In 1886, German physicist Heinrich Hertz, made a startling discovery.
He noticed that a spark generated on one side of a room,
would cause another spark to appear between a metal gap
on the other side of the room, at the exact same time,
even though they were not connected.
This is because an electric spark creates an invisible wave of energy
that propagates outwards in a spherical pattern.
And when this wave passes through any piece of metal, such as a nearby wire,
it causes it to vibrate electrically,
and generates an electric current in the wire, known as electrical induction.
It was later discovered that these were actually invisible light waves, known as radio waves.
This discovery led to the radio telegraph.
The transmitter is simple, it’s just a powerful battery,
which sends electrical pulses through an antenna, whenever a key is pressed.
Each pulse of electrical current generates a radio wave,
and far away on the receiving end is an identical loop of wire or antenna,
which is connected to a device which can measure electrical current, known as a receiver.
By the 1980s, we needed a faster way to transmit a growing amount of digital data,
doing it by hand wasn’t practical.
To send digital data rapidly using radio waves is a two-step process.
首先 发射机发出连续的无线电波 我们称之为载波
First, the transmitter sends out a continuous radio wave, we call it carrier wave.
This can be done by sending an alternating electrical current through an antenna.
The second step is to send a message on top of the carrier wave.
This is done by changing the strength of the electrical pulses at the transmitter
between high and low, known as amplitude modulation.
On the receiving end, these low versus high amplitude waves
are converted into pulses of electrical current,
and the low waves are converted into zeros,
and the high waves are converted back into ones.
And that’s the basis of digital wireless.
And remember antennas send out signals in all directions, and just like the sound:
when a loud siren rings, everyone in the area can hear it.
So with a single powerful transmitter,
we can send signals to many devices in a general area,
and the signal will reach each device even as it moves around.
This works because radio waves can travel through
most nonmetallic surfaces, such as walls.
The only thing that blocks them are surfaces with high metal content,
such as metallic structures or rocks.
However when they hit a metallic surface,
they bounce just like light does.
So the signal can arrive thanks to reflections,
think of these as radio echoes.
And this makes it easier for signals to reach around corners from transmitter to receiver,
and it’s why we are used to getting a cell phone signal almost anywhere.
But of course in certain locations,
the positioning between the device and base station
is such that your signal can get lost,
and this can be caused by the unwanted consequences of these radio echoes.
They can interfere with each other.
Most often what happens is two or more copies reach the receiver.
如同在水中一样 这些电波相互重叠 相互影响
And just like in water, these overlapping waves interact with each other,
adding together to create a third wave.
The third wave represents the addition of both waves.
If the waves arrive at the same time,
then the third wave is amplified, resulting in a very strong signal,
known as constructive interference, it’s the good kind of interference.
We run into a problem though, when the waves arrive at different times.
This happens when two signals travel slightly different distances from transmitter to receiver,
because they follow different paths.
This results in one wave being shifted in time compared to the other,
we call this a phase shift.
If two signals arrive, and one is shifted exactly by half a wave cycle,
they cancel each other out, resulting in a lost signal.
This is known as destructive interference, it’s the bad kind of interference.
And there is one other case to consider:
this is when the arriving signals combine to give a signal
that is shifted by half a wave cycle, causing the wave to flip.
And this is also a good kind of interference,
since receiver just needs to detect high versus low waves.
And so it’s the balance between constructive and destructive interference
that determines the quality of the received signal.
We express this using something called a fading characteristic,
represented with the letter H.
例如 如果只有一个信号到达 没有其它干扰
So for example, if a single copy of a signal arrives with no other interference,
then there is no fading, we express this as H equals 1.
Usually what happens is there is some other imbalance of constructive and destructive interference.
So the key problem becomes:
how can we combat the situation when H equals 0?
In the mid 1990s, several researchers from the Information Theory Society,
introduced the concept of “Space-Time codes”.
It was based on the following insight:
we can use multiple observations to decrease the chances
that we will lose data, due to the destructive fading.
First, realize that when you have a bad signal,
someone nearby may have a good one.
And that’s because different environments experience different echo patterns or fading characteristics.
This is why moving your phone around will often result in better signals.
