Adaptive spatial combining for passive time-reversed communicationsa)
(Color online) Evolution of the ISI metric, quantifying the similarity between the symbol-rate-sampled QF and a discrete impulse, in a simulated environment resembling the conditions of the MREA’04 sea trial (see Fig. 2 ). Results are shown for plain TRM, DDPPC, and two simplified criteria for multichannel combining (MMAG and UMMSE).
(Color online) Site map for the MREA’04 sea trial, conducted off the west coast of Portugal in April 2004. The TR experiment took place in an approximately range-independent area (38.36°N, 9.00°W) with depth and downward-refracting sound-speed profile. The drifting receiver array had eight hydrophones at depths 10, 15, 55, 60, 65, 70, 75, and . The acoustic source was suspended from the NRV Alliance at depths of and towed at up to . Throughout the experiment the source-array range varied from .
(Color online) Evolution of amplitude-normalized estimated channel responses at depth (hydrophone 7) for packet 149 (400 baud). A horizontal slice through any of the plots represents a snapshot of the time-varying response. The coherence time for this channel was estimated to be about . Estimates are based on RLS transversal filtering, four-oversampling, filter order (41, 10) per polyphase component (for order notation see Sec. ??? ), and . (a) Before Doppler compensation, at the carrier frequency of . (b) After broadband Doppler compensation as described in Sec. II A .
(Color online) Estimated Doppler shift at the carrier frequency from packet data and GPS navigation data. GPS-based estimates were obtained by determining the source velocity along the source-receiver direction, calculating the time scaling factor according to Eq. (8) , and plotting . In packet-based estimates was directly obtained from the ratio between received and transmitted packet durations, averaged across all receiver hydrophones.
Estimated input SINR (see Appendix C ) based on channel identification [RLS transversal filtering, four-oversampling, order (21, 7) per polyphase component]. Forgetting factors were varied in the range , and observed MSE values were fitted to theoretical expressions accounting for excess adaptation MSE in RLS to estimate the actual power of interferences (ambient noise and reverberation). Signal power is directly given by the norm of the RLS coefficient vector for the best forgetting factor. SINR estimates are averaged across all receiver hydrophones. Values for 400 baud packets are omitted, as the required filter lengths are outside the valid range of theoretical expressions for excess MSE in RLS.
(Color online) Performance of multichannel decision-feedback equalization using RLS, two-oversampling, eight sensors, . For each packet the lowest MSE obtained in a set of candidate equalizer lengths is shown. In most packets the best equalizer has feedforward and three feedback coefficients (for notation see Sec. ??? ). The short feedback filter length suggests that the equalizer only exploits the arrivals shown in Fig. 3(b) up to .
Time evolution of the plain TRM output (real part) in PKT 155 (200 baud∕2-PSK) using eight hydrophones. Pulse shapes for time reversal were obtained by directly observing the responses to the single pulse (ping) that precedes each packet. Postprocessing for symbol∕phase synchronization and AGC is described in Sec. III C .
(Color online) Performance of plain TRM using eight hydrophones and TRM with postequalization by DFE or FSE. MSE performance is evaluated on a short-term interval . The equalizers use RLS, two-oversampling, . For each packet the lowest MSE obtained in a set of candidate equalizer lengths is shown. In most packets the best DFE has feedforward and 20 feedback coefficients, whereas the best FSE uses mostly coefficients. (a) Observed probes from a single transmitted ping before each packet. (b) Estimated probes by channel identification on a 400-symbol packet preamble. RLS parameters for identification were set as described in Fig. 3 .
(Color online) Impact of probe length on short-term plain TRM performance (eight hydrophones) for three individual packets (PKT 30, 104, 113) using direct probe measurements (obs.) or channel estimation from packet preambles (est.). Lowest MSE values are obtained for truncated probes of about duration, which discard much of the multipath structure shown in Fig. 3 . The trend for other packets (not shown) is similar, and in agreement with the short feedback filter lengths that were found for the equalization results shown in Fig. 6 .
(Color online) Impact of the number of sensors, , selected from top, on the short-term performance of plain TRM and TRM with DFE postequalization [RLS, two-oversampling, (mostly) feedforward and 20 feedback coefficients, ]. Probes estimated from packet preambles. (a) Output MSE, averaged over 200 packets. In this sparse TRM, saturation of MSE for sufficiently large is not yet visible. (b) Average bit error rate. [(c) and (d)] Scatter plots for PKT 155, plain TRM, and 8. [(e) and (f)] Scatter plots for .
(Color online) ISI reduction, on individual packets, of MC algorithms relative to plain TRM using eight hydrophones and estimated probes. Results are shown for MMAG, UMMSE, and DDPPC on short-term intervals , medium-term intervals , and long-term intervals . Larger ISI gains as increases indicate that the algorithms can compensate for some of the degradation in plain TRM due to environment mismatch. (a) Short-term ISI reduction. [(b)–(e)] Scatter plots for PKT 155 in short-term intervals for plain TRM, MMAG, UMMSE, and DDPPC. (f) Medium-term ISI reduction. [(g)–(j)] Scatter plots. (k) Long-term ISI reduction. [(l)–(o)] Scatter plots.
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