1. Relationships Among EVM, BER and SNR. 2. WiFi minimum SNR consideration 3. Relation between PER and BER

1. 1
Relationships Among EVM,
BER and SNR
+
WiFi minimum SNR
consideration
Jay Chang

2. Eb/N0 summery
the energy per bit to noise power spectral density ratio, dimensionless.
It is a normalized signal-to-noise ratio (SNR) measure, also known as the "SNR per bit".
Eb/N0 directly indicates the power efficiency of the system without regard to modulation type,
error correction coding or signal bandwidth.
But when the signal bandwidth is well defined, Eb/N0 is also equal to the signal-to-noise ratio (SNR)
in that bandwidth divided by the "gross" link spectral efficiency in [bps/Hz], where the bits in this
context refer to user data bits, irrespective of error correction information and modulation type.
Eb/N0 must be used with care on interference-limited channels since additive white noise (with
constant noise density N0) is assumed, and interference is not always noise-like.
Eb/N0 SNR relation
Eb/N0 Es/N0 relation P.S. (Es/N0) energy per symbol to noise power spectral density
2
0 0
M is the # of alternative modulation symbols, e.g. M 4 for QPSK and M 64
log
for 64-QAM.
s bE E
M
n n
= =
=
https://en.wikipedia.org/wiki/Eb/N02

3. Eb/N0
2
0 0
logs bE E
M
n n
= for digital modulation schemes
or called noise spectrum density
3

4. Eb/N0
4

5. Relationships Among EVM, BER and SNR as Performance Metrics
2
0
2
0
M is the # of alternative modulation symbols,
e.g. M 4 for QPSK and M 64 for 64-QAM.
log in
l
above equatio
o
n.
gs bE E
M
N
L M
N
= =
=
=
For high SNR BER of M-ary QAM can be
approximated by neglecting some of the higher order terms
same
1
( )
2 2
x
Q x erfc
 
=  
 
http://ieeexplore.ieee.org/document/4178493/
http://ieeexplore.ieee.org/document/883298/
2
0 0 0
10 10 2 10 2
0 0
now , and log
or SNR [in dB] 10log 10log log 10log ( log )
in above equations.
b s b
s b
E E E
r M
N N N
E E
M r M
N N
= =
   
= = =   
   
5https://www.keysight.com/main/editorial.jspx?ckey=847674&id=847674&nid=-11143.0.00&lc=eng&cc=UG

6. 6
由由由由cisco這篇文獻這篇文獻這篇文獻這篇文獻SNR Requirements_cisco.pdf得知得知得知得知

7. The receiver minimum sensitivity test ensures a device under test (DUT) is able to receive data with a
defined maximum packet error rate (PER) of 10% at a defined minimum signal power.
The minimum signal power depends on the channel bandwidth and modulation and coding scheme
(MCS) as specified in Table 22-25 of the IEEE 802.11ac standard (attached next page).
When the test is performed with hardware, each input antenna port on the DUT is connected
through a cable to a single output antenna port of a transmitter.
The following transmission parameters are specified for the test waveform:
• The number of spatial streams is equal to the number of transmitting antenna ports
• PSDU length of 4096 bytes (= 32768 bits)
• No space-time block coding (STBC)
• 800 ns guard interval
• Binary convolutional coding
WIFI RX Sensitivity
7

8. In IEEE Std
8

9. Error Vector Magnitude, EVM = Relative Constellation Error, RCE
SNR [in dB] EVM [in power dB]= −
RCE [in power dB]
9

10. Relation between PER and BER
60.1
3 10
32768
eP −
= ≈ ×
10

11. BER versus Eb/N0 using python theoretical simulation
11

12. 60.1
3 10
32768
eP −
= ≈ ×
BER versus Eb/N0 using python compare Figure 3. in paper
http://ieeexplore.ieee.org/document/883298/
12
WIFI的SNR min =
抓上面Pe~3E-6時對
應的SNR/bit + 3-5
dB 不同coder ate的
margin.
Std 802.11ac

13. 13
Thank you for your attention