IEEE 802.14-96/014

TITLE: Linear INTRA for Downstream CATV Modems
AUTHOR: Bill Miller

ABSTRACT: Based on preliminary simulation results, the Linear Information Transformation (Linear INTRA) modulation for the Downstream PHY layer for 802.14 CATV-based data networks should get >10^-8 BER on CATV at up to 65 Mb/s. can adapt its rotation matrix to distortions without an equalizer. can tolerate large harmonic impulse noise. requires about 40,000 logic gates.

The following paper is based on Document # IEEE 802.14-96/014 prepared to assist and submitted to the IEEE 802.14 WG Cable TV Protocol Working Group January 13, 1996.

Modulation Types

Three generic modulation types have been proposed for downstream use in the 802.14 WG----INTRA, n-QAM (n=64 or 256) and n-VSB (n=16). Some preliminary simulation results on Linear INTRA modems are presented in this paper. INTRA, a multi-dimensional modulation, offers very high data rates (50% higher than 16-VSB) with low-cost circuitry (estimated at 40k gates) due to its low computational complexity.

Modem Description

Downstream data transmission on CATV cable can utilize the Information Transformation (INTRA) described in 802.14-95/128 and -95/094. Information is viewed as an M-Dimensional vector which may be described by its projection onto either DATA coordinate axes or SIGNAL coordinate axes. The modem transmitter partitions the frames of data bits into M-2 data-coordinates and adds a sync-vector in the remaining 2 data-coordinates. The resultant vector is then baseband filtered using a Vector-Filter to become the M signal-coordinates (i.e. M samples) into a 12 bit D/A converter. The baseband signal is linearly translated to passband by a phase-locked carrier (not simulated). The receiver can lock to either a separate pilot or the sync-vector in its signal-coordinate representation to translate the received signal back to 6 or 8 MHz baseband. A matching Vector-Filter recovers the data and the sync-bits. The MxM tap weight matrices of the receiver's Vector-Filter can be adaptively adjusted by training at initialization or adjusted continuously if the system response changes. That is, INTRA can use an adaptive coordinate rotation with no separate equalizer filter. The complexity is low because the vector-rate is the sample-rate divided by M.

Predicted Performance

The 3-DB-Bandwidth, the stopband attenuation and the width of the transition to stopband are all design variables of the Vector-Filter, which is a very computationally efficient M-band multi-rate filter bank. If the modem occupies a 6 MHz channel the data rates shown in column 1 of Table 1 can be obtained by the selections shown in columns 2 and 3. Many other designs are possible. In 802.14-95/128 a 54Mb/s modem is proposed in order to provide easy connectivity to ubiquitous 51.84 Mb/s ATM networks. An 8 MHz system could be compatible with 6MHz transmissions by universally adopting the 51.84 rate, and the same INTRA Vector-Filter hardware could be used so an international ASIC may be feasible. For example, a 12-D modem at 53.3 Mb/s in 8 MHz would require a SNR of approximately 34 DB as shown in Table 1A.

 

Table 1. INTRA Data Rates exceed other proposals
Bit Rate (Mb/s)	Vector Dimensions	Bits / Coordinate	Bits / Vector	3 DB Bandwidth (MHz)	S/N 10^-8 BER (DB)
45	8	5	30	4.5	40
50	12	5	50	5.0	40
54	20	5	90	5.4	40
54	8	6	36	4.5	46
60	12	6	60	5.0	46
64.8	20	6	108	5.4	46

 

Table 1A. Typical 12-D design for 8 MHz channel spacing
Bit Rate (Mb/s)	Vector Dimensions	Bits / Coordinate	Bits / Vector	3 DB Bandwidth (MHz)	S/N 10^-8 BER (DB)
53.3	12	4	40	6.7	34
66.7	12	5	50	6.7	40

Since CATV subscribers demand near excellent analog video quality (see Table 2 and reference 2) on the downstream channels, cable TV systems have low noise levels. The S/N in Table 1 is feasible for CATV modems. Multidimensional error coding or Forward Error Correction (FEC) could be added. Using a smaller 3-DB-BW than 16-VSB has the advantage of lower cost IF filters in the RF circuitry. The ATSC 16-VSB modulation uses a 3-DB-BW of 5.38 MHz. In n-QAM and n-VSB the data bits are sent at high symbol rates (93 nanoseconds/symbol for VSB); whereas, in INTRA a vector is sent in around a microsecond (i.e. the 12-D modems) permitting a low cost implementation that should be relatively insensitive to small timing errors. The entries in Table 1 assume that the baseband signal is centered in the 6 MHz channel. A slight offset could, for example, permit the 12-D modem in row 2 to operate at 51.84 Mb/s. for compatibility with digital fiber networks.

