# Multiple Input Multiple Output Mimo Wireless Technology Computer Science Essay

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Multiple input-multiple output (MIMO) is called using more than two antennas at both transmit and receive ends. It is important for upcoming wireless communications. It has the capacity to increase the system capacity without using any extra bandwidth. Usually, MIMO is applied in two cases. One is in space-time coding systems [13] where the transmission quality is improved because of spatial diversity and the other case is in spatial multiple [14] access systems where individual data streams are transmitted using different antennas thus increasing the system capacity. In this project, the second situation is considered. On the other hand, orthogonal frequency division multiplexing (OFDM)[17] method has been utilized so many situations like (DAB)digital audio broadcasting, (DVB) digital video broadcasting, and broadband wireless local area networks (IEEE 802.11a)[16], because of its ability to reduce frequency selective fading. So, it is desirable to combine both OFDM and MIMO for high system model with good performance.

In MIMO-OFDM[15] systems implementation of signal detection is easy by a set of parallel per-subcarrier signal detectors when it is applied to flat fading channels over frequency selective fading channels when the channel length is less than or equal to the cyclic prefix length. If the channel length is greater than the cyclic prefix length, it causes inter block interference and it effects the orthogonal property of subcarriers, resulting in substantial performance decrease in the signal detection algorithm. As per the author's knowledge, two indirect algorithms (which need estimating the channel matrix before detecting signal) have been implemented for detecting the signals. The first algorithm is a frequency- domain algorithm or conventional detection algorithm, where the smoothened signal received from per subcarrier is transmitted to each subcarrier similar to smoothed received signal of a MIMO system.

The second algorithm is a time-domain algorithm, here the equalizer is first inserted to decrease the MIMO channels to ones with channel length less than or equal to the cyclic prefix length. The common signal detection algorithm for MIMO-OFDM systems is then applied. Unfortunately, here two algorithms need to estimate the channel matrix that requires channel length estimation as well as channel coefficient estimation. Usually, channel length is estimated using information theoretic criteria like Akaike's Information Criterion or Minimum Description Length (MDL) which is complex and computationally intensive. Also, exact channel length estimation is hard to achieve in practice and also estimation error normally occurs, which will decrease the system performance. As for channel coefficient estimation, the lease (is the number of transmit antennas in MIMO-OFDM systems, and is the maximum channel length) number of pilot symbols are required. The number of pilot symbols required linearly increase with the channel length also, thereby reducing the transmission efficiency if the channel length is large. [3]

## 1.2 Aim of the project

In this project, a time-domain signal detection algorithm depends on Second-Order Statistics (SOS) is introduced for general MIMO-OFDM systems above frequency selective channels. In this a new system algorithm is implemented. Here the ith received OFDM block is shifted towards left by J samples. The new system algorithm model has some structural properties that allow an equalizer to be designed to reduce most of the inter symbol interference (ISI) that depends on SOS of the received signals. At the receiver side of the equalizer, only two paths of the input signals are used and the signals can be easily detected. Due to the different structure of the new algorithm, it turns out that only columns of the channel matrix estimation are required. It follows that the least number of pilot symbols needed to estimate the columns of the channel matrix and it does not dependent on the channel length. This makes channel length estimation is not necessary, which means that the proposed algorithm has substantial advantage, according to computer as well as avoiding performance decrease due to channel length estimation error, in present algorithms.

And also, the proposed algorithm does not depend on channel length if the channel length is less than, equal to or longer than the cyclic prefix CP length. Simulation results give the effectiveness of the proposed algorithm, and also give the performance of existing ones in all cases. [3]

## 1.3 Scope of the project

In this paper, the performance of MIMO-OFDM system employing QPSK in Rayleigh fading channel is analysed. The use of multiple antennas at both ends of a wireless link (MIMO technology)[18] has newly been demonstrated to have the potential of achieving extraordinary data rates. Orthogonal Frequency Division Multiplexing decrease receiver complexity significantly in wireless broadband systems. The use of MIMO technology in combination with OFDM, i.e., MIMO-OFDM is a good attractive solution for future broadband wireless systems. [5]

## 1.4 Organization of dissertation

The rest of the paper is organized as follows. In chapter 2, the new MIMO-OFDM system model is introduced. The Modulation Technique proposed in this project is presented in Chapter 3, and Literature review about the present algorithms in Chapter 4, Simulation model and analysis of results in Chapter 5. Finally, Chapter 6 the conclusion.

