Skip to main content

Menu

Home 📘 Wireless Communication (Main Page) Constellation Diagrams BER vs SNR GMSK MSK Channel Impulse Response Modulation Schemes MIMO Technology OFDM MATLAB Projects Contact
Login Try App

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


People are good at skipping over material they already know!

View Related Topics to







Contact Us

Name

Email *

Message *

Popular Posts

BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...

📘 Overview of BER and SNR 🧮 Online Simulator for BER calculation of m-ary QAM and m-ary PSK 🧮 MATLAB Code for BER calculation of M-ary QAM, M-ary PSK, QPSK, BPSK, ... 📚 Further Reading 📂 View Other Topics on M-ary QAM, M-ary PSK, QPSK ... 🧮 Online Simulator for Constellation Diagram of m-ary QAM 🧮 Online Simulator for Constellation Diagram of m-ary PSK 🧮 MATLAB Code for BER calculation of ASK, FSK, and PSK 🧮 MATLAB Code for BER calculation of Alamouti Scheme 🧮 Different approaches to calculate BER vs SNR What is Bit Error Rate (BER)? The abbreviation BER stands for Bit Error Rate, which indicates how many corrupted bits are received (after the demodulation process) compared to the total number of bits sent in a communication process. BER = (number of bits received in error) / (total number of tran...
Read more

Calculation of SNR from FFT bins in MATLAB

📘 Overview 🧮 MATLAB Code for Estimation of SNR from FFT bins of a Noisy Signal 🧮 MATLAB Code for Estimation of Signal-to-Noise Ratio from Power Spectral Density Using FFT and Kaiser Window Periodogram from real signal data 📚 Further Reading   Here, you can find the SNR of a received signal from periodogram / FFT bins using the Kaiser operator. The beta (β) parameter characterizes the Kaiser window, which controls the trade-off between the main lobe width and the side lobe level in the frequency domain. For that you should know the sampling rate of the signal.  The Kaiser window is a type of window function commonly used in signal processing, particularly for designing finite impulse response (FIR) filters and performing spectral analysis. It is a general-purpose window that allows for control over the trade-off between the main lobe width (frequency resolution) and side lobe levels (suppression of spectral leakage). The Kaiser window is defined...
Read more

Constellation Diagrams of ASK, PSK, and FSK

📘 Overview of Energy per Bit (Eb / N0) 🧮 Online Simulator for constellation diagrams of ASK, FSK, and PSK 🧮 Theory behind Constellation Diagrams of ASK, FSK, and PSK 🧮 MATLAB Codes for Constellation Diagrams of ASK, FSK, and PSK 📚 Further Reading 📂 Other Topics on Constellation Diagrams of ASK, PSK, and FSK ... 🧮 Simulator for constellation diagrams of m-ary PSK 🧮 Simulator for constellation diagrams of m-ary QAM BASK (Binary ASK) Modulation: Transmits one of two signals: 0 or -√Eb, where Eb​ is the energy per bit. These signals represent binary 0 and 1.    BFSK (Binary FSK) Modulation: Transmits one of two signals: +√Eb​ ( On the y-axis, the phase shift of 90 degrees with respect to the x-axis, which is also termed phase offset ) or √Eb (on x-axis), where Eb​ is the energy per bit. These signals represent binary 0 and 1.  BPSK (Binary PSK) Modulation: Transmits one of two signals...
Read more

MATLAB code for BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ...

🧮 MATLAB Code for BPSK, M-ary PSK, and M-ary QAM Together 🧮 MATLAB Code for M-ary QAM 🧮 MATLAB Code for M-ary PSK 📚 Further Reading MATLAB Script for BER vs. SNR for M-QAM, M-PSK, QPSK, BPSK % Written by Salim Wireless clc; clear; close all; num_symbols = 1e5; snr_db = -20:2:20; psk_orders = [2, 4, 8, 16, 32]; qam_orders = [4, 16, 64, 256]; ber_psk_results = zeros(length(psk_orders), length(snr_db)); ber_qam_results = zeros(length(qam_orders), length(snr_db)); for i = 1:length(psk_orders) psk_order = psk_orders(i); for j = 1:length(snr_db) data_symbols = randi([0, psk_order-1], 1, num_symbols); modulated_signal = pskmod(data_symbols, psk_order, pi/psk_order); received_signal = awgn(modulated_signal, snr_db(j), 'measured'); demodulated_symbols = pskdemod(received_signal, psk_order, pi/psk_order); ber_psk_results(i, j) = sum(data_symbols ~= demodulated_symbols) / num_symbols; end end for i...
Read more

