2} denote the submatrix of A containing A’s rows with indices in set S1 and the columns with indices in set S2; a denotes the l2 norm of vector a; (·)H denotes the Hermitian of (·); (·)+ denotes the pseudo-inverse of (·); CK denotes the set of length K complex column vectors; CK×K denotes the set of size K × K complex matrices
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