## CHAPTER 2

## 2.1 Introduction

The figure of wireless services, systems and users are constantly increasing. The essential bandwidth turns out to be higher. In order to suit these desires we need different techniques, architectures and multiple system coding schemes which have been introduced in the literature. One among the most accepted modulations for the multi path channel is identified as Orthogonal Frequency Division Multiplexing (OFDM). Also, several antennas are using both in transmission and reception that is Multiple Input Multiple Output (MIMO), has concerned in several researchers and research fields (communications, radio frequency, etc)

MIMO (multiple input multiple output) has the capability to produce independent parallel channels and transmits multi-path data stream, and meets the demands for high-data rate wireless transmission. OFDM (orthogonal frequency- division multiplexing) to the great extent reduces the influence of multi- path fading by transforming frequency-selective waning channels to flat fading channels in frequency domain. We can generate what has been called a MIMO-OFDM system with employing multiple transmits and accept antennas in an OFDM communication system. This system can provide highly frequency spectral efficiency and is a shows potential approach with incredible prospective.

Commonly, MIMO is functional in two situations. One is in space-time coding systems where the transmission quality (bit-error rate (BER)) is enhanced due to spatial diversity other is in spatial multiplexing or spatial multiple access systems where self-governing data streams are transmitted over different antennas, thus increasing the transmission rate or improving the system capacity. In this paper, the final circumstances are considered. On the other hand, orthogonal frequency division multiplexing (OFDM) technique has been broadly utilized in (DAB) digital audio broadcasting, (DVB) digital video broadcasting, and broadband wireless local area networks (IEEE 802.11a) , due to its capability to oppose frequency selective fading. It is enviable to combine OFDM with MIMO for high system capacity, as well as superior act. [1]

The full form of MIMO is multi input and multi output. In this process signals are transmitted through multiple antennas as an alternative instead of one antenna like FDM. This is the better technique to increase data transmission rate in wireless communications.

## 2.1 MIMO antenna

It is an arrangement of both modulation and multiplexing. First multiplexing technique is applied to one independent channel, where a group of signals coming from the identical source is separated into a number of independent channels known as sub-set of the main signals. And every signal is modulated by detach carrier, and also multiplexed into an OFDM signal for easy transmission. Every channel from sub-set can be multiplexed by frequency or code division multiplexing.

## 2.2 MIMO-OFDM transmission

2.2 Characteristics of OFDM sub-channels

As mentioned that OFDM is a unique set of FDM, but what makes OFDM unique is the orthogonality of the sub-carries. Which capital every sub-channel of the main signal is multiplied by a carrier which is orthogonal to each other These Carriers are represented by sine or cosine wave and the area belongs to one sine and one cosine wave is simply zero. Orthogonal carrier means if we assume the first carrier frequency is f1 the second carrier will be 2xf1, and so on. This type of orthogonality of the carriers permits synchronized transmission of sub-carriers in a small spaced bandwidth without nosy from each other because each carrier is orthogonal to each other making the result of their multiplication a zero. Generally, OFDM signals are transmit via one transmitting antenna. While generated OFDM signal is transmitted during a number of antennas in order to accomplish variety or cap any gain (for higher transmission rate) this is known as MIMO-OFDM

Orthogonal Frequency Division Multiplexing is one of the most advanced physical layer technologies for speed data rate wireless communications because of its robustness to frequency selective fading, low computational complexity and spectral efficiency. OFDM can be used in connection with a Multiple-Input Multiple-Output transceiver to increase the diversity gain as well as the system capacity by using spatial domain. Because the OFDM system effectively produce number of parallel narrowband channels, MIMO-OFDM is considered as a one of the key technology in high-data rate systems like 4G, and IEEE 802.11n etc.

## 2.3MIMO-OFDM system

MIMO communication is nothing but using multiple antennas at both ends transmitter and receiver to exploit the spatial domain for spatial diversity and spatial multiplexing.

## 2.3 Spatial multiplexing

Spatial multiplexing has been mostly used to increase the system capacity of a MIMO link by sending individual data in the same time slot and frequency band at the same time from each transmit antenna, and the multiple data streams are separated at the receiver using channel information at each propagation path. [6]

## 2.4 Spatial multiplexing

## 2.5 Different types of multiplexing techniques

MIMO-OFDM Works similar to any other communication system. MIMO-OFDM system also has transmitter and receiver but it has more than one transmit and receiving antennas at both ends. MIMO system can be developed in different ways, if we need to take the variety of advantage to struggle diminishing then we must send the same signals via various MIMO antennas and at the delivery end all the signals inward bound by MIMO antennas will detect the same signals travelled through different paths. In this case the complete received signal must pass during un-correlated channels. If we are inserted to use MIMO for capability increase then we can send changed set of data i.e. not the same data like diversity MIMO through a number of antennas and the similar number of antennas will take delivery of the signals in the other end. For MIMO to be capable of antenna spacing need to be complete them very carefully need minimum half the wave length of the transmitting signal.

