Improve Diversity with OFDM Technique in V-BLAST Architecture

When any signal passed through air it has list numbers of interferences where core interference is ISI (Inter Symbol Interference). Integration applied on multipath air signal means it combine small number of signal division with fixed length assumption. Means integration is applied on time invariant signals but multipath air signals are always time variant. So, it is not applicable for wireless communication. Differentiation means large signal is divided into small number of signals with fix length. To process of total differentiation length of that signal should be fixed. That is why; it is not applicable to find-out the solution of wireless scenario [1].

TDM technique is fulfilling the criteria of wireless signaling. In general TDM means band-width is allocated to multiple users with division of time. It means TDM provide full bandwidth for small number of time to multiple users. But wireless signals take full time to transmit and receive the digital information. So, TDM technique is not fulfilling all the requirements. FDM technique delivers small bandwidth for full time. But the problem is if numbers of users are more than the division of that small band-width is very small and if those small band-width signal transmissions changes its phase in air than error output will captured. Whenever signal change its phase vector also shift its position to its original co-ordinates. When vector shifts than it produce disturbance on other user channel. It creates timing disturbances.

       (1)

This is nothing but process of aliasing at side of receiver with digital multipath signals. Another drawback is those digital signals are finite in time (time limited) but infinite in band (band unlimited) so ideal receiver cannot give adequate output. Solution of above drawback is orthogonally (OFDM) signal transmission. Orthogonal FDM deliver better algorithm compare with all other previous technology [2,3].

Orthogonal signal means projection of output vector in two vectors with minimum angle. Spectral is also orthogonal where dot product of those two vector is zero. That means projection is zero and gives largest hemming distance (Figure 1).

Figure 1: Vector OFDM (small error and large hemming distance).

MSE in OFDM

If any function f (t) filtered under ag (t) filter where “a” is the weighted co-efficient of that filter for t₁ to t₂ time then, (Figure 2) Signal approximation f(t) by g(t); f(t) ≈ ag(t) over (t₁, t₂) and error is: e(t) = f(t)-ag(t).

Figure 2: Pass frequency over t₁ to t₂.

     (2)

     (3)

MSE minimum at partial differenciation w.r.t. “a” when,

     (4)

This is orthogonal condition for minimum MSE where two vectors A and B are orthogonl and gives minimum error e(t) because of magnitude of A and B is equal with appropriate phase angle θ [1].

Throughput relation

As we seen before auto co-variance, integrator and differentiator is not used in transmitter.

Let or (Pythagoras)

But or orthogonal so; then,

“a” is optimally chosen then,

In signals;

=

Total Energy = Individual Energy + 2(Cross Energy)

For orthogonal cross energy is zero than through put becomes high.

Gain adjustment in OFDM

Let’s take more than one gain with its respective weighted coefficient than, ag (t) = a₁g₁(t) + a₂g₂(t); where a₁ and a₂ are weighted co-efficient with optimal value of gain g₁(t) and g₂(t).

The system is orthogonal so a₁ and a₂ are adjusting value and individual each other.

Motive of FFT in OFDM

If multiplication of total gain with its weighted code is taking more than one separate gain and weighted summation then,

ag (t) = a₁g₁(t) + a₂g₂(t);

     (5)

Orthogonal that is why a1 and a2 are adjustable values and individual with each other. So, it is solved by gain adjusted pre-coding.

V-BLAST architecture: There are four BLAST technologies like D-BLAST, V-BLAST, H-BLAST and T-BLAST. D is known as Diagonal BLAST same as V for Virtual, H for Hybrid and T for Turbo. In these four technologies V-BLAST is very important technology. D-BLAST gives output but it is diagonally BLAST means Diagonal matrix have maximum energy (minimum error). V-VLAST has virtually division so it reduces time and increase accuracy over large bandwidth. H-BLAST and T-BLAST are faster than V-BLAST but suitable work for narrow bandwidth only [4-6].

Result analysis:

Probability where random signal: If < 0.5 than Zero otherwise One.

Convert 0 and 1 to -1 and 1: Polar Signal Conversion

The combination of 2 × 2 antennas

sHat1 (2 × 2 Tx-Rx antenna):

sHat2 (2 × 2 Tx-Rx antenna):

sHat3 (2 × 2 Tx-Rx antenna):

sHat4 (2 × 2 Tx-Rx antenna):

Vector analysis:

J01 vector for MMSE (2 × 2 Tx-Rx antenna):

J10 vector for MMSE (2 × 2 Tx-Rx antenna):

J11 vector for MMSE (2 × 2 Tx-Rx antenna):

Rvec (Received Vector) takes all the data from its individual vector J00, J01, J10, J11.

Dd (Destination decimal Value-Which Antenna have Minimum Error Signal)

“U” identifies which vector has a lowest signal error:

nErr (n no. of Error where n is user defined):

Ber3=nErr/N (Ex: 72179/1000000=0.072179):-ML

Same as ber 1-MMSE:

And Ber2-ZF:

For any random input signal threshold (or cutoff) is identified. In this paper cutoff is 0.5. Means for any random input signal if the value is higher than 0.5 outputs is 1 otherwise 0. Polar form conversion is used because check signal parameters in three dimention and gives the values -1 and 1 (Table 1 and Figures 3 and 4).

Table 1: Parameters overview.

Figure 3: Table parameters (decoded ouput).

Figure 4: V-BLAST flow chart.

This signal goes to 2 × 2 antenna (Means Two transmitters and Two receivers). So, It has four different combinations. By performing above blocks signal is in frequency domain, to idenify how much amount of noise will be added in signal convert signal to time domain by using IFFT. Receiver antennas received noisy signals and send to the FFT. FFT converts time domain signals to frequency domain for easy identification of noise. Now, “Rvec” collect and identify which vector has less amount of noise by which combination. “U” identify the amount of error. After this act techniques will come for point analysis of BER and SNR [7,8].

A purpose of this paper is to analyze and compare to identify the behavior of different receiver techniques. Practical performance using Mat-Lab gives you the disturbance in signal due to the noise at receiver.

By performing above parameters disturbance in ML (Minimum Likelihood) is in 10^-4.9 BER and 18 dB SNR. But for smaller SNR values ML gives sharper output (Less BER) compare with MMSE and ZF.

In MMSE (Minimum Mean Square Error) disturbance is in 10^-4.3 BER and 32 dB SNR. When perform with high SNR with less fluctuation MMSE is used.

In ZF (Zero Force) disturbance is in 10^-3.9 BER and 32 dB SNR. When perform with large range of SNR ZF is used.

I would like to thank to Miss. Hetal N. Rao and Prof. Kiran Parmar. I also thank to my almighty.

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