# What’s next for DOCSIS: Modulation options and impacts in HFC networks: COFDM and low-density parity check, Part 2

**This is the second in a two-part series. See Part I [1], which covered many of the basics of DOCSIS modulation.**

Many wonder how today’s HFC networks will support high order modulations such as 4096-QAM. There are two technologies in the DOCSIS 3.1 specification that will enable this without requiring changes to existing outside plant. The first is Coded Orthogonal Frequency Division Multiplexing (COFDM). This is a method for taking many QAM channels, with, say 25 kHz wide spacing instead of 6 or 8 MHz, and acting as an “envelope” for these many closely packed together “carriers.” COFDM also has dynamic properties. If you have a block of 960 QAM channels (or “carriers”) where each QAM channel is only 25 kHz wide, then the COFDM channel would occupy 24 MHz of bandwidth.

A second technology in the proposed DOCSIS 3.1 specification is called low-density parity-check (LDPC). LDPC is the “C” (coded) part in COFDM and replaces the older Reed-Solomon forward error correction (FEC). Predictive models have shown LDPC enabled 4096-QAM will operate just like 256-QAM under similar impairment conditions. With LDPC in place, 4096-QAM in COFDM will be just like 256-QAM without COFDM. In DOCSIS terminology we will refer to COFDM as just OFDM and drop the “C” since it is implied.

**Single Carrier (SC) versus Multi-Carrier **Today’s HFC plants employ signal modulation using single carrier (SC) methods.

Table 1 compares advanced SC modulation technique capabilities with respect to spectral efficiency, minimum signal-tonoise ratio (SNR) to maintain 10-6 minimum bit error ratio (BER), and worst case peak-to-average power ratio (PAPR).

Table 1 reveals that of the available SC modulation techniques, only 4096-QAM and 65536-QAM (64k-QAM) offers the spectral efficiency (SE) required to meet DOCSIS 3.1 data rate requirements stated below (for 10+ Gbps downstream and 1+ Gbps upstream that equates to a SE requirement > 10 b/s/Hz with a BER of ≤10-6).

SC modulation techniques are not being considered at present for DOCSIS 3.1 employment by the engineering committee.

The reason is that the DVB-C2 adopted approach of using OFDM multi-carrier modulation with an inner FEC layer employing low density parity check (LDPC) coding and an outer layer using BCH meets DOCSIS 3.1 requirements at a lower cost to implement.

**OFDM Overvieww **Figure 1 shows how a single OFDM downstream physical layer (PHY) channel is formed by multiple sub carriers of differing modulation types, such as 256- QAM, 1024-QAM, and 4096-QAM. These carriers are transmitted together in a block with each carrier individually adjustable.

Because each sub-carrier is narrow in frequency, a DOCSIS 3.1 enabled plant with OFDM can adjust to channel conditions and by-screen subscriber demand with kHz resolution. Operation at the former “band edge” is now possible, effectively freeing up between 10 percent and 16 percent of the presently underutilized downstream bandwidth (10 percent for digital channel filtering at the band edge by downstream channel and 16 percent for analog channel underutilization at the band edge). Effective use of OFDM means that HFC and FTTP (fiber-to-the-premises) plant is no longer restricted to six or eight MHz channels.

Channel bandwidth can be assigned to match exact real-time subscriber demand or channel impairment conditions or both.

OFDM also offers a path to lower cost per delivered bit. How? Let’s list the ways below. OFMD:

• Scales to large bandwidths (BWs) (>100s of MHz) more cost effectively than bonding many single carrier QAM channels;

• Permits easier channel synthesis; • Is less complex at the MAC (medium access channel) layer; • Allows additional capacity from the existing plant as described above;

• Allows incremental capacity additions as needed based on spectrum availability without new cable modem or CMTS/ CCAP deployments;

• Is a widely adopted technology that may offer US cable operators better economies of scale from alignment with other OFDM-based RF standard;

• May allow U.S.-based cable industry to attract new chipset and system suppliers to our market.

**Unlocking the Magic of OFDM** The multi-carrier approach helps mit igate the effects imposed by intersymbol interference (ISI) by dividing the high-rate data into many low-rate parallel streams, each conveyed by its own carrier, of which there are a large number. The European DVB-T2 standard permits a maximum number of 6912 sub-carriers.

You might think using a very large number of sub-carriers would present daunting impacts on transmitter and receiver design – we would need many modulators and demodulators and filters to accompany them, correct? Also, won’t we need an increase in bandwidth to accommodate all these carriers? Both worries are dispelled through the use of evenly spaced carriers at F = 1/Ts, where Ts is the “useful” or “active” symbol period over which the receiver integrates the demodulated signal. When this is the case, the carriers form an orthogonal set. We employ the common procedure of demodulating a carrier by means of multiplying it by a carrier of the same frequency, which is called “beating it down to zero frequency,” and then integrating the result. This action is performing an orthogonal demodulation. A carrier not on the same frequency gives rise to “beat tones” that are at integer multiples of the “error” frequency. The unwanted beat tones have an integer (real number) of cycles during the integration period, Tu, and are thus integrated to zero.

