Data transmission via multi-path channels using orthogonal multi-frequency signals with differential phase shift keying modulation

Abstract

A method and an apparatus relating to an OFDM data communications system where the sub-carriers are modulated using differential quadrature phase-shift keying (DQPSK). The multi-carrier transmitted signal is directly generated by means of summation of pre-computed sample points. As part of the multi-carrier signal generation, a signal for the guard interval is established. In an acoustic application of this approach, direct radiation of the sub-carrier approach is facilitated. Symbol synchronization in the receiver is based on signal correlation with the missed sub-carrier. Separation of the sub-carriers in the receiver by means of correlation of the received signal and reference signals that are derived from a table of pre-computed values. Optimal non-coherent processing of the sub-carriers without any phase tracking procedures is achieved.

Claims

1. A data communications system, for use over a multi-path channel, comprising: an orthogonal frequency division multiplexing (OFDM) sub-carrier signal generator that outputs a plurality of OFDM sub-carrier signals; a differential quadrature phase shift keying (DQPSK) modulator that modulates each OFDM sub-carrier signal of the plurality of OFDM sub-carrier signals in response to input data, and forms a plurality of modulated OFDM sub-carrier signals in response to the input data; a summer that combines the plurality of modulated OFDM sub-carrier signals to form a transmitted signal; a receiver to output a received signal in response to the transmitted signal transmitted through the multi-path channel, the received signal having a missing sub-carrier signal at a center frequency located in the middle of a frequency spectrum of the received signal, the missing sub-carrier signal having zero amplitude; an OFDM sub-carrier reference generator that outputs a plurality of OFDM sub-carrier reference signals, the plurality of OFDM sub-carrier reference signals including an OFDM sub-carrier reference signal located at the center frequency; a non-coherent synchronizer that synchronizes an OFDM symbol interval to a demodulating interval by nulling a correlation between the received signal and the OFDM sub-carrier reference signal located at the center frequency; and a demodulator, using a DQPSK multi-carrier detector, that demodulates the received signal to form an output signal.

2. The data communications system of claim 1, wherein the OFDM sub-carrier signal generator uses pre-computed sample points.

3. The data communications system of claim 1, wherein the synchronizer nulls the correlation between the received signal and the OFDM sub-carrier reference signals OFDM sub-carrier reference signal located at the center frequency by shifting a synchronization pulse based on a comparison of respective correlations of an advanced time interval and a delayed time interval.

4. The data communications system of claim 1, wherein the transmitted signal is an acoustical signal.

5. The data communications system of claim 1, wherein the demodulator does not use a phase tracking approach.

6. The data communications system of claim 1, wherein the DQPSK modulator comprises a decimal transformation device, a modulo-4 summation device, and a switch controller device.

7. The data communications system of claim 1, wherein the demodulator comprises a correlation device, a transformation device, and a decision device.

8. The data communications system of claim 1, wherein the synchronizer nulls the correlation between the received signal and the OFDM sub-carrier reference signal located at the center frequency by locating a timeframe that minimizes a length of a vector formed by correlating the received signal and the OFDM sub-carrier reference signal located at the center frequency.

9. A data receiver, for use over a multi-path channel, comprising: a receiver to output a received signal in response to a transmitted signal transmitted through the multi-path channel, the received signal having a missing sub-carrier signal at a center frequency located in the middle of a frequency spectrum of the received signal, the missing sub-carrier signal having zero amplitude; an orthogonal frequency division multiplexing (OFDM) sub-carrier reference generator that outputs a plurality of OFDM sub-carrier reference signals, the plurality of OFDM sub-carrier reference signals including an OFDM sub-carrier reference signal located at the center frequency; a non-coherent synchronizer that synchronizes an OFDM symbol interval to a demodulating interval by nulling a correlation between the received signal and the OFDM sub-carrier reference signal located at the center frequency; and a demodulator, using a differential quadrature phase shift keying (DQPSK) multi-carrier detector, that demodulates the received signal to form an output signal.

10. The data receiver of claim 9, wherein the synchronizer nulls the correlation between the received signal and the OFDM sub-carrier reference signal located at the center frequency by locating a timeframe that minimizes a length of a vector formed by correlating the received signal and the OFDM sub-carrier reference signal located at the center frequency.

