9/10/15 COMP 635: WIRELESS NETWORKS
NOISE, INTERFERENCE, &
DATA RATES
Jasleen Kaur
Fall 2015
1 Power Terminology
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dB – Power expressed relative to reference level (P0)
= 10 log10 (Psignal / P0)
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J: Can conveniently represent very large or small numbers
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J: multiplication of ratios can be done by simply adding or
subtracting
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L: complicates addition and subtraction
dBm = 10 log10 (Psignal / 1 mW) – Power in dB relative to 1 mW
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1 mW = 0 dBm
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30 dBm = 1 W
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40 dBm = 100 W
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80 dBm = 100 kW
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SNR – Signal-to-Noise Ratio (dB) = Psignal / Pnoise
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PAPR – Peak-to-Average Power Ratio (typically, dB)
2 © Jasleen Kaur, 2015 1 9/10/15 Typical Transmission Power Levels
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80 dBm (100 kW) – FM radio station with 50 km range
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60 dBm (1 kW) – Microwave oven (leak ~ -60 dBm, 1 nW)
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50 dBm (100 W) – total thermal radiation emitted by a
human body
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40 dBm (10 W) – Power Line Carrier transmit power
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21 - 33 dBm (125 mW - 2 W) – Mobile Phones
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15 - 30 dBm (32 mW - 1 W) – Wireless LANs
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0 - 20 dBm (1 - 100 mW) – Bluetooth radio
3 Typical Receive Signal Power
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© Jasleen Kaur, 2015 Receive Signal Power:
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7 dBm (5 mW) – AM receiver
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-100,-10 dBm (0.1 pW, 100 µW) – min,max of 802.11 variants
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-60 dBm (1 nW) – magnitude +3.5 star, rcvd per m2 of Earth)
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-127.5 dBm (0.178 fW) – from GPS satellite
“Thermal Noise” Power (frequency-dependent):
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-92 to -101 dBm – WLAN channels
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-111 dBm – commercial GPS channel
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-114 dBm – Bluetooth channel
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-121 dBm – GSM channel
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-132.24 dBm – one LTE subcarrier (15 KHz)
4 2 9/10/15 Shannon Limits: Noise & Data Rates
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Channel capacity:
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Max rate of information transfer over a given channel
When channel is only impaired by Gaussian white noise,
C = BW * log2 (1 + S/N)
§ BW – bandwidth available for communication
§ S – received signal power
§ N – power of white noise
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Factors fundamentally limiting data rate:
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S/N – signal-to-noise-ratio
BW – available bandwidth
5 Shannon Limits: Noise, BW, Data Rates
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Channel capacity: C = BW * log2 (1 + S/N)
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Factors fundamentally limiting data rate: S/N & BW
Assume communication with information rate, R
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Received signal power can be expressed as: S = Eb * R
§ Eb – received energy per information bit
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Noise can be expressed as: N = N0 * BW
§ N0 – constant noise power spectral density (W/Hz)
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R ≤ C = BW * log2[1 + (Eb*R)/(N0*BW)]
§ ρ ≤ log2[1 + ρ * Eb/N0]
– ρ: radio-link bandwidth utilization (R/BW)
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Lower bound on required received energy per info bit:
Eb/N0 ≥ 2ρ – 1 / ρ
6 © Jasleen Kaur, 2015 3 9/10/15 Min Required Energy & BW Utilization
Bandwidth u=liza=on (ρ = R/BW) q
Eb/N0 ≥ 2ρ – 1 / ρ ;
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When ρ << 1, Eb/N0 is relatively constant, regardless of ρ
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S = Eb * R;
Given N0, min signal power increases linearly with data rate
When ρ > 1, Eb/N0 increases rapidly with ρ
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Increase in R (and not BW), implies much larger increase in S
7 Implications for Noise-limited Scenarios
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When noise is the main source of radio-link impairment,
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Data rate always limited by available S/N
§ Any increase in R will require at least same increase in S
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Power-limited Operation: when R << BW,
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If sufficient S available, any R can be provided, given a BW
Increase in R requires same increase in S
Increase in BW doesn’t impact the S required for a given R
Bandwidth-limited Operation: R > BW,
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Any increase in R, requires a much larger increase in S
§ Unless BW is increased in proportion to increase in R
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Increase in BW reduces the S required for a given R
For efficient use of available S/N,
BW should be at least same order as R to be provided
8 © Jasleen Kaur, 2015 4 9/10/15 How to Increase Received S/N?