Without any special filtering we can separately demodulate all the carriers without any mutual crosstalk just by our choice of carrier spacing. We have not wasted any spectrum either. The carriers are closely packed so they occupy the same spectrum total as a single carrier – if the single carrier were modulated with all the data and subject to ideal filtering.

In practice, our carriers are modulated by complex numbers that change from symbol to symbol (this is part of error correction coding and decoding). If the integration period spans two symbols (as for delayed paths) not only will we have the dreaded same-carrier ISI, but also inter- carrier interference, ICI, as well because the “beat tones” from other carriers may no longer integrate to zero if they change in phase and/or amplitude during the period.

This is avoided by adding a guard interval ensuring that all information integrated comes from the same symbol and appears constant during integration.

The symbol period is extended so it exceeds the receiver integration period, Tu.

Since all carriers are cyclic within Tu, so too is the whole modulated signal. Therefore the segment added at the beginning of the symbol to form the guard interval is identical to the segment of the same length at the end of the symbol. As long as the delay of any path with reference to the main (shortest) path is less than the guard interval, all the signal components within the integration period come from the same symbol and the orthogonality criterion is satisfied.

ICI and ISI only occur when relative delay exceeds the guard interval.

Guard interval length is chosen to match the level of multipath expected. The guard interval should not form too large a fraction of Tu, otherwise too much data capacity (and spectral efficiency, SE) is lost. DAB uses a guard interval of 63 * Tu/256 = 0.246 * Tu. DVB-T has more options, of which Tu/4 is the largest.

Many other things can cause a loss of orthogonality and hence also cause ICI. They include error in the local oscillator (LO) or sampling frequencies of the receiver, and phase noise in the LO.

**Low Density Parity Check (LDPC) Codes **LDPC codes were first introduced by Robert G. Gallager in his Ph.D. thesis in 1960, but due to the computational effort in implementing encoder and decoder and the introduction of Reed–Solomon codes, they were mostly ignored until recently.

LDPC codes are now used in many high-speed communication standards, such as DVB-S2 (Digital Video Broadcasting - Satellite), DVB-C2, WiMAX, Wireless LAN (IEEE 802.11n), 10GBase-T Ethernet (802.3an) and G.hn/G.9960 (ITU-T Standard for networking over power lines, phone lines and coaxial cable) and the People’s Republic of China (PRC) Advanced Broadcast System – Satellite (ABS-S).

**Delivery of Artifact-Free All-Digital Content **Quality issues in visual media can take many forms, and one form is the consumer’s view of multi-media quality. Standards organizations are working on requirements for new Internet Protocol Television (IPTV) systems that include, or refer to, the number of artifacts per hour.

A drawback of the OFDM transmission technique is the presence of high peaks at the OFDM modulator output. Nonlinear amplification of these high peaks may clip the waveform during transmission. The distortion due to clipping has been extensively studied recently, and various mitigation techniques have been proposed. One method of mitigation involves prevention through the use of an amplifier capable of linear power amplification with a combination of fast rise and fall time and a peak to average power ratio (PAPR) rating with enough headroom to transmit OFDM-high integer QAM content without clipping.

The aim of providing this transmission capability is to deliver “artifact-free” digital content to subscribers.

**Peak-to-Average Power Ratio (PAPR) reduction techniques **Two PAPR-reduction techniques, Active Constellation Extension (ACE) and Tone Reservation (TR) are supported in DVB-T2, leading to a substantial reduction of PAPR, at the expense of a small average-power increment and/or at most 1 percent reserved sub-carriers. Early practical implementations have shown a reduction of 2 dB in PAPR (at 36 dB MER). The ACE technique reduces the PAPR by extending outer constellation points in the frequency domain, while the TR reduces the PAPR by directly cancelling out signal peaks in time domain using a set of impulse-like kernels made of the reserved sub-carriers.

The two techniques are complementary, i.e., the ACE outperforms the TR in a low-order modulation while the TR outperforms the ACE in a high-order modulation. The two techniques are not mutually exclusive and a combination of them can be used. However, ACE cannot be used with rotated constellations.

**Final thoughts **OFDM multi-carrier modulation equipped with two levels of error correction appears to offer a path to meet DOCSIS 3.1 goals. One caveat is the development of means to mitigate the potential impact to the delivery of artifact-free signals from potentially high transmitter peak-to-average power ratio. ■