# Transmit diversity vs multi-path?

Are transmit diversity signal and the multi-path signal same? Multi-path contains LOS+delayed and attenuated/distorted versions of it and transmit diversity signal contains LOS1+delayed LOS2+ +delayed and attenuated/distorted versions of the two.

Kindly, elucidate in terms of the impact of each type of signal on the equalization used at the receiver.

Thanks, JK

Multi-path is a property of the communication channel (mostly the wireless channel). The received signal $r(t)$ is the sum of delayed and weighted versions of the transmit signal $x(t)$: $$r(t) = \sum_{i} a_i x(t-\tau_i)$$

Transmit diversity is a property of the transmitter. It describes a technique using multiple transmit antennas, thus creating multiple communication channels that are different because the antennas are placed at different locations in space. The idea is to transmit the same information at the same time at different antennas.

For example, let's assume one receive antenna and two transmit antennas (2x1 multiple-input single-output (MISO)) the received signal is a superposition of both multi-path channels: $$r(t) = \sum_{i} a_i x(t-\tau_i)+\sum_{j} b_j x(t-\tau_j)$$ The hope is that if transmission on one channel fails you will still receive a useful signal through the other channel thereby increasing the robustness of the system.

There is also the concept of receive diversity where multiple receive antennas are used (SIMO). And of course you can use multiple antennas on both receiver and transmitter side (MIMO).

When using the scheme of transmitting the same data at the same time, an FIR filter can be used no matter if transmit diversity is applied or not, because to the receiver it will just appear like an ordinary multi-path channel. Advanced equalizer structures include the fractionally spaced equalizer and the decision-feedback equalizer. If you apply some space-time coding a the transmitter an according space-time decoder is required at the receiver.

• And the equalization? – GJK Jun 5 '14 at 9:39
• @GJK This is quite a broad question but I tried to answer it in my updated answer. – Deve Jun 6 '14 at 11:52
• In the case of transmit diversity, the equation for $r(t)$ shows that we get two LOS signals at the receiver in addition to different multi-path components. Now, the equalization problem here is to somehow send a single LOS signal to the demodulator which is not possible at all if the two LOS signals have equal power at the Rx. Am I missing something? Thanks.... – GJK Jun 9 '14 at 3:42
• @GJK The equation does not really show whether there is a LOS component or not. If there is LOS the according multipath component has the shortest delay and normally the greatest power. But for the rest isn't any different from the other multipath components. I did not really understand you doubt about equalization. Do you mean channel estimation? Do you have a reference for method you describe? – Deve Jun 9 '14 at 10:37
• I have a situation where two satellite transponders closely located send the same signal which I am trying to model as a channel with two LOS components (transmit diversity???) and trying to use CMA based blind equalization technique to somehow reduce the probability of error at the demodulator. Is this possible? I know that this channel transfer function has poles near the unit circle. – GJK Jun 10 '14 at 3:37