11. The data receiver of claim 9, wherein the demodulator does not use a phase tracking approach.

12. The data receiver of claim 9, wherein the demodulator comprises a correlation device, a transformation device, and a decision device.

13. The data receiver of claim 9, wherein the synchronizer nulls the correlation between the received signal and the OFDM sub-carrier reference signal located at the center frequency by shifting a synchronization pulse based on a comparison of respective correlations of an advanced time interval and a delayed time interval.

14. A method for data communications, comprising: receiving a received signal via a channel, the received signal having a missing sub-carrier signal at a center frequency located in the middle of a frequency spectrum of the received signal, the missing sub-carrier signal having zero amplitude; generating a plurality of orthogonal frequency division multiplexing (OFDM) sub-carrier reference signals, the plurality of OFDM sub-carrier reference signals including an OFDM sub-carrier reference signal located at the center frequency; non-coherently synchronizing an OFDM symbol interval and a demodulating interval by nulling a correlation between the received signal and the OFDM sub-carrier reference signal located at the center frequency; and demodulating, using a DQPSK multi-carrier detector, the received signal to form an output signal, wherein the generating, synchronizing and demodulating are performed by one or more circuits.

15. The method of claim 14, wherein the synchronizing by nulling the correlation between the received signal and the OFDM sub-carrier reference signal located at the center frequency includes locating a timeframe that minimizes a length of a vector formed by correlating the received signal and the OFDM sub-carrier reference signal located at the center frequency.

16. The method of claim 14, wherein the generating the plurality of OFDM sub-carrier reference signals uses pre-computed sample points.

17. The method of claim 14, wherein the synchronizing by nulling the correlation between the received signal and the OFDM sub-carrier reference signal located at the center frequency includes shifting a synchronization pulse based on a comparison of respective correlations of an advanced time interval and a delayed time interval.

18. The method of claim 14, wherein the transmitted signal is an acoustical signal.

Description

BRIEF DESCRIPTION OF THE DRAWINGS/FIGURES

(1) The accompanying drawings, which are incorporated herein and form a part of the specification, illustrate the present invention, and together with the description, further serve to explain the principles of the invention and to enable a person skilled in the pertinent art to make and use the invention.

(2) FIG. 1 is a high-level block-diagram of a data transmission system operating in a multi-path channel.

(3) FIG. 2 is an example of an OFDM signal in the frequency domain.

(4) FIG. 3 is an example of an OFDM signal in the time domain.

(5) FIG. 4 is an example of DQPSK signals in the phase plane.

(6) FIG. 5 is an example of an OFDM-DQPSK transmitter, according to an embodiment of the present invention.

(7) FIG. 6 is an example of a DQPSK encoder/modulator for an OFDM sub-carrier, according to an embodiment of the present invention.

(8) FIG. 7 is an example of a digital version of an OFDM-DQPSK transmitter, according to an embodiment of the present invention.

(9) FIG. 8 is an example of an OFDM-DQPSK receiver, according to an embodiment of the present invention.

(10) FIG. 9 is an example of a DQPSK detector for an OFDM sub-carrier, according to an embodiment of the present invention.

(11) FIG. 10 is an example of an OFDM acoustical signal in the time domain, according to an embodiment of the present invention.

(12) FIG. 11 is a flowchart diagram that illustrates a method for data transmission through a multi-path channel, according to an embodiment of the present invention.

(13) The present invention will now be described with reference to the accompanying drawings. In the drawings, like reference numbers indicate identical or functionally similar elements. Additionally, the left-most digit(s) of a reference number identifies the drawing in which the reference number first appears.

DETAILED DESCRIPTION OF THE INVENTION

(14) Methods and apparatus for data communications systems are described. Furthermore, methods and apparatus for a data communications system in an acoustic environment are also described. The present specification discloses one or more embodiments that incorporate the features of the invention. The disclosed embodiment(s) merely exemplify the invention. The scope of the invention is not limited to the disclosed embodiment(s). The invention is defined by the claims appended hereto.

(15) References in the specification to “one embodiment,” “an embodiment,” “an example embodiment,” etc., indicate that the embodiment described may include a particular feature, structure, or characteristic, but every embodiment may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with an embodiment, it is submitted that it is within the knowledge of one skilled in the art to effect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described.

