What is hiden behind WAM technology?

I’ve been thinking a little about a new breakthrough in telecom industry presented by Magna-Com. They have said that it has 10 dB gain, comparing to the 4096-QAM. What is it? How does it work?

Before they provide more details, we can only guess and this is what the following work about.

Sections:

1. Channel capacity. 4096-QAM performance

2. How could 10 dB gain be obtained? Possible solutions

3. Conclusion

1. Channel capacity. 4096-QAM performance.

        

Let’s consider limited-power regime. Channel capacity is a maximal information bit rate, that can be obtained by a communication system with arbitrary bit rate. It is limited by signal to noise power ratio. AWGN channel capacity limit is defined by the Shannon-Hartley theorem:

C = B*log2(1+S/N).

where                C is a bit rate [bit/s]

B is occupied bandwidth [Hz]

S is a power of a signal

N is a power of a noise.

        To exclude bandwidth we will consider not the highest bitrate, but the spectral efficiency [bit/s/Hz].

C/B = log2(1+S/N)

Shannon limit

        The point that I have chosen on the plot above is 10.8 bit/s/Hz. This spectral efficiency excludes pulse shaping filter bandwidth and pilot symbols. If I use QAM-4096 modulation (12 bit/s/Hz) and 9/10 code rate (12*9/10 = 10.8 bit/s/Hz) I would achieve that spectral efficiency.

        The question now is how high SNR the configuration needs to perform reliable connection?

        The most powerful technique which is used in real systems is Bit-Interleaved Coded Modulation (BICM). For example in 4096-QAM Gray mapping each bit has different level of protection and this fact is used by irregular LDPC codes. I took BICM configuration including mapping scheme, bit interleaving and code check matrix from DVB-C2 standard and estimated (by using the Monte Carlo method) the Bit Error Rate (BER) performance. I consider the signal on baseband without oversampling (FSAMP = FSYMB).

4096-QAM with 9/10 LDPC code BER performance

Reliable transmission regime would be expected if the SNR will be higher than 35dB. It exceeds a theoretical limit only by 2.5 dB. So, the question is...

2. How could 10 dB gain be obtained? Possible solutions.

To obtain 10 dB gain first of all 4096-QAM has to lose some performance. A real transmission channel is far from the AWGN, especially in 4096-QAM case. It also includes transmitter and receiver elements impairments such as quadrature imbalance, phase noise, nonlinearity of elements. The modulation with such high order is very sensitive to such impairments.

Nonlinearity

Let’s see how other systems deal with nonlinearity problem. For example in DVB-S2X this impairment is overcomed by using APSK (up to 256 modulation order) instead of QAM.

256 APSK constellation (DVB-S2X)

        There are some pre-distortion and post-compensation techniques for APSK are discussed and developed.

In multicarrier systems, like OFDM, other techniques are used. They mostly reduce PARP (peak to average power ratio).

Phase noise

        Some non-uniform constellations are designed to be robust to the phase noise. For example, this patent http://www.google.com/patents/US5832041 describes a solution.

Ideal QAM-64 signal states

Phase noise effect on different signal constellations

        You can see here, that on the non-uniform constellation signal states stay being protected.

        AWGN

        There are some techniques that could be used to improve performance of the system in AWGN channel, but state-of-the-art systems are already very near to the theoretical limit. Struggle now is for the tenth of a decibel. These methods redistribute interstate distances to improve BICM performance.

        

        Both of above constellations has normalized power. The idea was to use two Normally distributed orthogonal PAM constellations. It can be done by using the probit function.

        I have estimated its BER performance. You can find bit interleaver and code check matrices that I have used here in the DVB-C2 standard (http://www.etsi.org/deliver/etsi_en/302700_302799/302769/01.01.01_60/en_302769v010101p.pdf).

4096-QAM 9/10 LDPC performance

        You can see at the picture above that it has roughly 0.35 dB gain in AWGN channel. It is not so much, comparing to 10 dB, but it saves about 8% of a power.

        Somebody could say that it’s PARP becomes higher and it rises requirements to the amplifier linearity. Then I would answer that if we use OFDM, PARP doesn’t change.

        Another might say that demapper becomes much more complex. It is complex, but not so much. Both of the components (real and imaginary parts) stay orthogonal, and we can process them independently.

        Once I have tested its performance I found that this technique was discussed here (http://downloads.bbc.co.uk/rd/pubs/whp/whp-pdf-files/WHP257.pdf), you can find there some helpful details if you need.

        Conclusion

So, WAM can be just another kind of uniform constellation, which suits to the specific system parameters or it may be some other new technique, that… also reduces specific impairments affect. Questions that remained are:

- What is the reference 4096-QAM modem? Is it maximally robust?

- What are system parameters? What are the impairments?

Answers to these questions don’t require to open the solution but are very important, and would let us evaluate real significance of the invention.

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