## 2.6 Throughput of MIMO systems

## 2.4 MIMO-OFDM

The reason for growing significance to high speed communication is rise in demand of multimedia and development of internet related contents. The limitation for wide bandwidth and suppleness require the use of proficient transmission modes that would fit to the quality of wideband channels particularly in wireless environment where the channel is extremely demanding. In wireless environment the signal is transmitting from the transmitter to the receiver along quantity of different paths, together referred as multipath. While transmitting the signal, power slumps of due to three possessions path loss, macroscopic fading and fading of the signal can be affected by dissimilar diversity procedures. To attain diversity, the signal is propagated through several independent fading paths e.g. in time, frequency or space and pooled helpfully at the receiver. Multiple input- multiple-output (MIMO) utilize spatial assortment by having numerous transmit and receive antennas. If the paper "MIMO principles" supposed frequency flat fading MIMO channels. OFDM is inflection process known for its potential to alleviate multipath. In OFDM the high speed data stream is alienated into Nr narrowband data streams, Nc consequent to the subcarriers i.e. one OFDM symbol consists of N symbols altered for example PSK. As a consequence the symbol interval is N times bigger than in a single carrier system with the similar symbol rate. The symbol period is made even longer by accumulating a cyclic prefix for every symbol. As long as the cyclic prefix is greater than the channel delay spread OFDM recommends inter-symbol interference (ISI) free transmission.

Another main benefit of OFDM is that it significantly decreases equalization convolution by facilitating equalization in the frequency domain. OFDM, executing with IFFT at the transmitter and FFT at the receiver, renovates the wideband signal, exaggerated by frequency selective fading, into N narrowband flat fading signals and the equalization can be executed in the frequency province by a scalar separation carrier-wise with the sub carrier associated channel coefficients. The channel should be identified or cultured at the receiver. The mixture of MIMO-OFDM is very ordinary and advantageous since OFDM facilitates hold of more antennas and well-built bandwidths since it shorten equalization significantly in MIMO systems. MIMO-OFDM is beneath exhaustive examination by researchers. This paper affords a general impression of this hopeful transmission procedure.

The common transceiver formation of MIMO-OFDM is available in Fig 2.7 shown below the system has N number of transmit antennas and M number of receive antennas. In this the cyclic prefix is supposed to be longer than the channel hold-up spread. The OFDM signal for individual antenna is attained by using IFFT and can be identified by FFT. The received MIMO-OFDM symbol of the nth subcarrier and the mth OFDM symbol of the ith receive antenna.

Then FFT can be written as

## (2.1)

where is the propagated data symbol on nth carrier and m:th OFDM symbol, and is the preservative noise involvement at ith receive antenna for the equivalent symbol in frequency domain and is the channel coefficient in the frequency domain between the jth transmit antenna and the ith receive antenna. The channel coefficients in frequency domain are acquired as linear arrangement of the dispersive channel taps

## 2.7 MIMO-OFDM system

, n=0,.....,N-1 (2.2)

Where 'I' is the number of channel taps in time domain and hm is modelled as an independent zero-mean random Gaussian process. The desire reaction of the Rayleigh fading channel can be uttered as

(t) (2.3)

Where hi is the tap gain and i is the delay allied to the ith tap. This delay can be considered to be time invariant. The channel impulse response is supposed to be static over one OFDM channel symbol duration T Channel =T+T', where T is the OFDM symbol duration and T' is the cyclic prefix duration. This corresponds to a slowly varying channel where the coherence time is longer than the channel symbol duration. This postulation avoid from understanding inter-carrier interference (ICI). The channel matrix H is an NxM matrix equivalent to the n:th subcarrier and mth OFDM Symbol.

## (2.4)

Taking the received data symbols of all antennas into account, the expression of the received data symbol can be presented in the matrix form as follows

## (2.5)

Where

## (2.6)

and

## (2.7)

are the Nx1 and Mx1 vectors of the transmitted and received data symbols. To obtain the transmitted data symbols equation (5) should be solved which is called MIMO-OFDM equalization.

