### Signal Vector Base Detector for Spatial Modulation

Signal vector based detector was investigated in spatial modulation to further reduce the complexity of an optimal detector. Actually, great improvement was achieved in terms of complexity reduction with the same performance and retaining the great features of spatial modulation.

The basic idea behind signal vector base detector is the correlation among the antennas. Finding the correlation angle among all the available transmit antenna Tx. This is then used to estimate the antenna index used for transmission.

In this article I will be going through signal vector base detector (SVD) but before you proceed with this article, kindly go through spatial modulation first to really understand the scheme very well. Click here to read the article on spatial modulation. Also, you can go through the brief performance analysis too by clicking here

Spatial Modulation scheme covered in the previous article by MathsCodes was based on Maximum Likelihood which imposes a bit high computational complexity on the scheme. However, SVD has been proposed to further reduce the complexity of the scheme considering the direction of the transmitted signal vector of spatial modulation does not change then the correlation between the antennas can be used to estimate the antenna index used for transmission.

For a single mode transmission following the example given in the article in spatial modulation in which the received signal is said to be:

Y = sqrt(p) hj*x + n ---------------------(1)

Where Y is the received signal that was transmitted across a fading channel H in the presence of AWGN noise n.

Signal vector based detector is in two stages. They are as follows:

- Using SVD to estimate the antenna index used for transmission. So as to reduce the overall search from M*Tx to just M.
- Using maximum likelihood to estimate the transmitted symbol.

I will give a very simple illustration of a signal vector based detector in spatial modulation.

Let us consider a 2×4 4-QAM system employing spatial modulation scheme with a Rayleigh fading channel H in the presence of AWGNn.

I believe we all know what spatial modulation scheme is all about (mode of transmission, complexity, e.t.c).You can go through spatial modulation system by clicking here. The received signal Y becomes equation (1)

The received signal Y can be demodulated optimally using ML but this will search across all possibilities of M*Tx and impose high complexity in the system. However, SVD can further reduce the complexity of ML by reducing the search from M*Tx to only M.

### Stage 1

The antenna index used to transmit the received signal Y is estimated first by finding the Hermitian angle between the channel H and received signal Y. using:

### Stage 2

In ML (Maximum Likelihood), the antenna index and the symbol are detected together resulting in a search across all the constellation points which in turn increase the complexity of the system. However, if the antenna index is estimated with the antenna correlation angle this leaves us with only a search for the transmitted symbol. Thus, this help to reduce the search across the constellation point in ML approach and reduce complexity achieving the same performance.

The transmitted symbol is estimated using ML. Recall, that the antenna index have been estimated before estimating the transmitted symbol. Therefore, the search done by ML will be across just M.

To access the full code of SM with SVD based detector click here