Spatial Modulation (SM) and Space Shift Keying (SSK) in MIMO

MIMO (Multiple-Input Multiple-Output) systems use multiple antennas at the transmitter and receiver to improve communication performance in wireless systems.

1. Space Shift Keying (SSK)

SSK is a special case of spatial modulation where only the antenna index carries the information. No modulation symbol (like QAM or PSK) is used.

How it works:

• Only one transmit antenna is active at a time.
• The active antenna index represents the information bits.
• All other antennas remain silent.

Achievable Rate:

For nt transmit antennas, the rate is:

log2(nt) bits per channel use (bpcu)

Example:

For nt = 4, we can encode log₂(4) = 2 bits:

Input Bits	SSK Vector	Active Antenna
00	[1, 0, 0, 0]T	Antenna 1
01	[0, 1, 0, 0]T	Antenna 2
10	[0, 0, 1, 0]T	Antenna 3
11	[0, 0, 0, 1]T	Antenna 4

SSK Detection Rule:

The received signal: y = Hxj = hj

ML Detection:

ĵ = argminj ||y - hj||²

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2. Spatial Modulation (SM)

Spatial Modulation extends SSK by using both:

• Antenna index (spatial position)
• Modulated symbol (e.g., BPSK, QPSK)

How it works:

• Only one antenna is active per symbol period.
• The antenna index transmits log₂(nt) bits.
• The symbol transmits m = log₂(M) bits, where M is the modulation order.

Achievable Rate:

Total bits per channel use:

m + log₂(nt) bpcu

Example:

With nt = 4 and QPSK (M = 4, so m = 2):

Input Bits	SM Vector	Active Antenna	Tx Symbol
00 + QPSK	[x, 0, 0, 0]T	Antenna 1	x ∈ AM
01 + QPSK	[0, x, 0, 0]T	Antenna 2	x ∈ AM
10 + QPSK	[0, 0, x, 0]T	Antenna 3	x ∈ AM
11 + QPSK	[0, 0, 0, x]T	Antenna 4	x ∈ AM

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3. SSK vs SM – Comparison

Feature	SSK	SM
Modulation Used	None (only antenna index)	Standard (e.g., QPSK, QAM)
Bits per Channel Use	log₂(nt)	m + log₂(nt)
Complexity	Lower	Higher
Spectral Efficiency	Lower	Higher
Energy Efficiency	High (one antenna ON)	Moderate

4. Example Walkthrough

• Number of transmit antennas: nt = 4
• Modulation scheme: QPSK
• Modulation order: M = 4 → m = log₂(4) = 2 bits/symbol

Part 1: Space Shift Keying (SSK)

Step 1: Bits per Channel Use

log₂(nt) = log₂(4) = 2 bits per channel use

Step 2: Bit Mapping

Input Bits	Active Antenna	Transmit Vector
00	Antenna 1	[1, 0, 0, 0]T
01	Antenna 2	[0, 1, 0, 0]T
10	Antenna 3	[0, 0, 1, 0]T
11	Antenna 4	[0, 0, 0, 1]T

Step 3: Transmission Example

Input bits: 10 → Activate Antenna 3

Transmit vector: [0, 0, 1, 0]T

Part 2: Spatial Modulation (SM)

Step 1: Total Bits per Channel Use

log₂(nt) + m = 2 + 2 = 4 bits per channel use

Step 2: Bit Mapping Example

Input bits: 1101

• First 2 bits: 11 → Antenna 4
• Next 2 bits: 01 → QPSK symbol = -1 + j

QPSK Symbol Mapping

Bits	QPSK Symbol
00	+1 + j
01	-1 + j
11	-1 - j
10	+1 - j

Step 3: Transmit Vector

Only Antenna 4 is active and sends -1 + j:

[0, 0, 0, -1 + j]T

Summary Table (SM Example)

Input Bits	Antenna (log₂(nt))	Symbol (log₂(M))	Transmit Vector
1101	11 → Ant 4	01 → -1 + j	[0, 0, 0, -1 + j]T
0010	00 → Ant 1	10 → +1 - j	[+1 - j, 0, 0, 0]T
1000	10 → Ant 3	00 → +1 + j	[0, 0, +1 + j, 0]T

Another Example: Bit Stream 1010 in Spatial Modulation (SM) and SSK

Spatial Modulation (SM)

Input Bit Stream:

1010

Step 1: Antenna Index (First 2 bits)

10 → Decimal 2 → Activate Antenna 3

Bits	Antenna
00	Antenna 1
01	Antenna 2
10	Antenna 3 ✅
11	Antenna 4

Step 2: QPSK Symbol (Last 2 bits)

10 → QPSK Symbol: +1 - j

Bits	QPSK Symbol
00	+1 + j
01	-1 + j
10	+1 - j ✅
11	-1 - j

Step 3: Transmit Vector

Only Antenna 3 is active and transmits +1 - j:

x = [0, 0, +1 - j, 0]T

SSK Case (Same Bit Stream)

SSK uses only the antenna index. So we only take the first 2 bits: 10

10 → Activate Antenna 3

No symbol is transmitted — only antenna index matters.

x = [0, 0, 1, 0]T

Final Summary

System	Bits Used	Active Antenna	Symbol Sent	Transmit Vector
Spatial Modulation (SM)	1010 → 10 (antenna) + 10 (symbol)	Antenna 3	+1 - j	[0, 0, +1 - j, 0]T
SSK	10 → antenna only	Antenna 3	None	[0, 0, 1, 0]T

Further Reading

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