Table 2. High S/N is typical on CATV
Broadcast TV Picture Quality	Peak Signal / rms Noise (DB)
Excellent	55
Good	45
Fair	35
Poor	25

Simulations

Simulation results in Figures 1, 2, and 3 show the Signal+Noise spectrum for 45, 50 and 54 Mbps The Power Spectral Density in DB is plotted over the 6 MHz channel for 1000 vectors using a -40 DB Guassian noise source to simulate the cable noise. The 12-D design (see reference 1) used for simulation has only 5 tap matrices versus 9 taps for the 8-D Vector-Filter design , which is why the 8-D modems show the -40 DB Guassian noise in the stopband more clearly.

Figure 1. 8-D Signal + Noise at 45 Mb/s

 

Figure 2. 12-D Modem + Noise at 50 Mbps

 

Figure 3. 8-D Modem + Noise at 54 Mb/s

The available S/N on a cable can be inferred from the upper end of the 802.14WG Upstream Cable Channel Model (802.14-95/133), which shows the noise at -40 DB and typical modem signals with a peak power above +10db. This is consistent with the TV picture quality observations in Table 2 for a peak/rms ratio of 50 DB. Note that the simulations in this paper use several DB less peak power than may be allowed on CATV systems in order to measure the BER during simulation. The BER in Figure 3 is 10^-6, as determined by the observed standard deviation of the threshold error margin. Based on the Eb/No error curve, less than 2 DB of additional signal power (or coding gain ) is required for a 10^-8 BER with the signal power as shown in Figure 3.

 

Adaptive Rotation

To illustrate the adaptive coordinate rotation concept, the S+N receiver input of Figure 1 was passed through a "channel filter" that approximates an inexpensive SAW device in the IF stage. The result is shown in Figure 4. The channel filter has a -40 DB attenuation at the channel edges (0 and 6 MHz) with a 750KHz transition to a flat 0 DB gain from 1/8 to 7/8 of the band (i.e. the 3-DB-Bandwidth of the 8-D INTRA output). The error margin is plotted in Figure 5 for one vector coordinate (sub-band 2) as the receiver's rotation matrix adapts to the distorted signal. Note that there is no distinct equalization filter.

Figure 4. Distorted Signal + Noise at 45 Mb/s after channel filter.

Figure 5. Adaptive rotation of 8-D modem at 45 MB/s with channel filter

Table 3 summarizes the simulated experiment with a SAW channel filter, which might be used in a receiver's IF stage. Without the filter the standard deviation of the error margin is 10.3% for coordinate 2, which is the lowest data carrying sub-band. The error margin is the percent distance to the threshold, so the BER in Figure 1 is extremely good as the threshold is 10 standard deviations away. A BER of 10^-8 requires the threshold be 5.6 sigma from the noise. The 40.7% deviation in Table 3 indicates that 1.4 % of the bits will be in error on coordinate 2 unless the rotation matrix is adapted to the distortion as in Figure 5. Note that the adaption succeeded without sending a training sequence. The middle sub-bands are unaffected by the SAW filtering (an advantage for INTRA), so the 20-D modems in Table 1might send fewer bits in the edge sub-bands with only a small reduction in data rate and without unduly expensive IF filter parameters.

Table 3. INTRA equalizes without an equalizer
Configuration	Std-Dev (error-margin)
without channel filter (Fig 1)	10.3 %
with filter, without adapting	40.7 %
with filter, after adapting	10.7 %

Non-Guassian Noise

Harmonic noise was added to the Guassian noise before the channel filter. On every 7 th sample a constant was added to the noise generator samples, so the 8-D modem experiences an impulse in every frame of 8 samples. The resulting noise spectrum for 1000 frames is plotted in Figure 6.

 

Figure 6. Harmonic impulses + Guassian Noise

The effect of the harmonic bursts in Figure 6 can be seen in Table 4 which shows the standard deviation of the error margin after decision directed adaption of the rotation matrix to the channel filter. The sub-bands that contain the harmonic have more error but the BER is well over 10^-8 in all sub-bands (coordinates). Coordinate 2 may be compared to the last row of Table 3. Coordinates 1 and 8 contain sync bits only ( zero entropy). The receiver's transversal Vector Filter uses a weighted average of many samples to demodulate the data, so INTRA can tolerate the Non-Guassian noise in Figure 6. INTRA should work upstream!

