802.11 n and ac Transmit Beamforming: Crash Course

Theory

Beamforming: Form the beam in the direction of destination. Simple, isn't it? Well for starters that's the aim, but we have lot of obstacles in the path, read the mathematics part and you will "its not that simple after all." :-).

Traditional antenna, radiates omnidirectionally meaning everywhere, but for some use cases we need to focus on specific areas/directions, like when there are multiple destinations we want to make sure the one with whom we are speaking gets the best SNR.

For 11n, this was simpley a SNR improvement technique, but for 11ac with the introduction of MU-MIMO we need to communicate with multiple users simultaneously without any cross-interference. So the need for beamforming is more in 11ac.

Generally we use this in cases where the No of antennae are more than the no of spatial streams like 4X2, 8X4 etc.

Beamforming gains are expected to be approximately 3 dB in the transmitted direction. In practice, this gain will typically be one step up in data rates (increasing one MCS number) for a mid-range transmission.

Beamforming is achieved by combining elements in a phased array in such a way that signals at particular angles experience constructive interference while others experience destructive interference

Basic Mathematics

Lets take a look at how do we arrive at those angles, and lets try to keep the mathematics simple and not delve in the gory details.

MIMO communication can be modeled as below

Yk = HkXk + n

X ==> Vector of Tx signal using Ntx antennae [ x1 x2 …xNtx]
Y ==> Vector of Rx signal using Nrx antennae [y1 y2 …yNrx]
H ==> Channel Matrxix Ntx X Nrx.
k  ==> Subarrier
n  ==> Constant Noise in the Channel

Now in order to make sure transmitted signal is steered towards the receiver, we have to tune the transmit signal in such way that we control the phase and amplitude so that the resulting signal will be received by that particular receiver with good SNR.

In mathematical form, we need to calculate the matrix Qk referred as steering matrix, such that Yk is optimized.

Yk = HkQkXk + n

Qk has values known as weights to control phase and amplitude for all Transmit Antennae for that particular subcarrier k.

X is the beamformer
Y is the beamformee

Still with me? Lets do the same for MU-MIMO,

Yku = HkuQkuXku + n

u==> user, specific beamformee.

Qku has values known as weights to control phase and amplitude for all Transmit Antennae for that particular subcarrier k and for that particular beamformee u.

Types 

Explicit Feedback

Qk is formed based on the Feedback from the receiver. So Y will send some training data known as sounding data, based on which X estimates the channel characteristics and derives Qk.

This sounding known as NDP (Null Data packet) sounding uses a special packet with Length 0 as the name indicates.

Here channel need not be reciprocal, as feedback is given based on NDP (from beamformer-beamformee) which is same direction as data packet.

Implicit Feedback

Beamformer X chooses Qk, and adjusts it based on the feedback of beamformee Y.There is not extra data being sent by beamformer, it only prepares the feedback based on the normal data signal from beamformee.

But as the feedback is based on the channel characteristics from Y to X, based on which X decides Qk for X to Y, so this only works when the channel is reciprocal.

Uncompressed

The feedback sent by beamformee comprises of entire beamforming feedback matrices, known commonly as Vk based on which Qk is derived.

Compressed

The feedback sent by beamformee comprises of angles instead of the full matrix which will be decompressed in to full matrix Vk at beamformer.

To understand how we derive Qk from Vk we need to understand SVD (Singular Value Decomposition) which is complex matrix factorization technique outside the scope of this article.

For 11ac only compressed beamforming technique is allowed.

That's the most we can go without getting our hands dirty with some advanced mathematics (SVD, matrices) etc. Hope this throws some light on inner details of beamforming.

References:

1) IEEE specs

2) Wikipedia.

3) 11ac survival guide: beamforming basics

Revision Info:

1) Fixed the definitions of explicit and implicit beamforming: Thanks to Ashok Bandi.

Why are some of the MCS combinations invalid in 11ac?

11ac boosts the WLAN rates tremendously in to the gigabit range, but it also introduces a slight problematic area which is not really focused in 11n (because its not much of a problem) "the no of BCC encoders."

