ber and mer fundamentals

© 2007 Cisco Systems, Inc. All rights reserved. Cisco Public

BER and MER

Fundamentals 1

BER and MER Fundamentals

Ron Hranac


BER and MER

Fundamentals 2

What is BER?

Graphics courtesy of Trilithic and JDSU


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Fundamentals 3

What is BER?

Errored bit

Received at the CMTS: 010001

Transmitted by the cable modem: 010101

Impulse noise


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BER: The Math

bits) of number (total

)bits errored of number(BER =

period) tmeasuremen x rate (bit

)period tmeasuremen in count error(BER =


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BER Example

� Let’s say that 1,000,000 bits are transmitted, and 3 bits out of the 1,000,000 bits received are errored because of some kind interference between the transmitter and receiver

� BER in this example is calculated by dividing the number of errored bits received by the total number of bits transmitted:

BER = 3/1,000,000 = 0.000003

� Most BER measurements are expressed in scientific notation format, so 0.000003 = 3 x 10-6

� 3 x 10-6 also can be written as 3 x 10^-6 or 3.0E-06


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Scientific Notation

1,000,000 = 1 x 106 or 1.0E06100,000 = 1 x 105 or 1.0E0510,000 = 1 x 104 or 1.0E041,000 = 1 x 103 or 1.0E03100 = 1 x 102 or 1.0E0210 = 1 x 101 or 1.0E011 = 1 x 100 or 1.0E001/10 or 0.1 = 1 x 10-1 or 1.0E-011/100 or 0.01 = 1 x 10-2 or 1.0E-021/1,000 or 0.001 = 1 x 10-3 or 1.0E-031/10,000 or 0.0001 = 1 x 10-4 or 1.0E-041/100,000 or 0.00001 = 1 x 10-5 or 1.0E-051/1,000,000 or 0.000001 = 1 x 10-6 or 1.0E-06


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Pre- and Post-FEC BER

Graphic courtesy of Sunrise Telecom


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� Let’s say that in our earlier example of 3 errored bits received out of 1,000,000 bits transmitted (BER = 3 x 10-6), the receiver’s FEC is able to fix only 2 of the 3 errored bits

� The pre-FEC BER is, of course, the “raw” BER of 3 x 10-6

� The post-FEC BER is 1 x 10-6, since there is still 1 errored bit remaining after the FEC did its magic and fixed the other 2 broken bits

� Most QAM analyzers would report these values as 3.0E-06 and 1.0E-06 respectively


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A Quick Side Note

In reality, a QAM receiver’s Reed-Solomon decoder can easily fix the three bit errors in the previous example, although it is still a good illustration of the principle involved. In fact, the Reed-Solomon decoder in a DOCSIS cable modem can fix any three errored Reed-Solomon symbols in a codeword. This capability is commonly expressed as “t = 3”. Each Reed-Solomon symbol is a group of seven bits. A Reed-Solomon codeword or block consists of 128 Reed-Solomon symbols, of which 122 are actual data symbols and six are “parity” symbols that allow for error correction. It doesn’t matter to the decoder if one bit is wrong in a symbol or if all seven bits are wrong; the symbol is still considered wrong. So, in three erroredReed-Solomon symbols there can be anywhere from a total of three to 21 bit errors. Thus, the Reed-Solomon decoder can correct up to 21 bit errors in a codeword, depending how the bit errors are grouped.


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What’s the BER?

� If we’ve measured a BER of 3.0E-06, is that really the BER?

It depends!

� A major consideration is the number of bits transmitted during the measurement. The greater the number of bits, the better the quality of the BER estimation.

� Ideally, an infinite number of bits will give us a perfect estimate of error probability, but that’s simply not practical!

� So, how many bits are enough?


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� One rule of thumb is that transmitting 3 times the reciprocal of the specified BER without an error gives 95% confidence level that the device or network meets the BER spec.

� If one wants 99% confidence level, the multiplier is 4.61 rather than 3

These multipliers are derived from some gnarly statistics mathematics involving binomial distribution function and Poisson theorem

How Many Bits are Enough?


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� Let’s say we want to ensure the BER at a cable modem’s input is 1 x 10-8 (1.0E-08), at a 95% confidence level.