## (2.8)

This equalization works well in case of small noise and no ISI or ICI. In the presence of ICI and ISI the received signal can be written as in [2]

## (2.9)

where

## (2.10)

These all above equation are from [7]

are the useful term. In order to be able to terminate the interference the ISI and ICI terms should be calculated and then subtracted from the received signal. [7]

## 2.5 Advantages of MIMO-OFDM

Low interference

Diversity gain

enhance data ability

Power efficiency

Bandwidth gain

## 2.6 Restrictions of MIMO-OFDM

Spacing between the antenna must be suitable depending on the type of channels

Very compound transmitter and receiver

## 2.7 MIMO-OFDM Research ideas

Application of CMDA in MIMO-OFDM

OFDMA

Adaptive MIMO antenna selection algorithms.

Frequency hopping in the presence of frequency selective channels.

Noise forbearance and interference cancellation

MIMO channel estimation procedure improvement

## CHAPTER 3

## 3.1 Introduction

Different types of modulations allow you to transfer more bits per symbol and achieve more throughputs and better spectral efficiencies as well. But, better signal-to-noise ratios (SNRs) are required to reduce any interference and maintain good Bit Error Ratio (BER) when a modulation technique such as 64-QAM is being used.

The use of modulation allows a wireless system to select the highest order modulation depending on the condition of the channel. Normal estimate of the channel conditions required for different modulation techniques can be seen in the Fig 3.1. For ranges closer, higher order modulations like QAM64 can be used to get higher throughput which allows the system to reduce fading and interference and to increase the range, lower modulations like QPSK are required to step down.

## 3.1signal strength in different modulation

QAM and QPSK are the modulation techniques which are used in IEEE 802.11 (Wi-Fi*), IEEE 802.16 (WiMAX*) and 3G (WCDMA/HSDPA) technologies. The modulated signals are detected at the receiver side and then demodulated to get original signal can be recovered. The use of modulation permits wireless technologies to optimize throughput, yielding higher throughputs and also covering long distances. [8]

## 3.2 QPSK Modulation

QPSK modulation and demodulation is presented step wise in this chapter. Usage of advanced QPSK modulation converts analog communication to digital. Euler's relation is used to evaluate the multiplication of sine and cosine signals, and SPICE simulation is used to show QPSK modulation of a 1MHz sine wave. Phase and frequency errors are eliminated by using digital transmission. With advancement of technology in electronics, the limits of local and global communication started depleting, ensuing in a world that is smaller and easily accessible to share the information. Local communication carried through wires is cost effective. But to share information to longer distances radio waves from a hardware standpoint can be used inspite of their drawbacks such as, the loss of information in poor weather conditions, hindrances, and interference from some other sources of electromagnetic waves.

Different modulation techniques give different solutions in terms of cost effectiveness and quality, but received signals remained analogous until recent times. Frequency modulation and phase modulation exist with certain immunity to noise, but amplitude modulation was same like demodulate. However, low-cost microcontrollers, domestic mobile telephones and satellite communications made digital modulation popular. Digital modulation techniques prove to have more advantages over analog transmission, like encrypted data with error correction along with limited bandwidth allocated to every service.

In traditional analog systems, digital modulation can utilize amplitude and frequency modulation with different advantages. Frequency and phase modulations are the opted scheme for most of the services used today as they offer more resistance to noise.

## 3.2.1 Digital frequency modulation

A small change from traditional analog frequency modulation (FM) can be implemented by giving a digital signal to the modulation input. Then the output takes the sine wave form at two distinct frequencies. The original waveform can be retrieved easily by passing the signal through two filters and converting the resultant back into logic levels. This form of modulation is called frequency-shift keying (FSK).

## 3.2.2 Digital phase modulation

Normally, digital phase modulation, or phase-shift keying (PSK), has nearly the same frequency modulation. In this modulation process, changing the phase of the transmitted waveform in the place of frequency, and this kind of phase changes represent digital data. In the easiest way, a phase-modulated waveform can be implemented by using the digital data to change between two signals of same frequency but opposite phase. If the output, waveform is multiplied by a sine wave of same frequency and as a result, two components are generated. They are the cosine waveform of twice the received frequency and, frequency-independent for which the amplitude is relative to the cosine of the phase shift. Therefore, filtering out the higher-frequency term returns the original data prior to transmission.

QPSK: Mainly known as quaternary Phase shift Keying, or 4-psk or, quadriphase PSK. Normally four points constellation diagram used by QPSK, aligned around a circle with four phases. It can encode two bits per symbol as shown in the diagram, to decrease the bit error rate (BER) which is sometimes nearly double the BER of BPSK. The QPSK can be used either to increase the data rate nearly two-fold compared to a BPSK system using the same bandwidth of the signal in mathematical analysis, or a BPSK systems needs only half the bandwidth to continue the same data-rate. In the second case, the BER of QPSK is nearly same as the BER of BPSK. QPSK transmits double the data rate in a given bandwidth when compare with BPSK at the same BER. And main disadvantage is QPSK transmitters and receivers are complicated than that of BPSK transmitter and receiver. And cost of the system is also high. [11]

## 3.2 Constellation diagram for QPSK

## 3.3 Implementation

The implementation of QPSK is more normal than that of BPSK and also gives the implementation of higher-order PSK. Converting symbols in the constellation diagram in sine and cosine terms to transmit the waves.

