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# Calculating Theoretical Cable Line Card Throughput

## Calculating Throughput on Downstream and Upstream by Modulation Profiles

TAC Carrier Services  1/29/2008

Objective:

Calculate the theoretical throughput given a cable modulation profile

Components:

UBR10K with Cable Line Cards Online Cable Modems

Overview:

Cable technology allows for different modulation profiles in the downstream and upstream transmissions. These profiles are specified in the DOCSIS specifications [2]. For DOCSIS 1.1 the modulation used for the downstream can be 256 QAM or 64 QAM. For DOCSIS 1.1 the upstream modulation profile for the upstream can be QPSK or 16QAM. Depending on the current IOS version, you may be able to use other modulation profiles. As of the 12.3(21a)BCx train you are allowed to do 64QAM in the upstream direction.

Upstream modulation profiles can be programmed into the CMTS. You have the capacity of determining different modulation profiles [1]. Given a modulation type and channel width you will be able to calculate the throughput. Let the UBR calculate the symbol rate for you and use the modulation type to compute the throughput. Keep in mind the symbol rate is directly proportional to the channel width. The general formula is:

`( x bits / symbol ) * (Symbol Rate) = Throughput`

The bits per symbol are determined by the modulation profile. Recall that QPSK is capable of representing 2bits per symbol. QPSK is two bits per symbol because of each quadrant in the QPSK symbol can represent one value. Four quadrants implies four values which implies 2 bits of information. On the same note 64QAM can represent 6 bits per symbol because each quadrant can represent 16 values:

`QPSK => 2bits16QAM => 4 bits64QAM => 6 bits256QAM => 8 Bits`

A few examples:

`Cable5/0/0 Downstream is upFrequency 609.0000 MHz, Channel Width 6 MHz, 64-QAM, Symbol Rate 5.056941 Msps...`

In the above case, the downstream is passing about 5.05Msym/sec, 64-QAM means 2^6 means 6 bits per symbol.

`(6 bits/symbol) * (5.05 M symbol/sec) = 30 Mbits/sec.`

Now for the Upstream:

`Cable5/0/0 Upstream 0 is upFrequency 29.008 MHz, Channel Width 1.600 MHz, QPSK Symbol Rate 1.280 Msps...`
`(2 bits/symbol) * (1.28 M symbol/sec) = 2.56 M bits/sec`

Here is an additional Explanation taken from the Cable RF FAQ[3]:

Q. What is the correlation between the minislot size and channel widths?

A. The minislot size and the channel width are related to a certain degree, but are not tightly coupled. You may already know that minislot size is in units of ticks, and each tick is defined to be 6.25 microseconds (μs). The channel width is just another way of saying symbol rate. They are related in the sense that, with modulation format (Quadrature Phase-Shift Keying [QPSK] or 16-quadrature amplitude modulation [QAM]) fixed, the higher the symbol rate, the more symbols can fit a chosen minislot size. For example, assuming QPSK, a minislot of 8 ticks can carry 64 symbols at 1280 ksym rate, or 128 symbols at 2560 ksym rate. Thus, the minislot size can also be expressed in terms of symbols or bytes. But a change of symbol rate does not always imply a change of minislot size, unless a certain minislot size is not valid after the symbol rate change. The minislot sizes are lower-bounded by the Data-over-Cable Service Interface Specifications (DOCSIS)—32 symbols—and upper-bounded by Broadcom cable modem termination system (CMTS) PHY chip (BCM3137)—256 symbols. All possible minislot sizes are:

QPSK             |           16-QAM

2560  1280  640  320  160  | 2560  1280  640  320  160 (ksym/s)

(us)  (ticks)        (bytes)              | (bytes)

---   ------   ----  ----  ---  ---  ---  | ----  ----  ---  ---  ---

12.5  2        8     -     -    -    -    | 16    -     -    -    -

25    4        16    8     -    -    -    | 32    16    -    -    -

50    8        32    16    8    -    -    | 64    32    16   -    -

100   16       64    32    16   8    -    | 128   64    32   16   -

200   32       -     64    32   16   8    | -     128   64   32   1

400   64       -     -     64   32   16   | -     -     128  64   32

800   128      -     -     -    64   32   | -     -     -    128  64

If your CMTS is at QPSK, 1280 ksym rate and 8 ticks minislot size, and then you change the symbol rate to 640 ksym, the minislot size is still valid. But if you change the symbol rate to 320 ksym, the minislot size becomes invalid; if this occurs, the CMTS changes the minislot size accordingly.

Resources:

[1] US Modulation Profile Guide: [[1]]

[2] DOCSIS Specifications Page: [[2]]

[3] Cable RF FAQ : [[3]]

Verification & Troubleshooting:

`Show cable modem verboseShow controller cable x/x/x`
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