MIMO Equalize MMSE

Equalization Algorithm in MIMO System

——Based on Minimum Mean Square Error Name:Cui Hao(崔浩) Number：416114416060

1.MIMO system

In radio, multiple-input and multiple-output, or MIMO, is a method for multiplying the capacity of a radio link using multiple transmit and receive antennas to exploit multipath propagation.MIMO has become an essential element of wireless communication standards.

At one time, in wireless the term \"MIMO\" referred to the use of multiple antennas at the transmitter and the receiver. In modern usage, \"MIMO\" specifically refers to a practical technique for sending and receiving more than one data signal simultaneously over the same radio channel by exploiting multipath propagation. MIMO is fundamentally different from smart antenna techniques developed to enhance the performance of a single data signal, such as beamforming and diversity.

MIMO can be sub-divided into three main categories, precoding, spatial multiplexing (SM), and diversity coding.

RX Figure 1.MIMO system

H is the channel matrix of the Nt and Nr columns, the elements of which are independent of each other and subject to cyclic symmetric complex Gaussian distribution with mean 0 and variance 1 (ie, 0.5 for the real and the imaginary variance), ie the channels are independent flat Rayleigh fading channel and the receiving end already knows the channel state information.

By figure 1 , we can get Rayleigh fading channel H

h11h21H...hNt1h12h22...hNt2...h1Nr...h2Nr.........hNtNrNr1 Nt2 … Ntn Nt1 Nt2 … Ntn h11h12h1nh21h22h2nh31h32h3nBy

(0)

Where

HNtNr denotes the channel Rayleigh fading coefficient from the Nt-th transmitting antenna to the Nr-th receiving antenna.

2.MMSE Equalization

2.1 Equalization

The insertion of a tunable filter in a digital communication system can correct and compensate for system characteristics and reduce the impact of intersymbol interference. This compensating filter is called an equalizer.

Equalizers are usually implemented using filters, which use a filter to compensate for distorted pulses. The demodulator output samples obtained by the decider are samples that have been corrected by the equalizer or have cleared the inter-symbol interference. Adaptive equalizer directly from the transmission of the actual digital signal in accordance with an algorithm to adjust the gain, which can adapt to the random channel changes, so that the equalizer is always the best state, which has better distortion compensation performance.

2.2 Minimum Mean Square Error

In statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality, of the fitted values of a dependent variable. In the Bayesian setting, the term MMSE more specifically refers to estimation with quadratic loss function. In such case, the MMSE estimator is given by the posterior mean of the parameter to be estimated. Since the posterior mean is cumbersome to calculate, the form of the MMSE estimator is usually constrained to be within a certain class of functions. Linear MMSE estimators are a popular choice since they are easy to use, calculate, and very versatile.

2.3 MMSE of a fading model System Model: Where:

y: received signal vector , y = [ y1 , y2 , ... , yNr ]. n : interference and noise , n = [ n1 , n2 , ... , nNr ]. x : input signal vector , x = [ x1 , x2 , ... , xNt ]. H: fading channel , please watch equation (0). It is assumed that n is statistically independent to x .

y Hx  n (1)

We want to estimate x from y by linear operation:

xˆ  G H y (2) where the G is selected to minimize the estimation error

e = x - xˆ (3) MMSE criterion is to minimize the following equation

J = E(eHe) = tr{E(eHe)} (4)

By (1)、(2)、(3) and (4) , we can get

J = tr{ E( eHe ) }= tr{ E[ ( x - xˆ )H ( x - xˆ ) ] }

= tr{ E[ ( x - G H y )H ( x - G H y ) ] }

= tr{ E ( xxH - xyHG - GHyxH + GHyyHG ) } (5) Let

JG0(6) (5) and (6) lead to the equation

GHRyy = Rxy (7) Where

Ryy = E{ yyH } = E{( Hx + n )( Hx + n)H } = E{ HxxHHH + nnH } Rxy = E{ xyH } = E{ x( Hx + n )H } = E{ xxHHH } Eventually , by (7) , we can get the final solution

GHHH1SNRI1HH(8)

3.Simulation steps Input Input: x=randn(1,num*Nt).The signal sequence is made up of 1 and 0 (total in num*Nt). Allocating signal: tx_bits=reshape(x,Nt,num). The signal sequence x is assigned to the Nt antennas. Modulation:tx_modu(a1,:)=modulation(tx_bits(a1,:),BITS).The sequence is modulated by QPSK. Allocating Signal Modulation Rayleigh Fading Channel: H=randn(Nr,Nt)+j*randn(Nr,Nt). Rayleigh Fading Channel HNtNr denotes the channel Rayleigh fading coefficient from the Nt-th transmitting antenna to the Nr-th receiving antenna. Equalization: G=inv(H'*H+Nt/(10^(0.1*SNR))*eye(Nt))*H'. Equalization We get the G from equation (8): Demodulation CalculatingBER:errors(i)=sum(sum(rx_demodu~=tx_bits))/(Nt*num); Compare input to output,calculate BER. Calculating BER

Figure 2. Simulation steps

4.Simulation result

Figure 3. 4x4MIMO & Unbalanced and Balanced Algorithm BER Performance Comparison

Figure 4. Different MIMO & Comparison of BER Performance of MMSE Equalization

5.Simulation analysis

I can conclude that

(1). Comparing balanced MIMO system by MMSE equalization algorithm and unbalanced MIMO system, tthe performance of BER has been a very good improvement in balanced MIMO system.

(2). With the increase of signal-to-noise ratio, the performance of BER is getting better and better in balanced MIMO system.

(3). With the increase of the number of transmitting and receiving antennas, the performance of BER is getting better and better in balanced MIMO system

6.References

[1].MIMO通信系统中的几种检测方法。

http://wenku.baidu.com/link?url=CtHSqFw-yW9GIb8uNNtQDyCuTsPjypLzEPVHTL7T1ZEFA0rhxV9D9LrFNqNjzLRUrbZfXoH123fmjA4h25vEnwwYJqJPMSPyXr3x3Wi5EDu

[2].Proof for MMSE in MIMO system.

http://www.docin.com/p-314075773.html

[3].MIMO均衡算法简介。

http://wenku.baidu.com/link?url=fB3F0xZmwig9r2M_1pK4BGN6VcHPW6F3NZuABWU4ye6edhxEZQ0Tue5cOFJRzk1rrLWkAlCAkoDfYvmoq6DYtm2lr-Hu5p81MhZEW8vxz1G