This yields the four phases and as required which results in a two-dimensional signal space with unit basis functions

First function has been used in-phase component and second function is used as the quadrature component.

Therefore, the signal constellation has the signal-space 4 points

Here 1/2 specifies that the total power is divided equally between the two carriers.

Compare these functions with BPSK gives clearly how QPSK can be looked as two independent BPSK signals.

QPSK systems can be developed in so many ways. Hear we shown one type the transmitter and receiver structure.

## 3.3 Conceptual transmitter structure for QPSK.

The binary data stream is divided into two components, namely, in-phase and quadrature-phase components. These streams are converted into two orthogonal basis functions separately. In this process, two sinusoids are used. Then, both the signals are superimposed giving QPSK signal.

## 3.4 Receiver structure for QPSK.

The corresponding filters can be changed with correlators. Every device uses a reference threshold value to decide whether a 1 or 0 is detected.

## 3.4 Bit error rate

Although QPSK can be shown as a quaternary modulation, also easy two independently modulated quadrature carriers. To modulate the in-phase component of the carrier even bits are modulated, while to modulate the quadrature-phase component odd bits are modulated of the carriers using Interpretation, which may change even to odd or odd to even. Therefore the probability of BER for QPSK is equals the probability of bit-error for BPSK:

However, in order to reach the same BER probability as Binary PSK, Quadrature PSK needs twice the power.

The error rate of the symbol is given by

If the signal-to-noise ratio is increased, the probability of the symbol error may be estimated.

All these above equations are from [12]

## 3.5 QPSK signal in the time domain

The two carrier waves are cosine and sine waves, as represented by the signal-space analysis. Here, the even-numbered bits are assigned for the quadrature Component and the even-numbered bits are assigned for the in-phase component. The resultant signal is depicted below. When we observe the signal I suddenly jump occurs in phase, can say that PSK changes the phase of each and every component at the start of each bit period.

## 3.6 Timing diagram for QPSK.

The binary data flow is represented beneath the time axis. Both the signal components along with their bit assignments are shown the top and the total signal is shown at the bottom.

The binary data that is conveyed by this waveform: 1 1 0 0 0 1 1 0.

The even bits are highlighted here, representing the quadrature-phase component: 1 1 0 0 0 1 1 0

The odd bits are highlighted here, representing the in-phase component: 1 1 0 0 0 1 1 0

## CHAPTER 4

## 4.1 Per-tone equalization (PTEQ)

A wireless communication link using multiple transmit and receive antennas is known as a multiple-input multiple output (MIMO) link, it will boost the capacity of system. Aiming at wireless and broadband communications, the multipath nature of the environment creates the multiple-input multiple output channels to be frequency selective. Orthogonal frequency division multiplexing (OFDM) can transmit such a frequency-selective MIMO channel into a group of parallel frequency-flat MIMO channels. If the channel order is less than or equal to the cyclic prefix (CP) length. In this approach, the data symbol vectors can be recovered easily using one-tap frequency-domain equalizer. However, If the channel length is more than CP length. This system does not work anymore.

We show in this case that by swapping the filtering process of the MIMO channel and the sliding fast Fourier transform(FFT), the data type for the smoothened received signal of each tone of the MIMO OFDM system is same like data type for the smoothened received signal of a MIMO(multiple input multiple output) single-carrier system. The difference is a column-compressed block Toeplitz matrix instead of a block Toeplitz matrix in the channel matrix, and the ISI contains of virtual data symbol vectors instead of original data symbol vectors. Therefore, the conventional equalization method for MIMO SC systems needs neither the channel matrix to be block Toeplitz or the ISI(inter symbol interference) to consist of original data symbol vectors, and also we can apply the conventional equalization method for MIMO SC systems to each tone of the MIMOOFDM system.

Per-tone equalization (PTEQ) method for MIMO OFDM systems is a good alternative to the recently implemented time-domain equalization (TEQ) method for MIMO OFDM systems. In this method, a time-domain equalizer is applied to decrease the MIMO channel to a square MIMO filter with order less than or equal to the CP length. So, the data symbol vectors can be recovered easily by a one-tap frequency-domain equalizer. Comparison between the PTEQ approach and the TEQ approach for MIMO OFDM as follows.

