OFDM in WLAN: 802.11n: Similar to 802.11a and 802.11g with minor changes

In the previous article we have discussed about OFDM in 802.11 a/g, now let's take a look at how OFDM works in 11n. 

OFDM has little to do with the drastic 11n rate boost, MIMO is the key player there. Lets leave the MIMO part aside, its a candidate for next article. As far as OFDM is concerned it will work per antenna, but the basic concept per antenna is the same as 11g with few changes.

20 MHz:  This is same as 802.11 a/g but 

a) With an extra 4 sub carriers.

In 802.11a/g we use 48 sub-carriers for data and 4 sub-carriers for pilot. But in 11n we make use of an extra 4 sub-carriers from the reserved for data sub-carriers.So this results in increased throughput.

b) Short Guard Interval (Optional)

we have short guard interval introduced in 11nIn the previous article we have take the guard interval as 1/4 of symbol time, now in 11n they have still decreased the guard interval to 1/8 of the symbol time. So it comes down to,                          3.2us *1/8=0.4us 

Lets take an example to understand:

a) Full Guard Interval

20MHz/64=0.3125; 1/0.3125 =3.2us + 1/4 * 3.2 us=4 us

b) Short guard Interval

20MHz/64=0.3125; 1/0.3125 =3.2us + 1/8 * 3.2 us=3.6 us

Note: Important point to note here is that while doing the calculations for the FFT period we have considered the maximum carriers 64 not the used carriers, so the above calculation of 3.2us holds good in spite of increased sub carriers.

40 MHz: 

Its same as 20MHz but the process repeated in both primary and secondary channels.

So as derived above the total no of sub-carriers in  a 40MHz channel is 52*2 (primary and secondary) + 4 (extra).

The reason for these extra 4 data sub carriers is that we don't need that many (8) pilot sub-carriers combined for both the channels, so we converted some of them to data sub carriers.

Data Sub-Carriers = 52 *2 = 104

Pilot sub-carriers  = 4 + 4  = 8

======================

Total Sub-carriers = 112 with 8 pilot sub-carriers.

Now out of that if remove 2 sub-carriers from 8 and convert them to 2 and add 2 more (why?) 

======================

Data Sub-carriers = 104+2 (from pilot)+2 (extra)=108

Pilot sub-carriers = 4-1 + 4-1=6

======================

Total sub-carriers = 108+6 =114

I am not sure of the exact rationale behind adding some number of sub carriers  but its safe to attribute that to the evolution, as the IEEE std progresses they are trying to make use of all the reserved sub-carriers in that process.

With the same logic in the previous article we can similarly derive the rate calculations for the above 20MHz and 40Mhz as well. The above tables from the IEEE 802.11-2012 will help you.

What is OFDM?: Simplified..

Lets take a look at the technology that literally commanding all and any form of wireless communications OFDM without requiring any prior electronics knowledge.

Orthogonal Frequency Division Multiplexing is the most sought modulation technique in today's cutting edge wireless either it be 802.11 (WLAN), 802.16(WiMax), 3GPP 36 series (LTE)..

Single Carrier Modulation:

In the traditional communications we make use of a single Tx antenna and a single Rx Antenna. All the incoming data is modulated using a single carrier and sent OTA, at the Rx side its is  demodulated and data after removing the carrier is given out.

Multi-Carrier Modulation:

FDM: 

But in order to gain high throughput a new scheme is introduced. Where in we divide the channel in to different sub channels and assign a carrier to each sub-channel for modulation known as sub-carrier and finally multiplex all the carriers+data and send using the single Tx Antenna.
But in order to avoid interference (inter-symbol interference) we use a guard spacing between the sub channels causing in bandwidth wastage.

OFDM: 

In order to save the wastage and use it effectively we choose the sub-channels and sub-carriers such that they are orthogonal to each other meaning they don't interfere with each other. So we can skip the guard spacing between the sub-channels and save bandwidth.

FDM Vs. OFDM

Truly speaking it should be termed as FDMO, as you will see why just in a moment. lets understand each word in detail in the acronym.

Frequency Division (FD):

Instead of modulating all data with one carrier, divide the bandwidth in to equally separated sub-channels and assign a carrier to each sub-channel called sub-carrier.

Multiplexing (M):

As we have multiple sub-carriers but a single Tx antenna we need to map all the sub-carriers rather we need to multiplex all of them and send OTA. We make use Parallel to Serial converter for this.

Orthogonality(O):

We all know from the high school maths that orthogonality means "product of slopes = -1" meaning one signal will not overlap with the other.

In a similar context in the time domain a sub channel is represents as a rectangle which in a frequency domain converts to a "sinc" wave, now if we multiplex the "sinc" waves of all sub carriers sub channels it will look something like the below.

Now at the Rx side we can decode this wave because of the orthogonality, see the "arrows" they represent the frequency at which impact of all other sub carriers is zero, so we get to Rx only that particular sub-carrier we are interested in.

*2: By using an IFFT for modulation we implicitly chose the spacing of the subcarriers in such a way that at the frequency where we evaluate the received signal (indicated as arrows) all other signals are zero.

Advantages:

1. Saves bandwidth
2. Carries more no of data than a conventional carrier.

Disadvantages:

1. Highly depends on the orthogonality achieved, need a good sync on Tx and Rx and also no multipath effect.
2. High PAPR: Peak to Average Power Ratio.

The reason for high PAPR is that, as we use many sub-carriers with same bandwidth, the sum of peak power of all the sub-carriers varies instantaneously.
OFDM exhibits peaks whose power strongly exceeds the mean  power: the signal is said to have a high PAPR. This prevents use of high-efficiency amplification devices (High Power Amplifiers, HPA), which can cause nonlinearities reuslting in in-band distortion and increases Out-Of-Band  Radiation (OOBR), inter Symbol Interference and a high Bit-Error-Rate (BER).

Mitigations

1. 

a) Pilot: Instead of using all the sub-carriers/channels for data, use some selected sub carriers to send with zero-data so that the Rx can tune itself with the Tx. These are kind of training subcarriers.

b)  Cyclic Prefix (CP): In order to overcome the MultiPath effect, OFDM implements a clever technique of CP where in we first need to find the "Doppler Spread" of the multipath channel and then copy that amount of time from the data signal from the last to the first. So that even if that signal undergoes the multipath fading, we still have the data intact only the copied part is lost.

Doppler Spread: The amount of delay induced by the multipath channel to the 1st signal causing to overlap with the 2nd singal leading to infamous inter symbol interference. 

2.  There are many methods but below are famous ones

• Clipping and Filtering

• Peak Windowing

References:

1. History behind OFDM
2. Orthogonality in OFDM

3. Why High PAR 

4. PAPR Reduction Techniques

Note: All the pictures here are taken from the references and some additional resources. The author do not claim any copy right.