Wireless Notes

Multipath Propagation in Wireless Communication

Learn multipath propagation with delay spread, coherence bandwidth, ISI inter-symbol interference, power delay profile, multipath effects, OFDM MIMO mitigation techniques explained for engineering students.

Multipath propagation occurs when the transmitted signal reaches the receiver through multiple paths (routes) – some direct, some reflected, some diffracted. These different copies arrive at different times and can either strengthen or weaken the received signal.

🔄 What is Multipath Propagation?

After leaving the transmitter, a signal reaches the receiver through multiple paths. These include the direct path, reflected paths (from buildings), diffracted paths (from edges), and scattered paths (from rough surfaces).

╱───▶		───╲
Path 2 ╱		╲ Path 2 (reflected)
Path 3 ╲──▶	Tree	───────╱ Path 3 (scattered)

🏢 Causes of Multipath

Mechanism	Object	Scale	Hindi
Reflection	Buildings, ground, water	Large surfaces (>> λ)	Badi surfaces se bounce
Diffraction	Building edges, hills	Sharp edges	Edges ke around wave mudi
Scattering	Trees, lampposts, cars	Small objects (≈ λ)	Chhoti cheezon se scatter
Refraction	Atmosphere layers	Gradual density change	Atmosphere mein moda

Environment Impact:

Environment	Multipath Severity	Typical Delay Spread
Indoor (small room)	Moderate	10-50 ns
Indoor (large building)	High	50-300 ns
Urban (dense)	Very High	1-20 μs
Suburban	Moderate	0.2-2 μs
Rural/Open	Low	0.1-0.5 μs
Hilly terrain	High	3-30 μs
Mountain	Very High	Up to 100 μs

⚡ Effects of Multipath

1. Signal Fading (Constructive & Destructive)

Constructive (signals add)	Destructive (signals cancel):
Path 1	╱╲╱╲╱╲ Path 1: ╱╲╱╲╱╲
Path 2	╱╲╱╲╱╲ (in phase) Path 2: ╲╱╲╱╲╱ (180° out)
Result	╱╲╱╲╱╲ (STRONG!) Result: ──────── (ZERO! Deep fade)

2. Time Spreading (Delay Spread)

Different paths arrive at different times
Causes pulse broadening
Limits maximum data rate

3. Frequency Selective Fading

Some frequencies enhanced, others attenuated
Channel response varies across bandwidth
Causes distortion of wideband signals

4. Doppler Spread

Moving objects/user → frequency shifts
Different paths have different Doppler shifts
Causes time-varying channel

⏱️ Delay Spread

Delay spread indicates how much difference there is in the arrival times of different copies of the signal.

Power Delay Profile (PDP):

	█ Direct path (strongest, first to arrive)
	█
	█ █ First reflection
	█ █
	█ █ █ Second reflection (weaker)
	█ █ █
	█ █ █ █ Scattered (weakest)
	τ₀ τ₁ τ₂ τ₃
	◀── Maximum Excess Delay (τmax) ──▶
	◀── RMS Delay Spread (στ) ──▶

Key Parameters:

Mean Excess Delay

τ̄ = Σ(Pₖ × τₖ) / Σ(Pₖ)

RMS Delay Spread

στ = √[Σ(Pₖ × (τₖ - τ̄)²) / Σ(Pₖ)]

Maximum Excess Delay

τmax = last significant path delay - first path delay

Parameter	Indoor	Urban	Suburban	Mountain
RMS Delay Spread	10-50 ns	1-5 μs	0.2-2 μs	5-30 μs
Max Excess Delay	50-300 ns	5-20 μs	1-10 μs	20-100 μs

📊 Coherence Bandwidth

Coherence bandwidth is the frequency range within which the channel response remains approximately the same (flat). If the signal bandwidth exceeds this, frequency selective fading occurs.

│ Coherence Bandwidth	│
│ If Signal BW < Bc	Flat fading (simple) │
│ If Signal BW > Bc	Frequency selective (complex) │

Example:

Urban environment: στ = 2 μs

Bc ≈ 1/(5 × 2×10⁻⁶) = 100 kHz

→ Any signal wider than 100 kHz will experience frequency selective fading

→ 4G LTE (20 MHz) >> 100 kHz → definitely frequency selective!

