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||²2. 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) = 2bits/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]TSSK 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]TFinal 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 |