As mentioned previously, 95% confidence level requires transmitting 3 times the reciprocal of the specified BER withoutan error

� First, let’s figure out the reciprocal of the BER in question:

1/(1 x 10-8) = 1/0.00000001 = 100,000,000

� The required number of bits to be transmitted is 3 x 100,000,000 = 300,000,000

300,000,000 bits is the same as 3 x 108 bits

How Many Bits are Enough?


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� Assume 256-QAM at 42.88 Mbps

3 x 108 bits/42.88 x 106 bits per second = 6.996 seconds

� What about 64-QAM at 30.34 Mbps?

3 x 108 bits/30.34 x 106 bits per second = 9.89 seconds

� If your BER target is something more aggressive like 1 x 10-10 (1.0E-10) at 99% confidence level, the required number of bits that must be transmitted error free is [1/(1 x 10-10)] x 4.61 = 46,100,000,000

� The minimum test time for 256-QAM is 4.61 x 1010

bits/42.88 x 106 bits per second = 1,075 seconds, or 17.9 minutes

How Long Does it Take?


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How is BER Estimation Performed?

Source: Maxim Technical Article HFTA-010.0: “Physical Layer Performance: Testing the Bit Error Ratio (BER)”

� A data source transmits a bit pattern through network or device being tested

� The error detector has to either reproduce the original pattern or somehow directly receive it from the data source

� The error detector compares on a bit-by-bit basis the original pattern with the one received from the device or network being tested


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How is BER Estimation Performed?

� This method is usually an out-of-service test, so it isn’t used very often—at least not on cable networks

� Most QAM analyzers don’t perform BER measurements this way

� Instead, they use an internal algorithm to derive a BER estimate based upon what the FEC is doing

� As noted previously, in a typical QAM analyzer pre-FEC BER is estimated after the Trellis decoder, descrambler (derandomizer), and deinterleaver, but before RS decoding. Post-FEC BER is after RS decoding.


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Factors Affecting BER Estimation

� The type of data sent during a BER measurement can affect the outcome

� A long string of the same bits—say, all 0s—will generally yield different BER numbers than when doing the same measurement with a pseudo-random bit stream (PRBS)

This is unlikely to be a problem with DOCSIS signals: A randomizer or scrambler is used in the data transmitter to make sure all constellation points are approximately equally populated, and that a long string of identical bits isn’t transmitted over the channel

� Why is a long string of the same bits a problem? That long string of identical bits may result in something called deterministic jitter (and other distortions) which could affect the integrity of the BER measurement

� For these reasons, most true BER measurements use a PRBS


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Avoid “False” BER

� Under some circumstances a QAM analyzer might incorrectly indicate the presence of bit errors

� Two typical scenarios are too much or two little RF input signal level

Too much input signal level may overload the QAM analyzer, which causes bit errors to be generated inside the analyzer

Too little input signal level means low carrier-to-noise ratio at the analyzer input, which also causes bit errors to be indicated

� Make sure the QAM analyzer’s RF input levels are within the range specified by the test equipment manufacturer


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A Few Causes of Degraded BER

�Adjacent channel interference

�Spurious signals from other channels

�Sweep transmitter interference

�Laser clipping

� In-channel ingress (including impulse or burst noise)

� Improperly aligned or defective amplifiers (poor CNR, excessive distortions, incorrect levels)

� Improperly installed, loose, damaged or intermittent connections

�Severe impedance mismatches (think micro-reflections, amplitude ripple/tilt, group delay)

� Incorrect signal levels


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What About MER?

� To understand modulation error ratio (MER), we first need to understand the basics of digital modulation!

� Information such as sound (audio), images (video), and digital data can be transmitted from one point to another using radio waves

� This is done by modulating an RF signal—a carrier—with the information to be transmitted

� Modulation is the variation one or more properties of an RF signal to represent the information being transmitted: frequency, amplitude, phase


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Basic Digital Modulation Formats

� FSK—Frequency shift keying: Information is transmitted by shifting between two frequencies to represent zeroes and ones

01


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� ASK—Amplitude shift keying: The amplitude of a carrier is shifted between two states to represent zeroes and ones

01


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� PSK—Phase shift keying: The phase of a carrier is varied between two states to represent zeroes and ones

01

If the phase shift between the two states is 180 degrees, the

modulation is called BPSK, or biphase shift keying


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A Look at Carrier PhaseAmplitude


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More About Carrier Phase

� These graphics represent

RF carriers in the time

domain with different

phases relative to one another. They all have the

same frequency and the

same amplitude.

