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Technology Frequently Asked Questions

Q1. What is the theory behind Broadband Physics Wavelet modem immunity to RF interference?

A. There are three mathematically equivalent ways to view Broadband Physics Wavelet Modem Technology. In Broadband Physics’ Wavelet modulation model:

1. Signal coordinates or data coordinates can represent information that is defined in a vector space. A contiguous set of N samples into the D/A converter are the signal coordinates of an N-dimensional information vector. Broadband Physics’ transmitter is a baseband modulation operator [M] that provides the coordinate transformation to rotate data into signals. The receiver uses the demodulation operator [D] for counter-rotation. Broadband Physics uses invertible baseband transformations. Since operators must commute for rotations--for example, [D][M]=[M][D]—Broadband Physics’ Wavelet modulation demonstrates it's unique properties. See IEEE 802.14-95/128, page 2.

2. A transmitter can send bits as overlapping wavelets. The wavelets overlap in both time and frequency without interference due to the cross-correlation properties of the wavelet waveforms. The receiver recovers the bits by correlating the received signal with the matching transmitted wavelets. See IEEE 802.14-96/127, page 3

3. A baseband multi-rate filtering sends the data bits in overlapping sub-bands. A matched filter-bank is used to recover the bits. The transmitter filter is called a synthesizer and the receiver filter is called an analyzer. Thus in Broadband Physics’ Wavelet modulation , the filter banks must have nearly commuting polyphase filter matrixes with coefficients that form wavelets. See IEEE 802.14-95/128, page 3.

Q2. Is there a block diagram?

A. Yes. Broadband Physics’ Wavelet modems are vector filters. You can view diagrams in IEEE 802. 14-96/127 Figure 2, and in IEEE 802.14-95/128, Figures 1 and 2.

Q3. What is the computational complexity of Broadband Physics’ Wavelet modulation when implemented in Silicon or other methods?

A. Multiplication requires a lot of silicon real estate. It is often used to quantify the difficulty of algorithms. Broadband Physics’ Wavelet modulation for CATV cable modems has zero computational complexity in both the transmitter and receiver. The set-top's upstream cable transmitter is a look-up table driving a D/A and 75- ohm cable amplifier. The set-top's downstream receiver has no A/D converter or digital signal processor (DSP). Instead it performs a wavelet correlation using a surface acoustic wave filter (SAW) at VHF frequencies in the IF stage of the set-top box. This is a very low cost design. See IEEE 802.14-96/127, Figure 1a and Figure 5.

Q4. What happens to the complexity of the set-top receiver if a SAW filter is not used?

A. In chip designer's terms, the set-top receiver is the equivalent of approximately 40,000 gates for a 50 Mbps downstream Broadband Physics’ Wavelet Cable Modem. See IEEE 802.14-96/014, Table 5.

Q5. Does that calculation include the computational complexity of the equalizer?

A. A separate equalizer is not used because Broadband Physics’ wavelet modulation takes advantage of adaptive rotations. The wavelets can be adapted at either the transmitter or the receiver end, because the vector filter is of the Finite Impulse Response (FIR) form. You can adapt the wavelets using any adaptation algorithm--for example, least mean squares (LMS). Broadband Physics’ wavelet modulation is its own multi-band equalizer. Such exact equalization might be unnecessary since Broadband Physics’ wavelet modulation correlates--that is, compares waveshapes--over many samples to demodulate the data. See IEEE 802. 14-96/014, Figure 5 and Table 3.

Q6. There are many non-linear effects in the CATV plant. How does Broadband Physics’ wavelet modulation handle non-linearities and nonGaussian noise?

A. Broadband Physics’ wavelet modulation provides immunity to non-Gaussian noise such as:

upstream CATV ingress. See IEEE 802.14 -96/097, Figure 3 and Page 4.
HFC laser clipping. See IEEE 802.14-96/127, Figure 4 and Table 1.
harmonic interference. See IEEE 802.14-96/014, Figure 6 and Table 4.

Q7. Does Broadband Physics equalization method provide immunity to upstream interference?

A. While equalization helps, immunity to interference is an intrinsic feature of Broadband Physics’ wavelet modulation due to the gain realized during the receiver’s correlation processing.

Q8. Is this processing gain resemble spread spectrum techniques?

A. Yes. Both Broadband Physics’ wavelet modulation and direct-sequence spread spectrum (DS-SS) have correlation processing gain. But DS-SS spreads the spectrum while Broadband Physics’ approach does not. Broadband Physics’ wavelet modulation provides the advantage of processing gain to suppress interference without the disadvantage of bandwidth inefficiency found in DS-SS.

Q9. How is this possible?

