IEEE 802.14-96/127

 

TITLE: INTRA Characteristics
AUTHOR: Bill Miller

ABSTRACT: Upstream INTRA performance with clipping is presented with implications for laser clipping models. Design characteristics and architectures for Upstream and Downstream modems are discussed including an INTRA receiver that uses SAW filters instead of multipliers and A/D converters.

The following paper is based on Document # IEEE 802.14-96/127 prepared to assist and submitted to the IEEE 802.14 WG Cable TV Protocol Working Group April 24, 1996.

Upstream

An example of an INTRA design was given in IEEE 802.14-96/097 and is repeated in Figure 1 and 2 below.

Figure 1a. An all-digital Upstream transmitter

Another variation of Figure 1 is shown in Figure 2 that may be less cost for more than 2 bits per symbol.

Figure 1b. A variation of Fig. 1a

The coefficients for the tap matrices can be easily derived from a much smaller table than is indicated in Figure 1 so that a RAM for one band instead of a the ROM design shown might be better. This would also allow the modem to pre-equalize (for microreflections) or, to reconfigure the number of bands and bandwidth of each band to dynamically match the MAC layer requirements.

These are , of course, just two of many ways to implement a vector filter. The general form of a vector filter transmitter and receiver is illustrated in Figure 2 for 4 tap matrices performing the rotation of coordinates.

 

Figure 2. Vector Filtering

Each data input at the left of Figure 2 corresponds to a sub-band. As symbols pass thru the filter they generate wavelets, which are the impulse responses of the sub-band filters. By design, the wavelets are (nearly) orthogonal to all other symbols on the same sub-band and on all other sub-bands. Since the transmitted signal has an orthogonal composition, the vector filter on the right of Figure 2 can counter-rotate the vector of A/D samples to recover the vector of data symbols.

The number of taps in the vector filter controls the stopband attenuation up to the limit of the coefficient precision (16-bit coefficients have been assumed). Figures 3a and 3b illustrate the effect of using 9 taps on a 12 band and a 42 band design respectively. Both designs have about -95db stopband attenuation in each sub-band filter although one uses 3MHz modem spacing and the other (Fig 3b) uses 1MHz modem spacing . The modem spacing is shown by superimposing two filter response curves (db vs MHz) for adjacent modems (one solid and one dotted curve). Overlapping impulse responses (wavelets) are orthogonal.

Figure 3a. 3 MHz spacing

Figure 3b. 1 MHz spacing

As can be seen from Figure 3, the sample rate and number of sub-bands can be varied to determine the modem spacing (Fig 3a uses 72MHz and 3b uses 84MHz) for a wide range of designs. Because of the overlapping of bands, the bandwidth efficiency of INTRA for a CATV network using all the upstream bandwidth exceeds the efficiency for n-QAM.

The stopband attenuation in Figure 3 may be useful for broadcast but is certainly unnecessary for CATV, so the number of taps can be reduced to 5 or 6 by truncating the taps (coefficients) farthest from the center (these designs use linear phase filters). Furthermore, the resulting stopband attenuation is only one parameter of interest, so optimization is done. An LMS adaption of the coefficients by a simulated modem receiver is a simple way to optimize. Alternatively, the correlation functions and response can be used.

The auto-correlation of each filter's impulse response evaluated at multiples of M contributes to the Inter-Symbol Interference (ISI) of a single modem, while the cross-correlations at n*M of adjacent bands contributes to the Adjacent Channel Interference (ACI) from overlapping modems. Note also that these correlation functions when evaluated at small deviations from multiples of M determine the change in BER due to timing jitter at the receiver. The long length of a symbol' s wavelet and its sharp auto-correlation near sync allows ranging to a fraction of a sample time for this type of modem.

Laser Clipping

The models for laser clipping are still under investigation. A simple burst noise source does not seem to describe the affects on the modems responsible for the clipping. To study the clipping for INTRA modems, a combination of 3 adjacent modems with 1 MHz spacing was simulated using a 72MHz sample rate and 6 taps. Each modem produced 4 MB/s for a total of 12 MB/s. The transmitter output is shown in Figure 4a and the assumed ingress is shown in Figure 4b. At this PSD laser clipping should not occur but it was forced for simulation purposes by clipping the input to the receiver.

Fig 4a. Transmitter Outputs (3x4 MB/s)

Fig 4b. Ingress Noise

Figure 4c shows the resulting Rx PSD after clipping compared to the unclipped PSD shown in Figure 4d. Clipping causes non-uniform clipping noise, which appears as humps in Figure 4c . The histograms in Figures 4e and 4f show how the clipping was accomplished by limiting all A/D inputs above 1.5 and below -1.0 millivolts.

Fig 4c. Received Signal with Clipping	Fig 4d. Receive Signal without clipping
Fig 4e. A/D Output showing clipping	Fig 4f. A/D output without clipping
Fig 4g. Coefficient adaption with clipping	Fig 4h. Coefficient adaption w/o clipping

The transmit wavelets were not optimized before transmission, but instead the receiver was allowed to adapt its coefficients using an LMS update over 500 vector frames (3000 bits). The adapted coefficients were then saved and used to find the RMS error for the entire 3000 bits. The peak errors in RMS Figure 4g are not much larger than the 3 std deviations (as in guassian statistics), and using the adapted values with a change of the seed gives about the same result as in Table 1.

Table 1 RMS error margin
Band (MHz)	9-10	10-11	11-12
with clipping	7.64%	7.46%	6.48%
without clipping	4.34%	3.97%	2.03%

Since (guassian) error margins of over 17% still give BER >10^-8, the limiting apparently did not greatly affect INTRA's performance. INTRA correlates each symbol over many samples so the clipped input samples do not cause errors. But clipping produces the out-of-band noise humps seen in Figure 4c. This out-of-band noise may not be truly random noise and the channel model for laser non-linearity may have to model clipping appropriately.

Downstream

Since multipliers and A/D converters contribute to the cost of a downstream modem, it is worth noting that an INTRA receiver doesn't need multipliers or A/Ds. Figure 5 illustrates a 45 MB/s modem operating in a 6 MHz downstream CATV channel. Surface Wave Acoustic filters counter-rotate the INTRA signal at IF frequency. This is then thresholded at the low 1 1/2 MHz symbol rate using a strobe dervived from the sync bit's peak correlator output. By the definition given in 802.14-96/014 the computational complexity factor is zero.