� Assume that the top

carrier is assigned an

arbitrary phase value of 0°

� The second carrier’s

phase relative to the first one is delayed 45°, the third

carrier is delayed 90°, the

fourth carrier 135°and so on

0°

45°

90°

135°

180°

225°

270°

315°


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Fundamentals 25

Vectors

A vector is a quantity that has magnitude and

direction. Examples of vector quantities include displacement, velocity and force. A vector can be

represented graphically using an arrow. The length of the arrow corresponds to the vector’s magnitude, while the way the arrow points is its

direction.

Two vectors can be added together, or subtracted from each other.

EAST2 miles

+ =0.5 0.5 1

1- =

0.5 0.5

-1+

0.5=

- 0.5

Wind vector graphic courtesy of U.S. Dept. of Commerce/NOAA


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Vector Components

A northwest vector has a northward part, and a westward part

= +

= +

An upward and rightward vector has an upward part, and a rightward part

West

Northw

est

No

rthU

p

Right

Upw

ard &

rightw

ard

=0.707

?0.7

07+

c 2

a2

b2

Adding these kinds of vectors is possible using Pythagorean’s Theorem: a2 + b2 = c2

(0.707)2 + (0.707)2 = 12

1

0.707

0.7

07


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Carrier Phase and Amplitude: A Graphical Representation

0°

180°

We can use a vector to graphically represent an RF

carrier’s relative amplitude and phase. For instance, a horizontal arrow pointing to the right might be used to

represent a carrier of a certain amplitude and phase. We’ll assign an arbitrary phase value of 0º—represented by the angle the arrow is pointing—and an amplitude—

represented by the arrow’s length—of 1.

If we flip the arrow horizontally so that it points the opposite direction, we can say that the carrier phase has

changed 180º from its original value. Note that its amplitude is the same as before.

1

1

Likewise, if we rotate the arrow so that it points up, we can say that the carrier phase has changed 90º from its original value. Here, too, the amplitude is the same as

before.

And we can change the amplitude, but leave the phase unchanged.

90°1

0.5


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A Closer Look at BPSK

≈

1 0 1 0 1 0 1 0 1 0 1 0

Low-pass filter

Oscillator

Balanced amplitudemodulator

Data RF

0° 180° 0° 180°


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A Closer Look at BPSK

1 0 1 0

0° 180° 0° 180°

Bit transmitted

RF envelope

Relative phase

Note phase shift when carrier power goes to zero between bits

Vector representation:


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I/Q Modulation

� Amplitude and phase can be modulated simultaneously and separately to convey more information than either method alone, but is difficult to do

� An easier way is to separate the original signal into a set of independent components or channels: I (In-phase) and Q (Quadrature)

� The I and Q components are considered orthogonalor in quadrature because their phases are separated by 90 degrees

� The I and Q components are summed in a modulator circuit


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Polar vs. Rectangular

Polar display—Magnitude and

phase represented together“I-Q” format—Polar to rectangular

conversion


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Polar vs. Rectangular: An Analogy



conversion

The relationship between polar and rectangular might be considered analogous to directions to get from one’s house to the grocery store. In polar representation, one could say that the

grocery store is “1 mile northeast of the house.” A rectangular representation would describe the store’s location as “0.71 mile east on Main St., then 0.71 mile north on 2nd Avenue.”

1 m

ile n

orthea

st

East

North

West

South

0.71 mile easton Main St.

0.7

1 m

ile n

ort

ho

n 2

nd

Ave

nu

e


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Polar vs. Rectangular: Vectors



conversion

Mag

nitude

= 1

0º

90º

180º

270º

Phase =45º

I value: 0.71

Q value: 0.71

“Q”

“I”

0º

+ =

0.7

12

0.712

12

0.7

1

0.71

1


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I/Q Modulator

� A single carrier generated by a local oscillator (L.O.) circuit is split into two paths.

� One path is delayed by an amount of time equal to ¼ of the carrier’s cycle time, or 90 degrees.

� The second path has no phase shift.

� The two carriers are amplitude modulated—one by the I signal, the other by the Q signal.

� The two modulated carriers are combined in a summing circuit.

� The output is a digitally modulated signal that is the vector sum of the amplitude modulated I and Q signals. The output signal contains amplitude and phase variations.

90°phase shift

Q

I

ΣL.O.

