INTRODUCTIONThe performance of an equalizer is very much affected by the selection of an algorithm for the error correction. The V-BLAST algorithm is used to provide the high gain. To improve the capacity of the receiver we use MIMO techniques. The performance of ZF and MMSE equalizers can be compared on the basis of BER using Rayleigh fading channel. The MMSE equalizer is the linear equalizer having high error correction capacities. The Rayleigh fading channel is considered for the multipath environment, therefore nonline of right cases is considered.

MIMO

MIMO is the use of multiple antennas at both the transmitter and receiver to improve communication performance.

It is one of several forms of smart antenna technology.

terms input and output refer to the radio channel carrying the signal, not to the devices having antennas.

ADDITIVE WHITE GAUSSIAN NOISE

(AWGN) is the statistically random radio noise characterized by a wide frequency range with regards to a signal in a communications channel.

AWGN is commonly used to simulate background noise of the channel under study, in addition to multipath, terrain blocking, interference, ground clutter and self interference that modern radio systems encounter in terrestrial operation.

RAYLEIGH CHANNELCooperative diversity is a transmission technique,

where multiple terminals pool their resources to form a virtual antenna array that realizes spatial diversity gain in a distributed fashion. In this paper, we examine the basic building block of cooperative diversity systems, a simple fading relay channel where the source, destination, and relay terminals are each equipped with single antenna transceivers. We consider three different time-division multiple-access-based cooperative protocols that vary the degree of broadcasting and receive collision. The relay terminal operates in either the amplify-and-forward (AF) or decode-and-forward (DF) modes.

Data generate

Modulator MIMO system

Rayleigh Fading Channel (NLOS)

MIMO System

Demodulator and V-BLAST system

Data Recovered

AWGN

BLOCK DIAGRAM

2×2 MIMO CHANNEL In a 2×2 MIMO channel, probable usage of the available

2 transmit antennas can be as follows:

1. Consider that we have a transmission sequence, for example

2. In normal transmission, we will be sending in the first time slot, in the second time slot, and so on.

3. However, as we now have 2 transmit antennas, we may group the symbols into groups of two. In the first time slot, send and from the first and second antenna. In second time slot, send and from the first and second antenna, send and in the third time slot and so on.

4. Notice that as we are grouping two symbols and sending them in one time slot, we need only time slots to complete the transmission – data rate is doubled

Transmit 2 Receive (2×2) MIMO channel

ZERO FORCING EQUALIZER FOR 2×2 MIMO CHANNEL

If the channel response (or channel transfer function) for a particular channel is H(s) then the input signal is multiplied by the reciprocal of it. This is intended to remove the effect of channel from the received signal, in particular the inter symbol interference (ISI).

The received signal on the second receive

antenna is,

Where, are the received symbol on the first and second antenna respectively,

is the channel from transmit antenna to receive antenna,

is the channel from transmit antenna to receive antenna,

is the channel from transmit antenna to receive antenna,

is the channel from transmit antenna to receive antenna,

are the transmitted symbols andis the noise on receive antennas.

For convenience, the above equation can be represented in matrix notation as follows:

Equivalently,

To solve for , The Zero Forcing (ZF) linear detector for meeting this constraint

. is given by,

To do the Successive Interference Cancellation (SIC), the receiver needs to perform the following:Using the Zero Forcing (ZF) equalization approach described above, the receiver can obtain an estimate of the two transmitted symbols ,i.e.

Take one of the estimated symbols (for example ) and subtract its effect from the

received vector and , i.e.

Expressing in matrix notation,

The above equation is same as equation obtained for receive diversity case.

MMSE EQUALIZER:In a previous post, we had discussed a 2×2 MIMO transmission using BPSK modulation in Rayleigh channel with a Zero Forcing equalizer. The simulated results with the 2×2 MIMO system with zero forcing equalizer showed matching results as obtained in for a 1×1 system for QPSK modulation in Rayleigh channel. In this post, we will discuss a different equalization approach called Minimum Mean Square Error (MMSE) equalization. We will assume that the channel is a flat fading Rayleigh multipath channel and the modulation is QPSK.

Where,

V-BLAST

some general geometrical ideas. This approach is based on the closed-form analytical models of the key V-BLAST and associated system components - interference nulling from yet to be detected symbols (Gramm-Schmidt `orthogonalization process), interference subtraction from already detected symbols, the optimal ordering procedure(based on the after processing SNR), optimal (maximum ratio or similar) combining, and a statistical (complex Gaussian) model of the matrix wireless propagation channel. In particular, we derive closed-form analytical expressions for the signal and noise vectors at each processing step for wireless channel with the general correlation matrix. Based on these results,

we give a rigorous proof that the diversity order at the i-th processing step is n-m+i (where n and m are the number of Rx and Tx antennas correspondingly) for uncorrelated Rayleigh channel and if no optimal ordering issued. At the moment, we are not able to analyze analytically the diversity order when the optimal ordering is implemented, but numerical Monte-Carlo analysis shows that the effect of optimal ordering is approximately to increase the after processing SNR by few dBs rather than to increase the diversity order (as one would intuitively expect based on the selection combining argument). Note that the analysis results above allows one to find the outage curves(i.e., fade level versus outage probability) and, hence, to estimate the average bit error rate (BER), in some cases – analytically as well.

V-BLAST ALGORITHMThe V-BLAST algorithm has been discussed in details elsewhere [5,9]. Here we describe its main points for completeness and in order to introduce notations. The main idea of the BLAST architecture is to split the information bit stream into several sub-streams and transmit them in parallel using a set of Tx antennas (the number of Tx antennas equals the number of sub-streams) at the same time and frequency. At the Rx side, each Rx antennas “sees” all the transmitted signals, which are mixed due to the nature of the wireless propagation channel. Using appropriate signal processing at the Rx side, these signals can be unmixed so that the matrix wireless channel is transformed into a set of virtual parallel independent channels (provided that multipath is rich enough)

1. The interference cancellation step: at the i-th processing step (i.e., when the signal from the i-th transmitter is detected) the interference from the first i-1 transmitters can be subtracted based on the estimations of the Tx symbols(which are actually assumed to be error-free) and the knowledge of H.

2. The interference nulling step: based on the knowledge of the channel matrix, the interference from yet-to-be detected symbols can be nulled out using the Gramm-Schmidt orthogonalization process (applied to the column vectors of H).

3. The optimal ordering procedure: the order of symbol processing is organized according to their after-processing SNRs in the decreasing order (i.e., the symbol with highest SNR is detected first).

REFERANCES[1] D. Gesbert, M. Shafi , D. S. Shiu, P. Smith, A. Naguib,

From Theory to Practice: An overview of MIMO space-time coded wireless systems. IEEE Journal on Selected Areas in Communications, VOL. 21, NO.3 ,Apr 2003.

[2] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Personal Communication., vol. 6, pp. 311-335, Mar. 1998.

[3] V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high data rate wireless communication: performance criterion and code construction,”, IEEE TRANSACTIONSON INFORMATION THEORY,VOL.44,NO.2, MARCH 1998.

[4] Wikipedia

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