In 802.11 there are 2 types of convolutional codes (FEC) defined,

 

• BCC (binary convolutional code)

• Encodes the data as per the coding rate, if multiple encoders are used demultiplexes the scrambled bits among NES (number of BCC encoders for the Data field) BCC encoders, in a round robin manner

• Punctures the Encoded output to achieve higher coding rate, by puncturing we mean we decrease the no of output bits (the denominator of the coding rate) there by resulting in an higher coding rate.

        

                   "Higher  rates are derived from it by employing 'puncturing.' Puncturing is a procedure for omitting some of the encoded bits in the transmitter (thus reducing the number of transmitted bits and increasing the coding rate) and inserting a dummy “zero” metric into the convolutional decoder on the receive side in place of the omitted bits. Decoding by the Viterbi algorithm is recommended."

• LDPC (low-density parity check code.)

• High performance error-correcting codes, lets us discuss these some other time.

Note: The same MCS table shall be used for both BCC and LDPC coded transmissions.

Lets take a look at both 11N and 11AC with regard to BCC encoding and MCS Rates Validity.

11N:

The rules of BCC encoder in 11N are:

1. A single BCC encoder can support up to 300 Mbps of data rate at most, after that for every 300 Mbps step we need to use an additional encoder.
2. NES values were chosen to yield an integer number of punctured blocks for each BCC encoder per OFDM symbol.
3. The number of BCC encoders is not limited

So if we observe the MCS's 21, 22, 23 they all use 2 BCC encoders as the Tx Rate is > 300 Mbps. When using multiple BCC encoders the encoder parser demultiplexes the scrambled bits among NES (number of BCC encoders for the Data field) BCC encoders, in a round robin manner. 

Process of Convolutional Coding: Multiple BCC Encoders

So the total number of bits must be multiple of no of encoders, else there will be some extra bits left at the end of the distribution.

For Eg: In case of 

optional 40 MHz, NSS = 3, EQM

MCS 21: 64QAM-2/3-1944-1296-2 Encoders

The total number of coded bits 1944 are split across   648 blocks of BCC encoders with 3 bit length, each block yields 2 bits resulting in 1296 Data bits/sub carrier.

11AC:

The rules for BCC encoder in 11AC are:

1. The maximum data rate per BCC encoder is 600Mbps
2. The number of BCC encoders for a particular combination of MCS, Nsts and BW is determined by the short GI data rate and the same number of encoders are used for the corresponding normal GI rate
3. The number of BCC encoders is not limited
4. NES values were chosen to yield an integer number of punctured blocks for each BCC encoder per OFDM symbol.

As shown in the 11N example, lets take the case of 

mandatory 20 MHz, NSS = 1, 

MCS-8: 256QAM-3/4-416-312

Here the total no of coded bits 416 should be split across 104 blocks BCC encoders with 4 bit length each block yielding 3 data bits resulting in 312 data bits/sub carrier.

MCS-9: 256QAM-5/6-416-??

Here the total no of coded bits 416 cannot be split across a interger number of encoders violating the above rule #4, hence this MCS combination is invalid.

mandatory 20 MHz, NSS = 3, 

MCS-9: 256QAM-5/6-1248-1040

1248/6 = 208 Blocks of 6 bits each yielding 5 bits output resulting in 1040 data bits, which is valid.

Similarly we can do for other MCS holes (Missing MCS rates which are thrown because they are considered invalid).

Conclusion:

So if we convert the above example in to a mathematical forumala...it sumps as below

The reminder of the division of Total no of coded bits/denominator of coding rate (the length of each convolutional code block) should be 0.

         "For BCC encoding, some of the MCS-N_SS combinations are excluded from the MCS table to avoid additional padding symbols. Allowed MCSs are selected such that the number of coded bits in each OFDM symbol contains an integer number of punctured blocks from all encoders, i.e., mathematically every allowed MCS-N_SS satisfies:"

Condition for a MCS to be valid: For definitions refer the IEEE spec

References:

1) IEEE 802.11ac-draft 5.0

2) IEEE 802.11-2012

3) 802.11ac: Survival Guide

4) IEEE Discussions-11ac spec

5) IEEE Discussion-11ac-MCS Holes