Comparisons among ASK, PSK, and FSK | And the definitions of each

📘 Comparisons among ASK, FSK, and PSK 🧮 Online Simulator for calculating Bandwidth of ASK, FSK, and PSK 🧮 MATLAB Code for BER vs. SNR Analysis of ASK, FSK, and PSK 📚 Further Reading 📂 View Other Topics on Comparisons among ASK, PSK, and FSK ... 🧮 Comparisons of Noise Sensitivity, Bandwidth, Complexity, etc. 🧮 MATLAB Code for Constellation Diagrams of ASK, FSK, and PSK 🧮 Online Simulator for ASK, FSK, and PSK Generation 🧮 Online Simulator for ASK, FSK, and PSK Constellation 🧮 Some Questions and Answers Modulation ASK, FSK & PSK Constellation MATLAB Simulink MATLAB Code Comparisons among ASK, PSK, and FSK    Comparisons among ASK, PSK, and FSK Comparison among ASK, FSK, and PSK Parameters ASK FSK PSK Variable Characteristics Amplitude Frequency ...
Read more

Coherence Bandwidth and Coherence Time

🧮 Coherence Bandwidth 🧮 Coherence Time 🧮 MATLAB Code s 📚 Further Reading Coherence Bandwidth Coherence bandwidth is a concept in wireless communication and signal processing that relates to the frequency range over which a wireless channel remains approximately constant in terms of its characteristics. Coherence bandwidth is inversely related to the delay spread time (e.g., RMS delay spread). The coherence bandwidth is related to the delay spread of the channel, which is a measure of the time it takes for signals to traverse the channel due to multipath. The two are related by the following approximation: Coherence Bandwidth ≈ 1/(delay spread time) Or, Coherence Bandwidth ≈ 1/(root-mean-square delay spread time) (Coherence bandwidth in Hertz) For instance, if the root-mean-square delay spread is 500 ns (i.e., {1/(2*10^6)} seconds), the coherence bandwidth is approximately 2 MHz (1 / 500e-9) in ...
Read more

Online Channel Impulse Response Simulator

  Fundamental Theory of Channel Impulse Response The fundamental theory behind the channel impulse response in wireless communication often involves complex exponential components such as: \( h(t) = \sum_{i=1}^{L} a_i \cdot \delta(t - \tau_i) \cdot e^{j\theta_i} \) Where: \( a_i \) is the amplitude of the \( i^{th} \) path \( \tau_i \) is the delay of the \( i^{th} \) path \( \theta_i \) is the phase shift (often due to Doppler effect, reflection, etc.) \( e^{j\theta_i} \) introduces a phase rotation (complex exponential) The convolution \( x(t) * h(t) \) gives the received signal So, instead of representing the channel with only real-valued amplitudes, each path can be more accurately modeled using a complex gain : \( h[n] = a_i \cdot e^{j\theta_i} \) Channel Impulse Response Simulator Input Signal (Unit Impulse x[n]) Multipath Delays (samples): Path Ampli...
Read more

MIMO Channel Matrix | Rank and Condition Number

MIMO / Massive MIMO MIMO Channel Matrix | Rank and Condition...   The channel matrix in wireless communication is a matrix that describes the impact of the channel on the transmitted signal. The channel matrix can be used to model the effects of the atmospheric or underwater environment on the signal, such as the absorption, reflection or scattering of the signal by surrounding objects. When addressing multi-antenna communication, the term "channel matrix" is used. Let's assume that only one TX and one RX are in communication and there's no surrounding object. Here, in our case, we can apply the proper threshold condition to a received signal and get the original transmitted signal at the RX side. However, in real-world situations, we see signal path blockage, reflections, etc.,  (NLOS paths [↗]) more frequently. The obstruction is typically caused by building walls, etc. Multi-antenna communication was introduced to address this issue. It makes diversity app...
Read more