Σ


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QPSK

� QPSK: quadrature phase shift keying

� Quadrature means the signal shifts among phase states that are separated by 90 degrees

� The signal’s phase shifts in increments of 90 degrees from 45°to 135°, 315°, or 225°

� Data into the modulator is separated into two channels called “I” and “Q” (in-phase and quadrature)

� Two bits are transmitted simultaneously, one per channel


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QPSK

� Each channel amplitude modulates a carrier

The two carrier frequencies are the same, but their phases are offset by 90 degrees—that is, they are “in quadrature”

� The two amplitude modulated carriers are combined and transmitted

� The resulting RF signal is a double-sideband, suppressed carrier signal, and is the vector sum of the original two “I” and “Q” carriers

� QPSK has four states because 22 = 4

2n is the total number of symbol states required to represent all possible bit combinations (n = number of bits/symbol)

� Theoretical bandwidth efficiency is two bits/second/Hz


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A Closer Look at QPSK Modulation

≈Low-pass filter

Oscillator

Balanced amplitude

modulator

90º phase shift

≈

Low-pass filter

Balanced amplitude

modulator

••

•Σ

0°180° 0°180°

0 1 0 1

0 0 1 1

90° 90°270°270°

225° 315° 135° 45°

00 10 01 11

0 1 0 10 1 0 1

0 0 1 1

0 0 1 1

0 0 1 0 0 1 1 1

Half of the bits go to

the I channel

The other half of the bits

go to the Q channel


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QPSK Symbol Mapping


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QPSK Constellation

Symbol Transmitted

Carrier Envelope Phase

Carrier Envelope Amplitude

00 225° 1.0

01 135° 1.0

10 315° 1.0

11 45° 1.0

I

Q

45°

0°

90°

135°

180°

225°

270°

315°


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QPSK Constellation

Symbol Transmitted

Carrier Phase Carrier Amplitude

00 225° 1.0

01 135° 1.0

10 315° 1.0

11 45° 1.0

Q

I

90°

45°

0°

315°

270°

135°

180°

225°


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QPSK Constellation

Symbol Transmitted


00 225° 1.0

01 135° 1.0

10 315° 1.0

11 45° 1.0

90º phase shift

(225º to 135º)

Q

I

90°

45°

0°

315°

270°

135°

180°

225°


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QPSK Constellation

Symbol Transmitted


00 225° 1.0

01 135° 1.0

10 315° 1.0

11 45° 1.0

180º phase shift

(135º to 315º)

Q

I

90°

45°

0°

315°

270°

135°

180°

225°


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QPSK Constellation

Symbol Transmitted


00 225° 1.0

01 135° 1.0

10 315° 1.0

11 45° 1.0

90º phase shift

(315º to 45º)

Q

I

90°

45°

0°

315°

270°

135°

180°

225°


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Fundamentals 44

16-QAM

� 16-QAM: 16-state quadrature amplitude modulation

� Four I values and four Q values are used, yielding four bits per symbol

� 16 states because 24 = 16

� Theoretical bandwidth efficiency is four bits/second/Hz


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16-QAM

� Data is spit into two channels, I and Q

� As with QPSK, each channel can take on two phases. However, 16-QAM also accommodates two intermediate amplitude values!

� Two bits are routed to each channel simultaneously

� The two bits to each channel are added, then applied to the respective channel’s modulator

� Each channel uses amplitude modulation

� The resulting RF signal is a double-sideband, suppressed carrier signal. It is the vector sum of the original two carriers, and has phase and amplitude variations.