(16) Furthermore, it should be understood that spatial descriptions (e.g., “above,” “below,” “up,” “left,” “right,” “down,” “top,” “bottom,” “vertical,” “horizontal,” etc.) used herein are for purposes of illustration only, and that practical implementations of the structures described herein can be spatially arranged in any orientation or manner. Likewise, particular bit values of “0” or “1” (and representative voltage values) are used in illustrative examples provided herein to represent data for purposes of illustration only. Data described herein can be represented by either bit value (and by alternative voltage values), and embodiments described herein can be configured to operate on either bit value (and any representative voltage value), as would be understood by persons skilled in the relevant art(s).

(17) The example embodiments described herein are provided for illustrative purposes, and are not limiting. Further structural and operational embodiments, including modifications/alterations, will become apparent to persons skilled in the relevant art(s) from the teachings herein.

(18) FIG. 1 shows a high-level block diagram of a data transmission system 100, operating over a channel 130 with multi-path interference. Input data from a data source 110 is input to the transmitter 120, which broadcasts over the channel 130. The transmitted power is subsequently received by the receiver 140, and is then output as the received data 150.

(19) To overcome the deleterious effects of multi-path effects, modern data communications systems utilize the OFDM (orthogonal frequency divisional multiplexing) carrier approach, which utilizes a multi-carrier signal containing orthogonal sub-carriers. FIG. 2 shows an example of an OFDM signal 200 in the frequency domain. A total of 17 equally-spaced sub-carriers 210A through 210Q are shown in this example. FIG. 3 shows an example of an OFDM signal 300 in the time domain. In OFDM modulation schemes, multiple sub-carriers are each modulated with a conventional modulation scheme, such as, for example, QAM, at a low symbol rate. Guard intervals are provided between intervals of information (active interval). An OFDM symbol interval 310 is defined herein as including two sub-intervals, namely the guard interval 320 and the active interval 330.

(20) Mathematically, an OFDM signal can be represented in the time domain as follows:

(21) $\begin{array}{cc}S\left(t\right)=\underset{k=1}{\overset{K}{.Math.}}{A}_k\sin \left[\left({\omega }_0+k*2\pi /T_a\right)t+{\Phi }_k\right],& \left(1\right)\end{array}$
where A.sub.k and Φ.sub.k are the amplitude and phase of the k-th sub-carrier, T.sub.a is an interval of sub-carrier orthogonality (active interval), and K is the number of sub-carriers.

(22) Many conventional OFDM-based data communications systems utilize the Quadrature Phase Shift Keying (QPSK) encoding technique. In this technique, the transmitter encodes data onto a high frequency carrier by quadrature modulation. However, in order to generate the set of orthogonal sub-carriers in the transmitter, this technique uses inverse Fast Fourier Transforms (IFFTs). Such transforms are comparatively complex computations since they require significant real time arithmetic operations with complex numbers. Moreover, the guard interval is generated by using a cycle prefix, which is also based on the above IFFT results. Within a QPSK-based OFDM receiver, separation of the sub-carrier signals requires the use of a Fast Fourier Transform (FFT), which as noted above, are comparatively complex computational algorithms. Moreover, signal detection in the receiver requires the use of coherent processing and the associated additional circuit complexity of special pilot signals or complex phase tracking. In addition, symbol synchronization in the receiver is based on preamble pulses and pilot signals, which in turn increases the required circuit complexity.

(23) In various embodiments of this invention, the use of a DQPSK encoding technique overcomes many of the circuit complexity and computational demands required under the QPSK technique. Specifically, the QPSK need for a pilot signal as a coherent reference is eliminated in a DQPSK receiver. Moreover, the set of transmitted orthogonal sub-carriers is directly (and therefore more simply) generated by means of summation of a pre-calculated table of samples, rather than from real time computations. No carrier modulation circuitry is required since the sum of the generated sub-carriers is fed to the output transmitter. In addition, the guard band is automatically established during the generation of the multi-carrier signal. Within the receiver, separation of the sub-carrier signals is simplified by using a direct correlation of the received signal and reference signals that are derived from an apriori computed set of values. In a further simplification of the computational requirements, the guard interval is not used in the correlation procedure in this DQPSK approach. Moreover, the signal detection in the receiver is invariant to the initial phases of the sub-carriers, and is non-coherent (does not require a pilot signal). Further, the symbol synchronization is straightforward since it is based on correlation with the missed sub-carrier.