So imagine we connected a second antenna to a mobile phone,
and separated them by some distance.
And let’s say receiver one experiences fading H1,
maybe it’s perfectly destructive, so H1 equals 0.
And receiver two experiences fading H2,
此例中 它没有受到干扰 所以H2=1
and in this case, it’s a clean signal, so H2 equals 1.
And now we have a better chance of receiving the signal,
because just one of the two possible channels needs to be good, in order to recover the data.
So for example, if we are sending a two bit message: 01,
each receiving antenna will measure the original signal multiplied by the fading characteristic.
Receiver one will measure 00,
receiver two will measure 01.
因此 如果其中一个信道 具有非零衰落特性
And so if one of the channels has a non-zero fading characteristic,
and in this case it’s receiver two, then we can recover the data.
The problem with this method is it’s not practical to
rely on multiple antennas for small devices.
The question is can we instead use multiple antennas
at the base station, or the transmit side,
to mimic the advantages of multiple receiver antennas?
For example, using a second transmit antenna,
separated by a distance, sending the same signal.
As before, because these signals travel unique paths,
they will fade differently: H1 and H2.
And this gives us two chances to receive the signal correctly
on the receiving end, with a single antenna.
然而 要使系统工作 还有个小问题要解决：
However, there is one subtle problem to address to make this system work:
it’s due to the fact that the transmitted signals will combine at the receiver antenna.
So from the receiver’s perspective,
it looks like a single signal was received,
with a new fading characteristic, let’s call it H3,
which is the addition of H1 and H2.
And so if H1 and H2 happened to be perfectly out of phase,
they will combine to form H3 equals 0, erasing the signal,
even though both of the channels were good on their own.
To address this problem, space-time codes were invented,
and we illustrate the idea with a well known construction by Alamouti.
Let’s say the message is two symbols long: A and B.
He sends two different symbols at each time step.
So transmitter one will send AB, and transmitter two will send BA.
And as before, the transmitters experience fading characteristic plus one and minus one.
Now let’s think about what would happen on the receiving end.
At the first time step, the receiver would measure a blend of both symbols,
and in this case: B minus A.
And at this point, the receiver doesn’t know those individual values of A and B.
例如 如果接收机检测出0 那A和B是多少？
For example, if it measures 0, what’s A and B?
A and B could both be 0 or both be 1.
We can’t say for sure yet, we don’t have enough information.
因此 接收机需要更多的信息 这便是下个时隙要做的事
So the receiver needs more information and that’s what the next time step is for.
Transmitter one will send B and transmitter two will send A.
And on the receiving end, it will measure: A minus B.
And let’s say this measurement works out to 0,
so we know A minus B equals 0.
Now we have two pieces of information.
But that still doesn’t help us because we don’t know if
A and B both equal 1 or A and B both equal 0.
The problem here is that our second measurement:
A minus B can always be found from our first measurement.
Multiplying the first equation by minus one, gives A minus B.
So our two transmissions effectively send the same information in different forms.
And Alamouti’s clever trick to make this work was to
make one of these measurements: A plus B.
One of the transmitter needs to send the negative value or amplitude
of one of the symbols at one of the time slots.
Alamouti chooses the first symbol from transmitter two to flip, using a negative.
So transmitter one sends A and then B,
transmitter two sends negative B and then A.
And if we do that, the receiver will measure two observations:
B minus A and A plus B.
And let’s say for example: A plus B was measured at two,
now the receiver knows for sure that A equals 1 and B equals 1.
And in the other case where A plus B worked out to 0,
then we know for sure that both A and B equal 0.
And that’s how the individual symbols and the message are recovered.
It works just like we received each symbol from two different receiving antennas,
but using a single receiving antenna.
This is an exciting insight because it increases the reliability of all receiving devices,
using a simple code, and one extra transmit antenna.
Increasing reliability is just one of the
many advantages offered by multiple antennas,
such systems are now known as multi input multi output, or MIMO.
And the researchers from the Information Theory Society have developed
the theory and practice of MIMO,
resulting in a new class of codes called Space-Time codes.
These systems have been in use for the past 10 years,
and new approaches for using MIMO systems are being explored
for future wireless communication systems.
信息时代: 空时编码 (MIMO)