ber and mer fundamentals
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© 2007 Cisco Systems, Inc. All rights reserved. Cisco Public
BER and MER
Fundamentals 1
BER and MER Fundamentals
Ron Hranac
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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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Fundamentals 4
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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Fundamentals 5
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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Fundamentals 6
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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Fundamentals 7
Pre- and Post-FEC BER
Graphic courtesy of Sunrise Telecom
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Fundamentals 8
Pre- and Post-FEC BER
� 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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Fundamentals 9
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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Fundamentals 10
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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Fundamentals 15
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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Fundamentals 16
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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Fundamentals 17
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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Fundamentals 18
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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Fundamentals 19
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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Fundamentals 20
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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Fundamentals 21
Basic Digital Modulation Formats
� ASK—Amplitude shift keying: The amplitude of a carrier is shifted between two states to represent zeroes and ones
01
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Fundamentals 22
Basic Digital Modulation Formats
� 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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Fundamentals 23
A Look at Carrier PhaseAmplitude
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Fundamentals 24
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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Fundamentals 26
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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Fundamentals 27
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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Fundamentals 28
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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Fundamentals 29
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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Fundamentals 30
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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Fundamentals 31
Polar vs. Rectangular
Polar display—Magnitude and
phase represented together“I-Q” format—Polar to rectangular
conversion
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Fundamentals 32
Polar vs. Rectangular: An Analogy
Polar display—Magnitude and
phase represented together“I-Q” format—Polar to rectangular
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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Fundamentals 33
Polar vs. Rectangular: Vectors
Polar display—Magnitude and
phase represented together“I-Q” format—Polar to rectangular
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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Fundamentals 34
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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Fundamentals 35
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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Fundamentals 36
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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Fundamentals 37
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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Fundamentals 38
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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Fundamentals 40
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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Fundamentals 41
QPSK Constellation
Symbol Transmitted
Carrier Phase Carrier Amplitude
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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Fundamentals 42
QPSK Constellation
Symbol Transmitted
Carrier Phase Carrier Amplitude
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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Fundamentals 43
QPSK Constellation
Symbol Transmitted
Carrier Phase Carrier Amplitude
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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Fundamentals 45
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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Fundamentals 46
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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16-QAM Constellation
Symbol Transmitted
Carrier 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
I
Q
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16-QAM Constellation
I
QSymbol Transmitted
Carrier 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
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16-QAM Constellation
I
QSymbol Transmitted
Carrier 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
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16-QAM Constellation
I
QSymbol Transmitted
Carrier 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
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Fundamentals 51
16-QAM Constellation
I
QSymbol Transmitted
Carrier 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
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16-QAM Constellation
I
QSymbol Transmitted
Carrier 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
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Fundamentals 53
16-QAM Constellation
I
QSymbol Transmitted
Carrier 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
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Fundamentals 54
16-QAM Constellation
I
QSymbol Transmitted
Carrier 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
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Fundamentals 55
16-QAM Constellation
I
QSymbol Transmitted
Carrier 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
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16-QAM Constellation
I
QSymbol Transmitted
Carrier 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
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Fundamentals 57
16-QAM Constellation
I
QSymbol Transmitted
Carrier 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
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Fundamentals 58
16-QAM Constellation
I
QSymbol Transmitted
Carrier 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
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Fundamentals 59
16-QAM Constellation
I
QSymbol Transmitted
Carrier 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
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Fundamentals 60
16-QAM Constellation
I
QSymbol Transmitted
Carrier 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
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Fundamentals 61
16-QAM Constellation
I
QSymbol Transmitted
Carrier 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
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Fundamentals 62
16-QAM Constellation
I
QSymbol Transmitted
Carrier 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
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Fundamentals 63
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
What About Impairments?
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
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Fundamentals 68
What About Impairments?
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”.
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Fundamentals 69
What About Impairments?
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
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Fundamentals 70
What About Impairments?
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
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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
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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
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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!
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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
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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
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Fundamentals 76
A Few Causes of Degraded MERTransmitted phase noise
Graphic courtesy of Sunrise Telecom
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Fundamentals 77
A Few Causes of Degraded MERLow carrier-to-noise ratio
Graphic courtesy of Trilithic
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Fundamentals 78
A Few Causes of Degraded MERNon-linear distortions (CTB, CSO, XMOD, CPD…)
Graphic courtesy of Trilithic
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Fundamentals 79
A Few Causes of Degraded MERLinear distortions (micro-reflections, amplitude ripple, group delay)
Graphic courtesy of Sunrise Telecom
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Fundamentals 80
A Few Causes of Degraded MERIn-channel ingress
Graphic courtesy of JDSU
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Fundamentals 81
A Few Causes of Degraded MERLaser clipping
Graphic courtesy of Sunrise Telecom
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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
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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
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Fundamentals 84
Pre- and Post-FEC BER
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.
Graphic courtesy of Trilithic
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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
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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)
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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
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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
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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
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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.
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