(24) FIG. 4 illustrates an example of a DQPSK signal 400 in the phase plane. A total of four symbols are available, namely symbol “00” (410), symbol “01” (420), symbol “10” (430), and symbol “11” (440). The symbols are encoded by transmitted dibits according to Gray code, as shown below in Table 1.

(25) TABLE-US-00001 TABLE 1 Decimal Dibit Phase difference presentation transmitted transmitted ΔΦ cosΔΦ sinΔΦ 0 00 0 1 0 1 01  π/2 0 1 2 10 3π/2 0 −1 3 11 II −1 0

(26) FIG. 5 illustrates the architecture of the OFDM-DQPSK transmitter 500, according to an embodiment of this invention. Data source 510 inputs data to data buffer 520, which accumulates data for the current OFDM symbol. For example, in an OFDM-DQPSK system using 16 sub-carriers, the data buffer 520 accumulates 32 bits (4 bytes) of data, and is combined into 16 dibits (one dibit for each sub-carrier). The dibits from data buffer 520 are differentially encoded, and the encoded dibits are input to the multiple DQPSK encoder/modulator 530, where each encoded dibit modulates the corresponding sub-carrier. Also input to the multiple DQPSK encoder/modulator 530 are the sub-carriers which are generated in the OFDM sub-carrier generator 540. The modulated sub-carriers are summed in the summer 550 for input to an optional output stage 560 prior to transmission. Such an optional output stage 560 may include functionality such as frequency upconversion, a transducer, etc., depending on the application.

(27) FIG. 6 illustrates the architecture of a DQPSK encoder/modulator 600 for each sub-carrier within an OFDM system, according to an embodiment of this invention. Note that there are a total of K DQPSK encoder/modulators 600 within each multiple DQPSK encoder/modulator 530, where K is the number of sub-carriers. The encoder/modulator 600 is composed of two sub-blocks, namely the DQPSK Encoder 610 and the DQPSK Modulator 620. Output from the data buffer 520 consists of Dibits (i.e. the symbols 00, 01, 10, 11) that are input to the Transform Function 630, that transforms the input data into decimal numbers, for example, to the numbers 0, 1, 2, 3, as shown in the first two columns of Table 1. After this transformation, the decimal number is summed, modulo 4, (640), with a number that was transmitted during the previous OFDM symbol and saved by delay element T (650).

(28) The output of the DQPSK encoder 610 serves as a control signal 655 for the DQPSK modulator 620. The control signal 655 controls a Logic Switch 660 in such a way that the output of the Logic Switch 660 is one of 4 sub-carrier variants ±sinkωt, ±coskωt according to the following modulation shown in Table 2.

(29) TABLE-US-00002 TABLE 2 Output of the Output of the DQPSK DQPSK Phase difference Encoder Modulator transmitted ΔΦ 0  sin (k*2π/T.sub.a)t 0 1 .sup. cos (k*2π/T.sub.a)t  π/2 2 −cos (k*2π/T.sub.a)t.sup.  3π/2 3 −sin (k*2π/T.sub.a)t π

(30) All DQPSK encoding operations (decimal transformation, modulo 4 summation, and switch controlling) are performed once per OFDM symbol. Thus, during the OFDM symbol interval, the chosen sub-carrier variant is transmitted without any changes.

(31) FIG. 7 illustrates a digital implementation of the OFDM-DQPSK transmitter, according to an embodiment of this invention. Comparing with the general block-diagram in FIG. 5, this transmitter has two different elements: a digital table of sub-carrier samples 710, and a digital-to-analog converter 720. In this case, the sub-carriers are generated by means of reading the table 710, which stores functions sin (k*2π/T.sub.a)t and cos (k*2π/T.sub.a)t in digital form. The table 710 contains K columns, where K is the number of sub-carriers, and rows, sufficient to represent at least one period of each sub-carrier. An example of such a table 710 is shown in Table 3 below. The table contains 13 columns for 13 sub-carriers and the first 26 rows of samples for those sub-carriers.