â€¢ Since the PTEQ method treats all tones individually, whereas the TEQ method treats all tones together the PTEQ method gives better performance than the TEQ method. And also, the performance of the PTEQ method is a much smoother function of the synchronization delay than TEQ method. Hence, for the PTEQ method the synchronization delay setting is less critical than for the TEQ method.

â€¢ Since the PTEQ method works at low rate in the frequency-domain and the TEQ method works at high rate in the time-domain the show-time complexities of the PTEQ method and the TEQ method are comparable, up to the fact that the PTEQ method has to carry out one FFT per OFDM symbol and per receive antenna and the TEQ method has to carry out one FFT per OFDM symbol and per transmit antenna.

â€¢ Since the PTEQ method uses a different type of equalizer coefficients for each tone and the TEQ method uses the same type of equalizer coefficients for each, the PTEQ method needs more memory space than the TEQ method, and the design of the PTEQ method is normally larger than the design of the TEQ method.

## 4.1 Block diagram of the PTEQ method

In the PTEQ method, which is shown in above diagram, we apply an Nt * Nr per -tone equalizer with order K to

## (4.1)

The main aim of the per -tone equalizer is to find from calculated at Î´ = Î”(Î” is the synchronization delay)

## (4.2)

The above equation can be rewritten as

## (4.3)

Where W(p) =[Wk(p),....,W0(p)]

Assume 0 â‰¤ Î” â‰¤ K + L -Ê‹ we can write equation as

## (4.4)

Zero-forcing per-tone equalizer is given by

## (4.5)

And MMSE per -tone equalizer, is given by

## (4.6)

Where S is the Nt Ã- (K+L-v+1) Nt and matrix is defined as

S:=[0 Nt Ã- (K+L-v-Î”) Nt, INt , 0Nt Ã-Î”Nt]

and and are noice and data covariance matrices is defined as

## (4.7)

## (4.8)

These above equation are from [4]

The above two covariance matrices can be simulated on the statistics of both data and noise. The sufficient condition for the existence of the ZF PTQ is that has column rank (K+L-v+1)Nt this needs that (K+1)â‰¥(K+L-v+1) which can be obtained with large K as long as Nr > Nt If we have extended the data model for OFDM system. This dimensionality condition for the per tone equalizer not clearly visible [4].

## 4.2 MMSE Algorithm

In this case, it is attractive to use the minimum mean square error algorithm that reduces the mean square error between each signal and its estimate, by means of that maximizing signal-to-interference and noise ratio. The MMSE weights need knowledge of noise-plus-interference statistics. Hence, it is very important to detect if the ambient environment is interference-limited or noise-limited, and to collect exact statistics by averaging on suitable time and frequency intervals. If the interferer is friendly the interferer's spatial signature is accessible to be used in the MMSE weights. If it is unfriendly interference from neighbouring cells, the spatial structure of interference is used to capture because of second-order statistics.[1]

## In MIMO-OFDM, one of the equalization methods called Minimum Mean Square Error (MMSE) equalization. Let us consider that the channel is 2Ã-2 MIMO channel and the modulation type is BPSK.

In a 2Ã-2 MIMO channel means probably using two transmit antennas.

1. Consider that we are transmitting like {X1, X2, X3,....Xn} sequence.

2. In general transmission, we will be sending X1 as a first time slot, X2 as a second time slot, X3 as s third time slot and so on.

3. However, here we are using 2 transmit antennas, we can group the symbols into 2 groups. In the first time slot sending X1 and X2 from the 1 and 2 antenna. In the second time slot sending X3 and X4 from the 1 and 2 antenna. In the third time slot sending X5 and X6 and so on.

4. Here we are combining two symbols and transmitting them in single time slot, we need only n/2 time slots for transmission.

5. This kind of simple explanation of a probable MIMO transmission types using two transmit antennas and two receive antennas.

4.2 2 Transmit 2 Receive (2Ã-2) MIMO channel

## Other Assumptions

1. In this case channel is flat fading.

2. The channel experienced between every transmitter to the receive antenna is independent and changing randomly in time and independent from the channel experienced by other transmit antennas.

3. For the transmit antenna to receive antenna, every transmitted signal gets multiplied by a randomly changing complex number . If the channel is a Rayleigh channel, the both real and imaginary parts of are Gaussian distributed having mean and variance .

4. On the receive antenna side, the noise has the Gaussian probability density function with

With and .

5. The channel is known at the receiver.

## Minimum Mean Square Error (MMSE)

Now it is math expression for two symbols which are interfered with each other. In the first time slot.