→ This is why LTE uses OFDM (each subcarrier 15 kHz < Bc = flat fading ✅)

📡 Inter-Symbol Interference (ISI)

ISI occurs when delayed multipath copies arrive in the next symbol's time slot – energy from the previous symbol interferes with the next symbol.

Transmitted Symbols:	Sym 1	Sym 2	Sym 3
Direct path (τ=0):	Sym 1	Sym 2	Sym 3
Delayed path (τ=Δ):	Sym 1	Sym 2	Sym 3
At receiver:	Sym1+	Sym2+	Sym3+
	part	part	part
	of prev	of Sym1	of Sym2

ISI Rule:

No ISI condition	Ts >> στ (symbol much longer than delay spread)
Or equivalently	Rs << Bc (symbol rate << coherence bandwidth)
Example: στ = 5 μs	Max rate ≈ 200 ksps without ISI
But 4G needs 14 Msps! Solution	OFDM (many slow subcarriers)

📐 Multipath Channel Models

Engineers use standardized channel models for simulation and testing:

Model	Type	Use
Two-ray ground	Deterministic	LOS + ground reflection
Tapped Delay Line	Statistical	General multipath
3GPP TDL	Standardized	4G/5G simulation
IEEE 802.11	Standardized	WiFi channel models
ITU-R	International	Various environments
WINNER II	Research	Advanced simulations

Two-Ray Model:

Direct path + single ground reflection
Good for flat terrain with elevated antennas
Shows oscillating signal strength with distance

🛡️ Mitigation Techniques

Modern solutions to combat multipath effects:

Technique	How It Helps	Used In
OFDM	Divides into narrow subcarriers (each < Bc)	4G, 5G, WiFi
Cyclic Prefix	Guard interval absorbs ISI	LTE, WiFi
RAKE Receiver	Combines multipath copies constructively	3G WCDMA
Equalization	Digital filter reverses channel effect	All systems
MIMO	Multiple antennas exploit multipath diversity	4G, 5G, WiFi
Beamforming	Focus energy to reduce multipath	5G
Interleaving	Spread burst errors over time	All systems
Diversity	Multiple copies via space/freq/time	All systems

OFDM Solution (Key Insight):

Problem: 20 MHz signal	symbol = 50 ns → ISI (delay > 50 ns)
Solution (OFDM)	Split into 1200+ subcarriers
Each subcarrier: 15 kHz	symbol = 66.7 μs >> delay spread
+ Cyclic Prefix	4.7 μs guard interval absorbs multipath
Result	NO ISI! Each subcarrier sees flat fading only.

📝 Summary

Concept	Key Point	Formula
Multipath	Signal arrives via multiple paths	–
Delay Spread (στ)	Time spread of multipath	στ = RMS of PDP
Coherence BW (Bc)	Flat-fading frequency range	Bc ≈ 1/(5στ)
ISI condition	Symbol duration < delay spread	Ts < στ → ISI
Flat fading	Signal BW < Bc	Simple amplitude change
Freq. selective	Signal BW > Bc	Different freq faded differently
OFDM	Narrowband subcarriers avoid ISI	Each < Bc
RAKE receiver	Combine multipath constructively	3G
MIMO	Exploit multipath as advantage	4G, 5G

❓ FAQ

Q: Is multipath always bad? A: No! MIMO systems actually exploit multipath. Multiple paths = multiple independent channels = more capacity. 5G Massive MIMO converts multipath into an advantage.

Q: How does OFDM solve multipath? A: OFDM divides the signal into 1000+ narrow subcarriers. Each subcarrier's bandwidth << coherence bandwidth, so each subcarrier sees flat fading (easy to equalize). Plus cyclic prefix absorbs multipath delay.

Q: Indoor vs outdoor mein multipath kaise different hai? A: Indoor: short delays (ns), many reflections (walls, ceiling). Outdoor: long delays (μs), fewer but stronger reflections (buildings). Indoor ke liye wider coherence bandwidth but denser scattering.

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