(32) TABLE-US-00003 TABLE 3 1. 0 0 0 0 0 0 0 0 0 0 0 0 0 2. 0.1254 0.1266 0.1279 0.1291 0.1303 0.1315 0.1327 0.1340 0.1352 0.1364 0.1376 0.1387 0.1399 3. 0.2170 0.2184 0.2198 0.2211 0.2224 0.2237 0.2250 0.2262 0.2274 0.2286 0.2297 0.2308 0.2319 4. 0.2500 0.2499 0.2498 0.2496 0.2493 0.2490 0.2485 0.2480 0.2475 0.2468 0.2461 0.2453 0.2444 5. 0.2155 0.2126 0.2095 0.2064 0.2031 0.1997 0.1962 0.1926 0.1889 0.1851 0.1813 0.1773 0.1732 6. 0.1229 0.1167 0.1103 0.1039 0.0973 0.0907 0.0840 0.0773 0.0704 0.0636 0.0566 0.0496 0.0426 7. −0.0029 −0.0114 −0.0200 −0.0285 −0.0370 −0.0454 −0.0538 −0.0622 −0.0704 −0.0786 −0.0867 −0.0947 −0.1026 8. −0.1279 −0.1364 −0.1446 −0.1527 −0.1605 −0.1680 −0.1753 −0.1822 −0.1889 −0.1953 −0.2014 −0.2072 −0.2126 9. −0.2184 −0.2237 −0.2286 −0.2330 −0.2369 −0.2403 −0.2432 −0.2456 −0.2475 −0.2488 −0.2497 −0.2500 −0.2498 10. −0.2500 −0.2494 −0.2482 −0.2463 −0.2438 −0.2407 −0.2369 −0.2324 −0.2274 −0.2218 −0.2155 −0.2088 −0.2014 11. −0.2141 −0.2064 −0.1980 −0.1889 −0.1793 −0.1690 −0.1583 −0.1469 −0.1352 −0.1229 −0.1103 −0.0973 −0.0840 12. −0.1204 −0.1064 −0.0920 −0.0773 −0.0622 −0.0468 −0.0313 −0.0157 −0.0000 0.0157 0.0313 0.0468 0.0622 13. 0.0057 0.0228 0.0398 0.0566 0.0732 0.0894 0.1052 0.1204 0.1352 0.1492 0.1626 0.1753 0.1871 14. 0.1303 0.1458 0.1605 0.1742 0.1871 0.1988 0.2095 0.2191 0.2274 0.2345 0.2403 0.2447 0.2478 15. 0.2198 0.2286 0.2359 0.2418 0.2461 0.2488 0.2500 0.2495 0.2475 0.2438 0.2386 0.2319 0.2237 16. 0.2499 0.2484 0.2450 0.2399 0.2330 0.2243 0.2141 0.2023 0.1889 0.1742 0.1583 0.1411 0.1229 17. 0.2126 0.1997 0.1851 0.1690 0.1515 0.1327 0.1129 0.0920 0.0704 0.0482 0.0257 0.0029 −0.0200 18. 0.1179 0.0960 0.0732 0.0496 0.0257 0.0014 −0.0228 −0.0468 −0.0704 −0.0934 −0.1154 −0.1364 −0.1560 19. −0.0086 −0.0342 −0.0594 −0.0840 −0.1077 −0.1303 −0.1515 −0.1711 −0.1889 −0.2047 −0.2184 −0.2297 −0.2386 20. −0.1327 −0.1549 −0.1753 −0.1935 −0.2095 −0.2231 −0.2340 −0.2421 −0.2475 −0.2499 −0.2493 −0.2458 −0.2395 21. −0.2211 −0.2330 −0.2418 −0.2475 −0.2499 −0.2491 −0.2450 −0.2378 −0.2274 −0.2141 −0.1980 −0.1793 −0.1583 22 −0.2498 −0.2468 −0.2403 −0.2303 −0.2170 −0.2006 −0.1813 −0.1594 −0.1352 −0.1090 −0.0813 −0.0524 −0.0228 23. −0.2111 −0.1926 −0.1711 −0.1469 −0.1204 −0.0920 −0.0622 −0.0313 −0.0000 0.0313 0.0622 0.0920 0.1204 24. −0.1154 −0.0854 −0.0538 −0.0214 0.0114 0.0440 0.0759 0.1064 0.1352 0.1615 0.1851 0.2056 0.2224 25. 0.0114 0.0454 0.0786 0.1103 0.1399 0.1669 0.1908 0.2111 0.2274 0.2395 0.2470 0.2500 0.2482 26. 0.1352 0.1637 0.1889 0.2103 0.2274 0.2399 0.2475 0.2500 0.2475 0.2399 0.2274 0.2103 0.1889