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By reducing distance between transmitter and receiver
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Reduces attenuation as signal propagates
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Achievable data rates can be increased by reducing range
§ Reduced cell sizes in cellular networks
§ Especially when R is same order (or larger) than BW
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Alternatively, high R available only in center of cell
§ Not over entire cell area
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By using additional antennas
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Multiple receiver antennas (spatial diversity)
§ Reduces S/N
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Multiple transmit antennas (beam-forming)
§ Boosts S
9 Increasing S/N: Multiple Antennas
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By using additional receive antennas (spatial diversity)
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Antenna diversity helps mitigate multipath loss situations
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Offer several observations of the same signal
§ Can be combined to better estimate transmitted signal
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S/N can be increased proportional to # of receive antennas
By using multiple transmit antennas (beamforming)
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Focus a given total transmit power in receiver direction
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Signals reach antenna elements at different times
§ Phases adjusted to achieve “constructive” superposition
– In direction of receiver (only)
10 © Jasleen Kaur, 2015 5 9/10/15 Multiple-Input Multiple-Output (MIMO)
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Multiple transmit (or receive) antennas efficient only
when R is power-limited (rather than bandwidth-limited)
Spatial Multiplexing:
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Use multiple antennas at both transmitter and receiver
§ Multiple-Input (M transmitters) Multiple-Output (N receivers)
§ M x N MIMO
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At transmitter, data split into M sub-sequences
§ Transmitted simultaneously using the same frequency band
– Data rate increased by factor M
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At receiver, sub-sequences separates by interferencecancellation algorithms
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Capacity of system grows linearly with min{M,N}
§ Typically, N ≥ M (for good error performance)
11 Interference-limited Scenarios
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Interference causes more radio-link impairment in cellular networks
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Especially in small cells with high traffic load
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Inter-cell as well as intra-cell
Impact similar to that of noise
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Max achievable R limited by available S/N
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Inefficient use of power when R > BW
Solutions also similar
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Reducing cell size – reduces intra-cell interference
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Multiple receive antennas – signal combining increases S/N
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Beamforming – reduces interference from others
Additionally, structure in interference allows suppression
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e.g., interfering signal from a certain direction can be suppressed
using spatial processing with multiple receiver antennas
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Differences in spectrum properties also used to suppress interferer
12 © Jasleen Kaur, 2015 6 9/10/15 If BW Scarce; But High S/N Available…
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Providing R > BW is inefficient – needs very high S/N
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But BW is often scarce and expensive!
And high S/N can be made available sometimes!
§ Small cells with low traffic load
§ Phones close to the cell tower
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How to take advantage of such scenarios?
Higher-order modulation
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More bits of info per modulation symbol
13 Higher-Order Modulation
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More bits of info per modulation symbol
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BW independent of size of modulation alphabet (4, 16, 64)
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Depends mainly on modulation rate (# of symbols / second)
Max BW utilization (bits/s/Hz):
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QPSK – 2 bits of info in each modulation-symbol interval
16QAM – 4 bits per symbol interval
64QAM – 6 bits per symbol interval
16QAM (or 64 QAM) – twice (or thrice) that of QPSK
L: Reduced robustness to noise and interference
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Need higher Eb/N0 (energy per bit) for a given bit-error probability
14 © Jasleen Kaur, 2015 7 9/10/15 QAM: Over-Dimensioned Amplifier
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High-order modulation – signal has larger variations in
instantaneous transmit power
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Transmitter power amplifier must be over-dimensioned
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Also has larger peaks
Avoids non-linearity at high power levels (signal corruption)
Power amplifier efficiency will be reduced
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Increased power consumption (and increased cost)!
Alternatively, average transmit power needs to be reduced
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L - phones need low power consumption and cost
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§ Reduced range!
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Higher-order modulation more suitable for downlink (base
station to phone)
15 Issues When Using Larger BW
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BW is scarce and expensive
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Wider BW needs more complex radio equipment
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Higher sampling rates, more power consumption, complex analogto-digital converters
Increased corruption of transmitted signal due to time dispersion
on the channel
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Multiple propagation paths lead to delay spread
§ Yields a non-constant frequency response (frequency selectivity)
§ Corrupts frequency-domain structure of transmitted signal
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Leads to higher error rates for a given S/N
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Frequency selectivity has larger impact for wider-band transmission
§ Also impacted by environment
– Less in small cells, and in obstruction free rural areas
16 © Jasleen Kaur, 2015 8 9/10/15 If Larger BW Available…
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Receiver-side Equalization:
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Counteract signal corruption
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Works well for BW up to 5 MHz
§ For higher BW, complexity increases significantly
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Multi-carrier Transmission:
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Send signal as several narrowband signals
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Frequency-multiplex the subcarriers
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J: Less impact of frequency selectivity due to smaller BW
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J: Easy evolution of radio equipment and spectrum
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L: Subcarriers can not be tightly “packed” (interference)
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L: Parallel transmission of subcarriers leads to large power variation
§ For legacy terminals, only individual subcarrier can be used
§ Lower bandwidth efficiency
§ Lower power amplifier efficiency; reduced range
§ More suitable for downlink
17 © Jasleen Kaur, 2015 9