A. Consider how each method works:

In DS-SS each data bit multiplies a binary code called the spreading sequence. To send a ONE ( 1) the code is sent without modification but to send a ZERO (= -1) DS-SS requires a complement for all the bits in the code before sending. If the code is 10 bits long, then DS-SS sends 10 times as many bits to the modulator (usually BPSK or QPSK) and the result is an increase in bandwidth by a factor of 10, giving a spreading gain of 10 dB = 10Log(10). The correlation of the received signal with the spreading code accounts for the gain.
Broadband Physics’ solution sends a wavelet for a ONE (=1) and an inverted wavelet for a ZERO (-1). The receiver's correlation of the signal with the wavelet accounts for the gain. The wavelet is a multi-valued code rather than a binary sequence.

Q10. Why isn't the bandwidth spread in Broadband Physics’ solution like that in DS-SS?

A. In DS-SS each bit generates a binary code and the codes follow one after another. In Broadband Physics’ solution the wavelets, which are non-binary codes, overlap in time without inter-symbol interference (ISI). DS-SS performs the spreading in binary and then sends it to the modulator. In Broadband Physics’ solution the modulation operator performs the addition of the overlapped wavelets as clearly seen in the vector filter. The Broadband Physics’ modulation operator spreads each symbol over the sub-band for that wavelet at the optimal bandwidth. It uses less bandwidth than QAM. See IEEE 802. 14-96/127, Page 3.

Q11. What does Broadband Physics mean by optimal bandwidth?

A. Because of the time overlap, there is no loss of bandwidth. Broadband Physics’ solution provides a bandwidth efficiency of 2*B bits per second per hertz when it sends B bits per symbol for each sub-band. Here 2B is the 3 dB bandwidth efficiency of the sub-band. Since orthogonal wavelets also overlap in frequency at the 3 dB points for each adjacent sub-band, the 20 dB bandwidth efficiency of the overall modem rapidly approaches 2B bps/Hz, which is the best a linear modem can do.

Q12. So, is the bandwidth efficiency of Broadband Physics’ solution better than QAM?

A. Yes. Its raised cosine filters limit the bandwidth efficiency of QAM. Broadband Physics’ approach doesn't use raised cosine filters. Non-linear algorithms, like trellis coded modulation (TCM), improve the efficiency but TCM can be applied to Broadband Physics’ solution as well.

Q13. Does Broadband Physics recommend we use TCM with Broadband Physics’ solution for Forward Error Correction?

A. Broadband Physics’ theory suggests that since the vector filter has the same FIR form as a convolutional encoder, Broadband Physics’ solution can do its own forward error correction (FEC) without TCM. This should provide a much better error-coding gain than TCM, because Broadband Physics’ solution does not waste entropy sending parity bits. You will dissipate much of the potential gain from conventional soft-error coding by trying to overcome the SNR loss due to sending parity bits. Although this topic demands more research, in the meantime you can use soft trellis coding (TCM) as well as hard-coded FEC.

Q14. Does Broadband Physics recommend interleaved block codes for Forward Error Correction Coding?

A. This may not be necessary because Broadband Physics’ solution has correlation processing gain. The trouble with block coding schemes is that there is always a maximum burst duration that the modem cannot handle, even with interleaving. Interleaving schemes can create long end-to-end delays for the data, which can cause other problems.

Q15. Can Broadband Physics provide more details about immunity to RF Interference?

A. Broadband Physics’ wavelet cable modem is immune to interference in the sense that the error rate is still good. Broadband Physics’ solution doesn't look at individual samples. Instead, it compares wave shapes (correlates) over many samples for each symbol. It suppresses interference because non-Gaussian interference doesn't have the same wave shape as a wavelet. Broadband Physics’ solution has a gain in Signal-to-Interference Ratio (SIR) in the receiver.

Consider the downstream results in IEEE 802.14-96/14, Figure 6. There, the modem operated at much better than 10 BER in spite of strong harmonic interference that randomly corrupted every seventh sample. Broadband Physics’ correlation processing gain provides immunity to the interference. There are even several cases in narrowband and broadband interference in which Broadband Physics’ solution, in theory, has zero interference at its demodulator output--that is, at the quantizer input. The correlation gain suppresses the interference but Broadband Physics’ solution did not spread the spectrum.

Q16. What else can Broadband Physics’ wavelet modulation do?

A. Calculations show that Broadband Physics’ solution should dramatically improve the data rate of wireless and twisted pair links compared to the current state-of-the-art. It also provides significant performance improvements over today's voice/video networks. As such, Broadband Physics’ solution creates an entirely new class of voice/video networks. This new class of communications works if, and only if, modulation and demodulation are commuting operators. Broadband Physics’ solution also solves several long-standing problems in communications security for both commercial and battlefield use. Broadband Physics’ wavelet modulation theory is closely related to encryption theory and spread spectrum theory.