(33) Implementation of a digital transmitter using a stored table for the sub-carrier values needs minimal computational operations, according to an embodiment of this invention. An example of a MATLAB® program that simulates the transmitter is shown below. The simulation code contains only 5 rows, that are repeated 16 times.

(34) TABLE-US-00004 STx=[ ]; Lpr=[ ]; %Initialization for sub=1:16 dib=Lpr(sub)+dibit(sub); %Differential encoding L=dib−4*floor(dib/4); %Modulo 4 sTx=WW(:,sub,L+1); %Choosing current sub-carrier waveform Lpr(sub)=L; %Saving current symbol STx=STx+sTx; %Forming OFDM symbol signal end

(35) In this example, the program is performed within a loop for 16 sub-carriers (for sub=1:16) and includes 5 operations for each sub-carrier. The operations are as follows: (a) first operation—summation of the current dibit (in decimal form) with the previous one (Lpr) for each sub-carrier; (b) second operation—modulo 4 calculation of the summation; (c) third operation—choosing current sub-carrier waveform (phase) sTx from the table of pre-stored values (the table WW is a 3-dimensional matrix with coordinates: sample number, sub-carrier number, index to one of 4 versions of ±sin and ±cos functions); (d) fourth operation—saving the current transmitted symbol: and (c) fifth operation—summation of the sub-carrier waveforms.

(36) FIG. 8 shows a general block-diagram of the OFDM-DQPSK receiver 800, according to an embodiment of this invention. The received signal 805 is fed to an optional input stage 810, prior to input to a symbol synchronization unit 820 and a DQPSK multi-carrier detector 830. Such an optional input stage 810 may include functionality such as frequency downconversion, a transducer, etc., depending on the application. Using sub-carrier waveforms from a generator 840, generated in the same manner here as in the transmitter, the DQPSK detector 830 estimates the sine and cosine functions of transmitted phase differences for all K sub-carriers. Based on these estimations, the DQPSK detector 830 provides K-dibit decisions, which are transformed in the data buffer 850 into a sequence of 2K data bits 860.

(37) FIG. 9 shows a block-diagram of the DQPSK detector 900 for a sub-carrier, according to an embodiment of this invention. The DQPSK detector 900 operates according to the following multi-step algorithm.

(38) The correlation module 910 computes the correlation coefficients between the received signal Rx(t) and the quadrature reference signals sin(k*2π/T.sub.a)t and cos(k*2π/T.sub.a)t:
X.sub.k=∫Rx(t)sin(k*2π/T.sub.a)tdt,  (2a)
Y.sub.k=∫Rx(t)cos(k*2π/T.sub.a)tdt.  (2b)
The transformation module 920 computes the sine and cosine functions of the transmitted phase difference:
S.sub.k=X.sub.kX.sub.k*+Y.sub.kY.sub.k*,  (3a)
C.sub.k=X.sub.k*Y.sub.k−X.sub.kY.sub.k*,  (3b)
where X.sub.k* and Y.sub.k* are the estimates (2a) and (2b) for the previous symbol interval.
The decision module 930 determines the resulting dibit values, in accordance with Table 1, namely:
If |S.sub.k|>|C.sub.k| and S.sub.k>0, then dibit=00,  (4a)
If |S.sub.k|>|C.sub.k| and S.sub.k<0, then dibit=11,  (4b)
If |S.sub.k|<|C.sub.k| and C.sub.k>0, then dibit=01,  (4c)
If |S.sub.k|<|C.sub.k| and C.sub.k<0, then dibit=10.  (4d)

(39) It should be noted that calculations (2), (3), and (4) are computed for each of the K sub-carriers.