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16-QAM Constellation

I

QSymbol

TransmittedCarrier Phase Carrier

Amplitude

0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0

0°

90°

180°

270°

45°

315°225°

135°


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Fundamentals 47


Symbol Transmitted


0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0

I

Q


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Fundamentals 48


I

QSymbol Transmitted


0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0


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Fundamentals 49


I

QSymbol Transmitted


0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0


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Fundamentals 50


I

QSymbol Transmitted


0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0


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Fundamentals 51


I

QSymbol Transmitted


0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0


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Fundamentals 52


I

QSymbol Transmitted


0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0


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Fundamentals 53


I

QSymbol Transmitted


0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0


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Fundamentals 54


I

QSymbol Transmitted


0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0


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I

QSymbol Transmitted


0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0


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I

QSymbol Transmitted


0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0


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I

QSymbol Transmitted


0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0


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I

QSymbol Transmitted


0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0


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Fundamentals 59


I

QSymbol Transmitted


0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0


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I

QSymbol Transmitted


0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0


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I

QSymbol Transmitted


0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0


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Fundamentals 62


I

QSymbol Transmitted


0000 225° 0.33

0001 255° 0.75

0010 195° 0.75

0011 225° 1.0

0100 135° 0.33

0101 105° 0.75

0110 165° 0.75

0111 135° 1.0

1000 315° 0.33

1001 285° 0.75

1010 345° 0.75

1011 315° 1.0

1100 45° 0.33

1101 75° 0.75

1110 15° 0.75

1111 45° 1.0


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16-QAM Symbol Mapping

Gray-Coded Symbol Mapping


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Fundamentals 64

16-QAM Symbol Mapping

Differential-Coded Symbol Mapping


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Fundamentals 65

64-QAM Digitally Modulated Signal

Frequency domain:Amplitude versus frequency

Time domain:Amplitude versus time

=

Spectrum analyzer view Oscilloscope view


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Fundamentals 66

What About Impairments?

This is what is transmitted—the RF

signal’s instantaneous amplitude and

phase represent the symbol “11”

I

Q


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Fundamentals 67


This is what is received after noise randomly

mixes with the transmitted signal

somewhere in the transmission path.

Because the received RF signal’s phase and amplitude didn’t change very much from

what was actually transmitted, the data

receiver interprets the signal as “11”.

I

Q


BER and MER

Fundamentals 68


I

Q

The next time the symbol “11” is transmitted,

the RF signal randomly mixes with noise

again. But this time the received signal’s

amplitude is a little lower, and the phase is shifted slightly. The received phase and

amplitude are still close enough to the ideal

position to be interpreted by the data receiver

as “11”.


BER and MER

Fundamentals 69


The same symbol transmitted multiple times mixes randomly each time with

noise in the transmission path. As a

result, each received symbol’s plotted position on the constellation is slightly

different. In this example, all of the

received signals’ phases and

amplitudes are able to be interpreted

as “11”.

I

Q


BER and MER

Fundamentals 70


Here a large burst of noise mixes with the RF signal, causing the received

phase and amplitude to be outside of

the “decision boundary” for the desired

symbol. The data receiver is not able to correctly interpret the received

signal as “11”, so an error occurs. As

we shall see, this generally does not affect MER!

I

Q


BER and MER

Fundamentals 71

Modulation Error Ratio: Modulation Quality

Modulation error

Transmitted (or received)symbol

Target symbol

Q

I

Modulation error = Transmitted symbol – Target symbol

Source: Hewlett-Packard


BER and MER

Fundamentals 72

Modulation Error Ratio

MER = 10log(average symbol power/average error power)

Average symbol

power

I

Q

Average error power

+

+

=

∑

∑

=

=

N

jjj

N

jjj

QI

QIMER

1

22

1

22

10log10

δδ

In effect, MER is a measure of how

“fuzzy” the symbol points in a constellation are.

Source: Hewlett-Packard


BER and MER

Fundamentals 73

Modulation Error Ratio

I

Q

I

Q

A large “cloud” of symbol points means low MER—this is not good!

A small “cloud” of symbol points means high MER—this is good!


BER and MER

Fundamentals 74

MER MeasurementsModulation Format Lower ES/N0

ThresholdUpper ES/N0

Threshold

QPSK 7–10 dB 40–45 dB

16 QAM 15–18 dB 40–45 dB

64 QAM 22–24 dB 40–45 dB

256 QAM 28–30 dB 40–45 dB

Good… Not so good…

Graphics courtesy of Filtronic Sigtek


BER and MER

Fundamentals 75

A Few Causes of Degraded MER

�Transmitted phase noise

�Low carrier-to-noise ratio

�Non-linear distortions (CTB, CSO, XMOD, CPD…)

�Linear distortions (micro-reflections, amplitude ripple, group delay)

� In-channel ingress

�Laser clipping

� Improperly aligned or defective amplifiers

�Severe impedance mismatches (see linear distortions)

� Incorrect signal levels

�Data collisions

� Improper modulation profiles


BER and MER

Fundamentals 76

A Few Causes of Degraded MERTransmitted phase noise



BER and MER

Fundamentals 77

A Few Causes of Degraded MERLow carrier-to-noise ratio

Graphic courtesy of Trilithic


BER and MER

Fundamentals 78

A Few Causes of Degraded MERNon-linear distortions (CTB, CSO, XMOD, CPD…)



