PE2-2.5 Wireless Communication, MIMO & OFDM

What this is and why it exists

Everything so far assumed a fixed channel. A wireless channel is not fixed. It changes as anything moves, including the receiver, the transmitter and everything between them.

That change is the subject here, and it ends with the field's most striking reversal. Multipath, which everything up to this point treated as a defect, turns out to be a source of extra capacity.

The vocabulary

• Orthogonal signalling — using signals chosen so they do not interfere with one another.
• Coherent detection — detection that needs the carrier phase.
• Non-coherent detection — detection that does not.
• DPSK — differential phase shift keying, where the change in phase carries the bit.
• Multipath — the signal arriving by several routes with different delays.
• Fading — the received strength varying as those paths add and cancel.
• Flat fading — the whole band affected equally.
• Frequency selective fading — different parts of the band affected differently.
• MIMO — multiple antennas at both ends of the link.
• Spatial multiplexing — sending different data streams from different antennas at once.
• OFDM — splitting a wide channel into many narrow ones carried in parallel.

The mental model

Orthogonal signalling first, because it underlies several schemes below. Two signals are orthogonal when their correlation is zero, so a receiver matched to one gets nothing from the other. That property lets several signals share a channel without interfering. It is the same orthogonality that made the previous topic's signal space work.

Non-coherent detection answers a practical difficulty. Coherent detection needs the carrier phase, and acquiring and holding a phase reference costs hardware. Worse, in a fading channel the phase moves unpredictably, so the reference can be lost exactly when it is needed. Non-coherent schemes avoid needing one at all, at a cost in error rate.

Differential keying is the standard example. Instead of encoding a bit in the absolute phase, encode it in the change of phase between one symbol and the next. The previous symbol becomes the reference, so no absolute phase is needed. It costs a small penalty in error rate and removes a large requirement, which is a trade this area poses repeatedly.

Now the wireless channel. The signal reaches the receiver by several routes. Reflections from buildings, the ground and vehicles all arrive with different delays and different phases. They add, and depending on those phases they can reinforce or cancel. Move the receiver half a wavelength and a deep cancellation can become a peak.

That is fading, and it changes the whole character of the problem. A fixed channel has one signal-to-noise ratio. A fading channel has a distribution of them, and the average performance is dominated by the moments when the ratio is poor. Simulating it is what makes this concrete: watching the received strength drop by tens of decibels for a moment explains more than the equations do.

When the delays are small compared with a symbol, the whole band fades together, which is flat fading. When they are not, different frequencies fade differently, which is frequency selective, and symbols smear into each other.

Then the reversal. With multiple antennas at both ends, those separate paths stop being a nuisance. Each pair of antennas sees a different combination of paths. The channel between the two arrays is therefore a matrix rather than a number. If that matrix has enough independent directions, several data streams can be sent at once through the same band, and separated at the far end.

Capacity multiplies without any extra spectrum or power. Multipath, the thing every earlier chapter treated as damage, is what makes those directions independent. A channel with no multipath at all would offer far less. The field took decades to see that, which is why it is worth pausing on.

Splitting a wide channel closes the course. Frequency selective fading is difficult because a wide signal sees a channel that varies across its band. Divide the band into many narrow subchannels and each one is narrow enough to fade flat. Each then sees a simple channel that a single number describes. Correcting a channel that is one number is straightforward. Correcting one that varies across the band is not. That is the whole idea, and it is why every current standard uses it.

What you should now be able to explain or do

Say what makes two signals orthogonal and what that buys. Explain what non-coherent detection avoids and what it costs. Describe how differential keying supplies its own reference. Explain multipath and fading, and distinguish flat from frequency selective. Say why multiple antennas turn multipath into capacity, and why splitting a band into narrow subchannels simplifies equalisation.

Check yourself