(40) The OFDM-DQPSK receiver can be also implemented digitally. In such a case, the analog-to-digital converter would be included into the receiver block-diagram FIG. 8 after the input data stream 805. The sub-carrier replicas are generated by means of reading the table, which stores functions sin (k*2π/T.sub.a)t and cos (k*2π/T.sub.a)t in digital form. The table contains K columns, where K is the number of sub-carriers, and rows, sufficient to represent at least one period of each sub-carrier. An example of a MATLAB® program that simulates the receiver is shown below. It contains 5 rows and decision making, each of which is repeated 16 times:

(41) TABLE-US-00005 for sub=1:16 X=sum(Rx.*Rs(:,sub)); %correlation of the received signal and reference Y=sum(Rx.*Rc(:,sub)); %correlation of Rx and the quadrature reference C=Xpr(sub)*X+Ypr(sub)*Y; %cos of the phase difference S=Xpr(sub)*Y−Ypr(sub)*X; %sin of the phase difference Xpr(sub)=X; Ypr(sub)=Y; %saving current projections if abs(S)>abs(C) %decision making if S>0 D=0; %dibit=00 else D=3; %dibit=11 end else if C>0 D=1; %dibit=01 else D=2; %dibit=10 end end end

(42) The program is performed within a loop for 16 sub-carriers (for sub=1:16) and includes 5 operations for each sub-carrier. The operations are as follows: (a) first and second operations—correlations of the received signal, Rx, and reference signals, Rs and Rc. The last ones are taken from the corresponding tables (2 dimensional matrices); (b) third and fourth operations—calculation of the trigonometric functions of the received phase difference; and (c) fifth operation—saving current correlation coefficients. The decision making procedure uses simple comparison and logic operations.

(43) The symbol synchronization 820 in the receiver operates according to the following algorithm. Using the assumption of initial synchronization, the interval of sub-carrier orthogonality is known. Let the beginning of this interval be t+nT, where n is the symbol number, and T is the symbol duration.

(44) Calculations are performed according to equation (2) for correlations X.sub.s and Y.sub.s of the received signal and reference signals for the missing sub-carrier. At perfect synchronization, these correlation values are equal to zero. Accordingly, the objective of the synchronization algorithm is to locate the timeframe t+nT that minimizes the length of vector (X.sub.s,Y.sub.s). The synchronization tracking procedure can be implemented as follows.

(45) Calculate the correlations using equation (2) for two intervals: X.sub.s− and Y.sub.s−, for an advanced interval (t−Δt)+nT, and X.sub.s+ and Y.sub.s+ for a delayed interval (t+Δt)+nT. The squared lengths of these vectors are:
L.sub.−=(X.sub.s−).sup.2+(Y.sub.s−).sup.2.  (5a)
L.sub.+=(X.sub.s+).sup.2+(Y.sub.s+).sup.2.  (5b)

(46) The synchronization tracking algorithm may be realized based on the average of L.sub.− and L.sub.+. Therefore, if L.sub.+>L.sub.−, the synchronization pulse should be shifted to the left. Conversely, if L.sub.+<L.sub.−, the synchronization pulse should be shifted to the right.

(47) The above embodiments find applicability in a number of environments, wherein multi-path fading is significant, circuit complexity is a challenge, or computational resources prove to be a challenge.

(48) One such environment is an acoustic environment, where multiple reflections of waves from different objects, surface areas, surface boundaries and interfaces in the channel environment result in significant multi-path propagation. In an embodiment of the invention implemented for an acoustic environment, FIG. 10 shows a 16 sub-carrier OFDM acoustic signal in the frequency domain. The signal contains 16 harmonics of a 10 kHz oscillation, with the harmonic numbers indicated on the frequency axis. In a further embodiment of the invention, as applied to an acoustic environment, the OFDM-DQPSK acoustic data transmission system uses the 92.sup.nd to the 108.sup.th harmonics, resulting in sub-carrier frequencies from 920 kHz to 1080 kHz respectively. It should be noted that the 100.sup.th harmonic, located exactly in the middle of the frequency spectrum, is not transmitted. Instead, this frequency location is used for symbol synchronization in the receiver.

