# Peak To Average Reduction In Mimo System Computer Science Essay

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In multiple-input multiple-output system, more than one antenna is used at each end of the communication link. MIMO signaling is a ground-breaking development pioneered during nineties and become a highly researched since large increases in capacity over the Shannon limit are available without increasing the power or the bandwidth. [1]

In multiple antennas system, high data rate can be achieved through multiplexing and the performance will be improved through diversity. Single-input multiple-output (SIMO) and multiple-input single-output (MISO) systems have been used in mobile communication to provide diversity gain. Moreover, by using multiple antennas at the transmitter and\or receiver (known as 'smart antenna'), ISI and interference from other users can be reduced in an interference limit cellular environment. Space division multiple access (SDMA) can provide array gain toward the wanted user while nulling the interferences. However, spectral efficiency gain often requires accurate instantaneous information about the channel at the receiver, and sometimes at the transmitter, which is not always available in an environment that the incoming signal experience some delay and spatial angular spreads. [2]

Figure 2.1 Different antenna configurations in space-time system

In MIMO system, in addition to diversity and array gain, spatial multiplexing introduces new capacity gain where highly scattered environment becomes a benefit rather than obstacle. When different data is transmitted simultaneously at the same time and frequency from each antenna element, the receiver is able to separate each channel since the scattered environment causes the channels to become partially orthogonal.

## 2.1.2 MIMO Channel

The basic channel model of MIMO system for a single user, flat fading channel with n transmit antenna and m receive antenna is shown bellow.[3]

Figure 2.2 Flat fading MIMO channel

The input-output relation is given by:

Y= H.s +w (2.1)

Where s= [s1 s2 s3 … sn]T is n x1 transmit vector and the channel matrix is:

(2.2)

The m x 1 receive vector is y= [y1 y2 … ym]T and the noise vector is give by w=[ w1 w2 … wm]T. In addition to the number of transmit and receive antennas and SNR that affect the capacity of the MIMO system, this capacity is also highly dependent on the variation of the channel matrix, H. in time domain the output from SISO system can be expressed as the convolution of input and channel impulse response.

y(t) = h(τ, t) * s(t) = (2.3)

the sampled version of the output is

y[k] = (2.4)

here L is the channel length measured in sampling periods. The received sampled signal is:

(2.5)

In MIMO channel it becomes:

(2.6)

Where y is the m x 1 received vector.

## 2.1.3 Array gain, diversity gain and spatial multiplexing

The performance improvements resulting from the use of MIMO system are due to array gain, diversity gain, spatial multiplexing gain, and interference reduction, whereas SIMO and MISO systems can offer only array gain and diversity gain.

## 2.1.3.1 Array gain

Array gain or beam-forming can be done through processing at the transmitter and the receiver to increase in average received SNR. Beam-forming provides diversity and array gain via coherent combining of the multiple signal paths. The performance gain is depending on whether or not the channel is known at the transmitter\receiver. Channel knowledge at the receiver is typically available; however, it is more difficult to maintain the channel state information at the transmitter.[4]

## 2.1.3.2 Diversity gain

In wireless system the signal power fluctuates randomly or fades. A SISO system in a Rayleigh channel can experience large fading. Time diversity, frequency diversity, and spatial diversity techniques are often used to reduce the chance of deep fading.

In time diversity, the data is transmitted after a delay of at least the channel coherence time so the channels become uncorrelated. However, this technique reduces the data rate as the several copies of the data are sent.

In frequency diversity, the data is transmitted simultaneously at different frequencies with coherent bandwidth separation. So the channels become uncorrelated. However, this is not desirable since the bandwidth is wasted.

In spatial diversity two or more antennas are used at the transmitter and/or receiver (MIMO) and it does not require the use of extra bandwidth. But it adds cost and complexity to the base station, mobile or both. It is preferred over time/frequency diversity as it does not require expenditure in transmission time or bandwidth. [5]-[6].

## 2.1.3.3 Spatial multiplexing gain

MIMO channel offer a linear increase in capacity and bit rate without using more power or bandwidth. This gain, referred to as spatial multiplexing gain, is realized by transmission of independent data signals from the individual antennas. In a rich scattering environment, the receiver can separate the different streams, as a result increasing in capacity.

Figure 2.3 MIMO used for spatial multiplexing gain

## 2.1.4 MIMO Channel capacity

The Shannon upper bound limit on capacity is given by:

C= log2[1+SNR] bps/Hz (2.7)

The MIMO system capacity becomes [7]:

If the channel knowledge is unknown for the transmitter and the signals transmitted from each antenna have equal powers, that is Rss =I. In this case the system capacity can be rewrite as[7].

C= log2 [det(IN + HHH)] (2.9)

Where det is the determinant, Im is the m by m identity matrix, m is the number of receive antenna element and n is the number of transmit antenna elements.

According to basis of these formulas it can be shown that multi-antenna system has indeed improved the channel capacity compared to single antenna system. This increase in channel capacity can be used to raise the information transmission rate or improve the reliability of communication systems by enhancing information redundancy in order to maintain the information transmission rate.

## 2.1.5 MIMO Space-Time Code

The space time coding technique is basically a two-dimensional space and time processing method. Since the input-output relationship of a MIMO channel is y=Hx + n, the symbol transmitted over each channel symbol time is a vector rather than a scalar, as in traditional modulation for the SISO channel.

Most space-time code are designed for quasi-static channel in which the channel is constant over a block of T symbol times and the channel is assumed to be unknown at the transmitter. Under this model, the channel input and output become matrices with dimension corresponding to space and time. Correlation of time and space is introduced between signals that are transmitted by different antennas so that the receiver can realize diversity reception. As a result, higher coding gain can be achieved by meant of space-time code without using more bandwidth which cases to enhance the capacity of the wireless system.

MIMO system can generally be divided into Space-Time Code (STC) and Spatial Multiplexing (SM). Classical STC includes Space-Time Trellis Code (STTC) and Space-Time Block Code (STBC). STBC is used to attain a full diversity gain by performing a maximum likelihood decoding algorithm. A typical Spatial Multiplexing technique is space-time structured and includes V-BLAST, H-BLAST, and D-BLAST. The V-BLAST is the most basic form which is widely used in a flat fading channel, but it cannot achieve spatial diversity gain.

## 2.2 Orthogonal Frequency Division Multiplexing (OFDM)

Different techniques have been studied in order to meet the demanding high data rate requirements for communication system. Among those, orthogonal frequency division multiplexing has become extremely popular and has been used in wireline applications such as digital subscriber lines (DSL) [9] (sthompson) . Also OFDM has been adapted in wireless applications such as wireless local area networks (LANs) under the IEEE 802.11standard [552] (sthompson), digital audio and video broadcasting (DAB and DVB) [392] (sthompson), ultra-wideband (UWB) system, wireless metropolitan networks (MANs), under the IEEE 802.16 (WiMAX) standard [160, 264,604] (sthompson).

## 2.2.1 Single Carrier and Multi-carrier System

The basic idea of the multicarrier modulation follows from willing to achieve high data rates and ISI free channels. The inter symbol interference appears when the symbol time duration Ts In order to have free ISI channels, the symbol time duration Ts has to be significantly larger than the channel delay spread τ. Digital communication systems simply cannot function if the ISI is presents. As a result error floor develops and as the Ts moves toward, or falls below τ, the bit error rate considerably increases.