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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

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

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