The signal received on the first receiver antenna is,

The signal received on the second antenna receiver is,

where

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

is the channel from 1st transmit antenna to 1st receive antenna,

is the channel from 2nd transmit antenna to 1st receive antenna,

is the channel from 1st transmit antenna to 2nd receive antenna,

is the channel from 2nd transmit antenna to 2nd receive antenna,

are the transmitted symbols and

,are the noise of 1st , 2nd receive antennas.

Let us assume that the receiver knows ,,and The receiver also knows and For convenience, and the equation can be represented in matrix notation.

Matrix notation as follows:

quivalently,

The Minimum Mean Square Error (MMSE) method tries to find a coefficient which minimizes the criterion,

Solving,

Compare this equation with zero forcing equalizer, apart from the term both the equations are comparable. Also when the noise term is zero, the MMSE equalizer reduces to Zero Forcing equalizer. [2]

## 4.3 Channel Estimation

The main use of channel estimation is to find the channel between each pair of both transmit and receive antennas. The signals are transmitted from each antenna are orthogonal to each other therefore that the channel from each transmit antenna can be recognized uniquely. The signals are spaced in frequency, with separating less than the channel's frequency coherence therefore that the channel can be interpolated between signals. The channel interpolation is optimized depending on channel delay spread, and it is also improved by time-domain filtering. In the downlink, a dedicated channel recognition slot is broadcast to all users like frame-by-frame basis. In the uplink, each slot both training and data tones since the traffic from the CPE can be busty, and the channel may change between bursts.[1]

## 4.4 Proposed algorithm

In this case, a time-domain signal detection algorithm based on SOS is introduced for MIMO-OFDM systems on the frequency selective fading channels. Following points are the general assumptions for proposed algorithm.

Signals coming from different transmit antennas are statistically not dependent, and signals coming from each transmit antenna at different subcarriers are independent with zero mean and unit variance. It means that each transmit antenna modulates all subcarriers with equal amount of power. This condition arises in spatial multiplexing and spatial multiple access systems as independent data signals are transmitted streams on different antennas and different subcarriers. This system is different from orthogonal frequency division multiple access systems where each transmit antenna vary the frequency of the subcarriers. The autocorrelation matrix of the signals before IFFT ci is defined as

where E{.} is the expectation operator.

Rc=E{cici*}=I2NP

The noise components are independently identically distributed and also it is independent of the signals from all transmit antennas.

The MN'x (L+N')P matrix H is of full column rank after taking off all-zero columns, that means the Nonzero columns are independent. This is the condition for detecting the signals based on SOS. In order to reach this condition, the no of receive antennas, M must be selected to satisfy MN'â‰¥ (L+N')P/N', so that there are more rows than columns. In some situations the number of receive antennas (M) is chosen equal to the number of transmit antennas (P) plus one, the above inequality will be fulfilled. Under this condition, the matrix H has the property

H*(HH*)# H=A(N'+L)P

in which(.)# represents A(N'+L)P pseudo inverse and is an (N'+L)P X (N'+L)P matrix with one along the major diagonal except the rows corresponding to the all zero columns of H, which is equal to zero. In other words, A (N'+L)P is an (N'+L)P X (N'+L)P identity matrix with all-zero rows corresponding to the all-zero columns of H.[3]

## 4.4.1 Zero-Noise Case

To simplify the derivation of the algorithm, zero noise is first assumed. The effect of noise on the algorithm is then examined.

Without noise can be expressed as

When can also be modeled as

1) Equalization and Signal Detection: It is apparent from (15) and (29) that the received signal vector includes path signals [each path signal refers to one sample signal,

see (15)] from each transmit antenna/user. Before deriving the equalizer designed to cancel most of the ISI, some useful properties are described first in the following.

Property 1: When the matrix is given by

In which when

Property2: the matrices satisfy

And

Here U is a matrix with only two entries having values of one at the positions and while all remaining entries are zeros.

Property 3:

The matrix has all zero columns except the th, and theth columns given by and respectively, where denotes the ath column of .

## CHAPTER 5

## 5.1 Simulation Model of MIMO-OFDM system:

A C.P.U is needed to simulate MIMO-OFDM system because manually it is very difficult to calculate. An MIMO-OFDM system is simulated using Matlab R2009a to enable different types of algorithms in Time-Domain Signal Detection Based on Second-Order Statistics for MIMO-OFDM model to differentiate and tested. The main aim of this project is to evaluate the performance of MIMO-OFDM systems using different algorithm schemes like PTEQ and TEQ.

