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d-blast algorithm in mimo technology - 7


~

y ~


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rr


x


w '

y =

1, 2 t = 11 12

1, 2 t +

1.2 t

(3.10)

2.2 t

~ 0 r

x

w '

y 2.2 t

22

2.2 t 2.2 t

We want to determine X 2,2 , we consider X 1,2 is noise, we rewrite the above formula as follows:

y ~ =r 12x

+r 11x

+w ' 1.2 t=r 12x

+v 1, 2 t

(3.11)

2.2 t

r

2.2t

0

1.2t

w '

r

2.2t

v

22

2.2 t

22

2.2 t

Now we can find X 2,2 by using the covariance matrix. Then the SNR ratio will be:

r 2 22 + r 2 12 /(1+ r 2 11 ) (3.12)

Replace r 2 22 as in the blast nulling case. The D-Blast architecture with Blast-MMSE decoding of 2x2 multi-antenna size, AWGN white noise channel with gain r 11 and r 2 22 + r 2 12 /(1+ r 2 11 ) is drawn as shown below.



Figure 23 BLAST-MMSE implementing 2 antennas.[6]


The total capacity of BLAST-MMSE is:

C BLAST-MMSE = log 2 (1+ r 2 11 )+log 2 (1+ r 2 22 + r 2 12 /(1+ r 2 11 ) = log 2 ((1+ r 2 11 )(1+

r 2 22 )+ r 2 12 ) = C channel (3.13)

The channel capacity of Blast-MMSE is maximum.

Most Blast-MMSE is optimal, while Blast-nulling is near optimal.

CHAPTER IV: EVALUATION OF D-BLAST PERFORMANCE


In this chapter we will present some simulation results of the D-Blast algorithm in some specific scenarios using references, from which we will draw some evaluation comments. We will also use both MMSE and ZF algorithms to compare the performance of the two algorithms.

4.1 Some simulation results



Figure 24: Case frame error probability

n t nr 2​

and 4 bit rate per channel [1]



Figure 25: Case frame error probability

n t nr 2​

and 8 bit rate per channel [1]



Figure 26: Frame error probability with

n t n r 4 , rate 16 bits per channel [1]



Figure 27: Frame error probability with


Comment:

n t 8 , n r 4 , rate 16 bits per channel [1]


- From figure 24 and figure 25 we see that when increasing the speed from 4 bits to 8 bits per channel, the frame error probability is 1 when SNR = 8 (dB) in the case of 4 bits and in the case of 8 bits the frame error probability is 1 when SNR = 14 (dB). We can easily see that the higher the speed, the lower the reliability.

- From figure 26, we draw the probability of frame error when the frame length is 240 symbol times and figure 27 draws the probability of frame error when the frame length is 200 symbol times. We realize that the number of transmitting antennas increases from 4 to 8 and with a larger frame length, the probability of frame error increases higher.

- The MMSE curve is always below the ZF curve, so the performance of MMSE is better than that of ZF in all cases.

4.2 Comparison between V-Blast and D-Blast



Figure 28: Comparison of diversity performance of V-Blast and D-Blast [1]


In the widely used Blast architecture family, we need to mention the V-Blast architecture. V-BLAST is referred to as a MIMO channel that achieves high data rates. The data stream is divided into smaller independent data streams and sent on different antennas. When studying V-BLAST, we see that the maximum channel diversity-recombination exchange is not achieved at low rates: the maximum diversity of data streams is limited by the number of receiving antennas. However, V-BLAST is not the maximum for high-speed channels either, the reason is: [1] for example, for a 2 x 1 channel, assume that one of the channels has a coefficient of 0 and the remaining channels satisfy (0,1). In this case, diversity is achieved by the data stream being sent on the first transmitting antenna with a multiplexing gain of 0, whereas the entire channel still has non-zero channel diversity exchange. Therefore, V-BLAST does not benefit from both diversity gain and multiplexing gain, so this architecture does not achieve optimal exchange for MIMO channels.

The D-BLAST architecture achieves maximum diversity on the MIMO channel. The data stream is divided into sub-streams and transmitted on independent channels on the cross-plane, the D-BLAST architecture with MMSE-SIC receiver transforms the MIMO channel into an equivalent parallel channel by the eigenvalue matrix transformation method, so the coding methods used for the parallel channel, such as permutation coding..., when used according to the D-BLAST architecture will be the code for the MIMO channel.


Figure 29. Diversity performance of D-BLAST architecture [1]


4.3 Some issues of D-Blast .

First, let's talk about error propagation. Decoding at later layers requires that the decoding at previous layers is correct. If a previous layer is decoded incorrectly, the error will propagate to the following layers and not stop at a few layers. Therefore, it is necessary to protect the layer with strong interference with adequate coding.

One way to interrupt propagation errors is to reinitialize the separation process: stop transmitting after a few layers and start again at new layers, which increases the initial setup when reinitializing.

The second issue is that the hierarchical structure will increase the delay. The coding length, the spread of the codewords will increase the delay time leading to an increase in the buffer length. However, long codewords are necessary to reduce error propagation.

The V-Blast algorithm is ineffective in slow fading channels because it does not fully utilize the spatial transmission diversity, so if any of the equivalent transmission lines are bad (deep fading), it cannot be saved. The D-Blast algorithm overcomes this drawback by allowing parallel data streams to be transmitted in alternating scans of symbols on the array of transmitting antennas. That is, using additional transmit diversity

In V-Blast each codestream extends horizontally across the spacetime grid and is placed vertically above each other. In D-Blast each layer is diagonally across the spacetime grid. A significant improvement of D-Blast over V-Blast is the cross-antenna coding. This averages out the randomness of the subchannels and performs better when the rate is close to the outage capacity.

Comparison of D-Blast and Alamouti : Alamouti scheme is also considered as a transmit architecture, it converts 2x1 slow fading MISO into slow fading SISO. Any code for SISO when used in conjunction with Alamouti scheme will give code for MISO. Compared to D-Blast it is simpler in signal processing and has no propagation errors or rate degradation problems. However D-Blast can work with an arbitrary number of transmit and receive antennas. (whereas alamouti scheme does not generalize to an arbitrary number of transmit antennas). Furthermore Alamouti scheme performs poorly in MIMO channel with multiple transmit and receive antennas. This is because unlike D-Blast, alamouti scheme does not utilize all the degrees of freedom available in the channel.

Here are some comparison results through simulation:

We perform simulations with 2 different speeds and 2 different constellation sizes:

+ Block error rate - 1020 bits with 6 b/s/Hz transmission rate using 64QAM and 256 QAM.

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