Table 4. Standard deviation of the error margin for noise in Figure 6.
Coord. 1	Coord. 1	Coord. 1	Coord. 1	Coord. 1	Coord. 1	Coord. 1	Coord. 1
10.4%	10.8%	14.6%	10.3%	15.1%	10.3%	165.2%	10.9%

Hardware Complexity

With 6 bits in each independent coordinate, the INTRA modem in Figure 3 is comparable to a QAM modem with a 4096 point constellation!!! Both achieve a nominal 3-DB-Efficiency of 12 b/Hz, but 4096-QAM is clearly beyond the state-of-the-art for QAM on CATV. The higher bandwidth efficiency of INTRA can be used to avoid distortions at the channel edges by using smaller 3-DB-Bandwidths, or it can be used for high data rates like the 64.8 Mb/s modem in Table 1. As explained below, INTRA should not require extraordinary expense for A/D converters or silicon real-estate to achieve its high performance. For the simulations above, the transmitter rotation matrices used 16-bit coefficients and the output was quantized to 12-bits resolution. Like VSB, only one A/D is required (QAM needs two).

For Table 5 below only multiplications are counted since they are assumed to dominate the silicon real-estate, but a pre-add (because there is linear-phase symmetry) and an accumulation are required for each multiply. If continuous adaption of the rotation coefficients is employed in the receiver then the number of adds and multiplies per frame would double, but continuous updating is probably unnecessary for CATV/HFC which changes slowly (sunrise/sunset). The transmitter and receiver Vector-Filters are identical and can even use the same coefficients (arranged differently). Furthermore, unitary symmetry and linear-phase symmetry reduce the number of unique coefficients as listed in Table 5 for the specific modem designs that were simulated. A filter for the 20-D modems in Table 1 was not available for simulation and complexity calculations, but the results should be similar because of the multi-rate design.

For the filters used in the 8-D simulation, 288 multiplications per frame are required to rotate a vector .in 0.67 microseconds ; whereas, the 12-D design uses 360 multiplications in a 1 microsecond frame. An ASIC would need 9 or 8 multiplier cells for 8-D or 12 -D respectively assuming each multiplier cell runs at 50Mhz.

Table 5. An INTRA Modem for downstream CATV needs about 40,000 logic gates.
Bit Rate (Mb/s)	Dimensions	Number of unique coefficients	Multiplications/s (Millions/s)	Multiplier cells per Vector-Filter
45 or 54	8	144	432	9
50 or 60	12	180	360	8
54-64.8	20	?	-	-

The off-the-shelf Harris FIR Filter, part# HSP43168 , is a 45Mhz multi-purpose digital filter having 8 multiplier cells, a ram bank for 256 unique filter coefficients, an output accumulator, pre-adders for linear phase symmetry, and a microprocessor interface, all in a 32,529 gate device. The Harris part is for 10-bit coefficients (but can be arranged for 20-bits».simulations indicate INTRA needs at least 14 bit coefficients). Since the Harris spec sheet gives the gate count, the HSP43168 provides a benchmark for estimating the silicon real-estate required to make a Vector-Filter for the INTRA modems in Table 1. (Note that with more parallel cells ---or multiple HSP43168's---, INTRA hardware could easily be designed for gigabit data rates over an appropriate bandwidth.)

Conclusion

These preliminary results are expected to extend to all the modems in Table 1. A low-cost downstream modem for running at over 51.84 Mb/s with >10^-8 BER appears to be a realistic goal for the 802.14WG based on the preliminary designs available for simulation. It was shown that Linear INTRA

Ø should get >10^-8 BER on CATV at up to 65 Mb/s in 6 MHz.
Ø may provide worldwide connectivity of 6 & 8 MHz via 51.84 Mb/s (OC-1).
Ø could be designed for the IF filter specifications so ACI is minimized.
Ø can adapt its rotation matrix to distortions without an equalizer.
Ø might tolerate large non-Gaussian harmonic noise.
Ø probably requires about 40,000 logic gates.

References

[1] Soman, et al, "Linear Phase Paraunitary Filter Banks: Theory Factorizations and Designs; Vol 41 No 12, IEEE Trans SP Dec 1993

[2] P. Fung, "Interface Parameters for CATV Set-top Boxes", Communication Systems Design Mag. Dec 1995.

Note: If included in an IEEE 802.14 standard the Information Transformation (INTRA) technology and INTRA Modems described herein will be licensed on reasonable and non-discriminatory terms and conditions.