(49) For this embodiment of the invention, an examination of the time domain reveals the following. The total symbol interval is 150 μs, broken into a guard interval of 50 μs and an active interval of 100 μs. Such a time division results in a symbol transmission rate of 6.67 ksymbols per second. With the number of sub-carriers equal to 16, and the use of DQPSK modulation, the total bit rate becomes 213 kbits per second. Other choices of guard intervals, active intervals, number of sub-carriers, and sub-carrier separation can be made. Table 4 illustrates possible choices of the OFDM-DQPSK data communications system, as relevant to an embodiment in an acoustic channel environment.

(50) TABLE-US-00006 TABLE 4 Number of Sub-carrier Bit Rate sub-carriers Separation Bit Rate Efficiency T.sub.a μs T.sub.g μs K kHz kbit/s bit/s/Hz 100 100 16 10 160 1.0 100 50 16 10 213 1.3 100 25 16 10 256 1.6 75 75 16 13.3 213 1.0 75 50 16 13.3 256 1.2 75 25 16 13.3 320 1.5 50 50 16 20 320 1.0 50 25 16 20 427 1.3 25 25 16 40 645 1.0

(51) The first and second columns of Table 4 show a variety of possible exemplary combinations of the active interval T.sub.a and the guard interval T.sub.g for an embodiment in an acoustic channel environment. Generally, the guard interval T.sub.g should exceed the maximum signal delay in the multi-path channel. For the example shown in Table 4, the maximum delay in the acoustic channel is assumed to be in the range 25 μs to 100 μs, depending on the carrier frequency used. It is preferred that the active interval exceed the guard interval in order to minimize energy loss. In the above example, the number of sub-carriers is chosen to be 16 in order to illustrate an embodiment of a simplified OFDM-DQPSK transmitter in an acoustic channel environment. In the exemplary combinations shown in Table 4, the active interval ranges from 25 μs to 100 μs, the sub-carrier frequency separation ranges from 10 kHz to 40 kHz, and the signal bandwidth ranges from 160 kHz to 640 kHz.

(52) FIG. 11 illustrates a flowchart 1100 for data transmission via multi-path channels using OFDM signals with DQPSK modulation, according to an embodiment of this invention. The invention described herein is not limited by the order of the steps in the flowchart 1100. In other words, some of the steps can be performed simultaneously, or in a different order, without deviating from the scope and spirit of the invention.

(53) In step 1105, a plurality of OFDM sub-carrier transmitter signals is generated.

(54) In step 1110, the OFDM sub-carrier signals are modulated using DQPSK to form a plurality of modulated OFDM sub-carrier signals.

(55) In step 1115, the plurality of modulated OFDM sub-carrier signals is summed to form a transmitted signal.

(56) In step 1120, the transmitted signal is transmitted through a multi-path channel.

(57) In step 1125, the transmitted signal is received to form a received signal.

(58) In step 1130, a plurality of OFDM sub-carrier reference signals is generated.

(59) In step 1135, the OFDM symbol interval and the demodulating interval are synchronized.

(60) In step 1140, the received signal is demodulated using a DQPSK multi-carrier detector to form an output signal.

(61) It is to be appreciated that the Detailed Description section, and not the Summary and Abstract sections, is intended to be used to interpret the claims. The Summary and Abstract sections may set forth one or more but not all exemplary embodiments of the present invention as contemplated by the inventor(s), and thus, are not intended to limit the present invention and the appended claims in any way.

(62) The present invention has been described above with the aid of functional building blocks illustrating the implementation of specified functions and relationships thereof. The boundaries of these functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternate boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed.

(63) The foregoing description of the specific embodiments will so fully reveal the general nature of the invention that others can, by applying knowledge within the skill of the art, readily modify and/or adapt for various applications such specific embodiments, without undue experimentation, without departing from the general concept of the present invention. Therefore, such adaptations and modifications are intended to be within the meaning and range of equivalents of the disclosed embodiments, based on the teaching and guidance presented herein. It is to be understood that the phraseology or terminology herein is for the purpose of description and not of limitation, such that the terminology or phraseology of the present specification is to be interpreted by the skilled artisan in light of the teachings and guidance.

(64) The breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.