An MIMO-OFDM system is model using Matlab as shown in Below Figure This model consists of three main blocks as Transmitter, Channel and Receiver.

## 5.1MIMO-OFDM system

## 5.1.1 Random Data In

This random data in used to generate a serial random binary data to pass into MIMO-OFDM transmitter

## 5.1.2 Serial to parallel conversion

serial to parall converter it means converts serial data into word size which is need for transmission and shifted into parallel form. The parallel information will be transmitted in parallel by giving each data information packet to one carrier in the transmission.

## 5.1.3 Modulation of Data

Data modulation is nothing but converts or encodes message into sequence of binary digits representing impulses of +ve and -ve polarity using different modulation scheme (BPSK,QAM,...etc). Then the data on every symbol is mapped to a phase angle depending upon Modulation order.

## 5.1.4 Inverse Transformation

After obtaining required spectrum an Inverse transformation is used to find the communicating time waveform. Then after at start of each symbol cyclic prefix is added.

## 5.1.5 Cyclic Prefix

Cyclic prefix is nothing but it's just a periodic extension of OFDM symbol of last part which is added in transmitter and removed in receiver before demodulation. The benefits of this cyclic prefix in mainly it prevents Inter symbol Interference (ISI) and Inter Carrier Interference (ICI)

## 5.1.6 Receiver

Basically Receiver does the contrary operation of transmitter. Cyclic Prefix is removed and DFT or DCT of each symbol is taken to find the transmitted spectrum. By demodulating the receiver phase, phase angle of each transmission carrier is then evaluated and converted back to data word. The data words are combined with same word size as the original data and renewed back to original binary form.

## 5.2 Simulation Results and Analysis

In this following section I am going to analyze the results which I got. These simulation results are plotted from performance evaluation of MIMO-OFDM systems by measuring Bit error rate. This performance were measuring for TEQ, PTEQ, proposed algorithm at different channel lengths (14,16,18,20) using QPSK modulation schemes.

## 5.3 Bit Error Rate (BER):

A bit error rate is defined as number of errors occurred in string of total number of bits sent.

If the transmission between transmitter and receiver is good then the signal to noise ratio is high and it results very small bit error rate.

## 5.4 Case 1: channel length is less than or equal to the CP length

In this case we are taking channel length is less than or equal to the CP length. In the TEQ, PTEQ algorithm channel length is estimated by one as and the channel coefficient is estimated using maximum likelihood method using two consecutive OFDM pilot blocks. The BER performance of different algorithms taken under consideration for and . It is shown in respectively. According to the results proposed algorithm performance is better than the other algorithms.

## 5.5 Case 2: channel length is grater then CP length

In this case we considered channel length is greater than CP length fig gives the performance of PTEQ, TEQ and proposed algorithms for. These results give the outperformance of proposed algorithm with existing ones. The main advantage of the proposed algorithm is no need to find the channel length. In practice estimation of channel length is using computationally intensive schemes like AIC or MDL hear usually estimation error will occurs this will degrade the performance of the existing algorithms.

## CHAPTER 6

## 6.1 Conclusion

In this thesis, we proposed new algorithm in time-domain signal detection based on second order statistics (SOS) for MIMO-OFDM system. In this A new system algorithm is implemented. Here the i th received OFDM block is shifted towards left by J samples. The new system algorithm model has some structural properties that allow an equalizer to be designed to reduce most of the inter symbol interference (ISI) depends on SOS of the received signals. At the receiver side of the equalizer, only two paths of the input signals are used and the signals can be easily detected. Due to the different structure of the new algorithm, it turns out that only columns of the channel matrix estimation are required. It follows that the least number of pilot symbols needed to estimate the columns of the channel matrix and it does not dependent on the channel length. That means channel length estimation is not necessary, which means that the proposed algorithm has substantial advantage, according to computer as well as avoiding performance decrease due to channel length estimation error, in present algorithms. And also, the proposed algorithm is does not depend on channel length if the channel length is less than, equal to or longer than the cyclic prefix CP length. Simulation results have shown the out performance of the proposed algorithm with the existing techniques.

The main aim in developing wireless communication systems are to improving throughput (bit error) and the capacity of the network. In this case the best alternative is MIMO (multiple input multiple output) that means using multiple antennas are applied at both the transmitter and receiver side, mainly in more scattering environment.

The main application of the MIMO is 4G (fourth generation) wireless local area networks. At present IEEE 82.11a and IEEE 802.11g are based on OFDM and high data rate extension of these techniques could be depends on MIMO. These systems are mainly improved in indoor environment. Because, these environments are typically characterized by a more scattered multipath.