BER and MER

Fundamentals 79

A Few Causes of Degraded MERLinear distortions (micro-reflections, amplitude ripple, group delay)



BER and MER

Fundamentals 80

A Few Causes of Degraded MERIn-channel ingress

Graphic courtesy of JDSU


BER and MER

Fundamentals 81

A Few Causes of Degraded MERLaser clipping



BER and MER

Fundamentals 82

A Few Causes of Degraded MER

Cable3/0 Upstream 0 is up Frequency 25.392 MHz, Channel Width 3.200 MHz, QPSK Symbol Rate 2.560 MspsSpectrum Group is overriddenBroadCom SNR_estimate for good packets - 26.8480 dBNominal Input Power Level 0 dBmV, Tx Timing Offset 2035

Data collisions or improper modulation profiles

The CMTS’s reported upstream “SNR” actually is MER


BER and MER

Fundamentals 83

Downstream Performance: QAM Analyzer

Pre- and post-FEC BER

MER64-QAM: 27 dB minimum

256-QAM: 31 dB minimum

Constellation

Graphics courtesy of Trilithic and Sunrise Telcom


BER and MER

Fundamentals 84


In this example, digital channel power, MER and the constellation are fine, but pre- and post-FEC BER indicate a problem—perhaps sweep transmitter interference, downstream laser clipping, an upconverter problem in the headend, or a loose connection.



BER and MER

Fundamentals 85

Troubleshooting—Integrated Upconverter

� Verify correct average power level

Integrated upconverter RF output should be set in the DOCSIS-specified +50 to +61 dBmV range

Typical levels are +55 to +58 dBmV

� Also check BER, MER and constellation

CMTS

88-860 MHz downstreamRF output

(+50 dBmV to +61 dBmV)

Attenuator(if required)

To headend downstream

combiner


BER and MER

Fundamentals 86

Troubleshooting—External Upconverter

� Verify correct average power level, BER, MER and constellation

CMTS downstream IF output

External upconverter IF input

External upconverter RF output

CMTS

RF upconverter

88-860 MHz downstream

RF output to CATV network

(+50 dBmV to +61 dBmV)

Attenuator44 MHz downstream

IF output

(e.g., +42 dBmV +/-2 dB)

44 MHz IF input to

upconverter

(typ. +25 dBmV to +35

dBmV)


BER and MER

Fundamentals 87

Combiner Output and Fiber Link

� Check signal levels and BER at downstream laser input and node output

Bit errors at downstream laser input but not at CMTS or upconverter output may indicate sweep transmitter interference, loose connections or combiner problems

Bit errors at node output but not at laser input are most likely caused by downstream laser clipping


BER and MER

Fundamentals 88

Out in the Field…

� If everything checks out OK at the node, go to an affected subscriber’s premises.

� Measure downstream RF levels, MER and BER, and evaluate the constellation for impairments. Look at the adaptive equalizer graph, in-channel frequency response and group delay. If your QAM analyzer supports it, repeat these measurements in the upstream.

� Measure upstream transmit level and packet loss

� Use the “divide-and-conquer” technique to locate the problem


BER and MER

Fundamentals 89

What’s Good?

� BER: Ideally, there should be no measurable bit errors shown on the QAM analyzer, anywhere in the system!

DOCSIS assumes a worst-case post-FEC BER at the cable modem input of 1 x 10-8 (1.0E-08) at specified RF input levels and carrier-to-noise ratios

� MER: The higher the better!

Good engineering practice says to keep unequalized MER 3 to 6 dB above the unequalized MER “failure threshold” for the modulation type in use

Many cable operators use the following unequalized MER values as minimum acceptable operational values: QPSK ~18 dB; 16-QAM ~24 dB; 64-QAM ~27 dB; and 256-QAM ~31 dB


BER and MER

Fundamentals 90

The Takeaway?

� BER and MER are not the same thing!

� BER is an estimation of the ratio of the number of erroredbits to the total number of bits, typically expressed in scientific notation.

� MER is, in effect, a measure of the “fuzziness” of a data constellation’s symbol landings, and is expressed in dB. MER is somewhat analogous to baseband signal-to-noise ratio.

� Both BER and MER should be measured. The two together tell a more complete story than either by itself.

ber and mer fundamentals

Documents

downstream

resulting

phase represented

suppressed

ber estimation

rf signal

graphic courtesy

data receiver