Concept of MIMO System

MIMO is a technology which exploits the rich scattering environment at the transmitter and/or receiver such that when multiple spatial data streams are launched into the chan-nel, they will be distorted independently by the channel; thereby increasing the probability of recovering the transmitted data at the receiver. One of the motivation for MIMO is to significantly increase the data throughput without additional bandwidth or transmit power. This is achieved by taking advantages of the rich scattering environment sur-rounding the transmission terminal and by using spatial multiplexing, where a high-rate source data stream is split into multiple low rate data streams according to the number of transmit antennas. Each data stream is then emitted by a different transmit antenna in the same bandwidth. In a rich scattering environment, the transmitter is able to transmit the signal in parallel channels with distinguished non-zero eigenmode. The transmission from different transmit antennas are hence distinguished. Through spatial multiplexing, multiple data streams can be transmitted simultaneously over independent parallel chan-nels, and therefore the transmission rate and capacity will be increased. Consequently, MIMO techniques are often applied for high speed broadband wireless communications.

Considering the trade-off between capacity and reliability, it is possible to increase the link reliability by the use of transmit diversity. If a single data stream is transmitted by multiple transmit antennas, several observations of the same stream will be obtained by multiple receive antennas. Under a rich scattering environment, the spatial diversity can be maximized for the fixed number of antennas. In this case, fading effects of channels are reduced such that the overall system becomes more reliable. STC techniques such as

2.2 MIMO-OFDM Systems Model 12

Chapter 2: Chapter

STTC and STBC are usually applied to MIMO systems with transmit diversity. The basic idea of STC is transmitting multiple and redundant copies of a data stream to achieve transmit diversity. An example of STBC using Alamouti code [25] is shown in Figure 2.6, which has a simple two-branch transmit diversity. A block of two modulated symbols, u1

and u2, is encoded by a coding matrix. The encoder outputs are then transmitted in

Modulator

Figure 2.6: A block diagram of the Alamouti space-time encoder

two consecutive transmission periods from two transmit antennas, which are denoted as u1 = [u1−u^∗₂] and u2 = [u2u^∗₁], respectively. In the first transmission period, u1and u2 are transmitted simultaneously from the first antenna and the second antenna, respectively.

During the second period, −u^∗₂ and u^∗₁ are transmitted from the first antenna and the second antenna, respectively. It is clear that the encoding involves with both space and time domains. Furthermore, the inner product of u1 and u2 is zero. In other words,

u1· u2 = u1u^∗₂− u^∗₂u1 = 0,

such that the transmit sequences from two transmit antennas are orthogonal. The key feature of this scheme is that a full diversity gain can be achieved with a simple maximum-likelihood decoding algorithm at the receiver with perfect CSI. STBC with the number of transmit antennas greater than 2 based on orthogonal designs are discussed in [26].

Obviously, a trade-off between spatial multiplexing and spatial diversity for MIMO exists.

2.2 MIMO-OFDM Systems Model 13

For a MIMO system with the fixed number of antennas, data rate and link reliability cannot be optimized simultaneously under the same channel [27].

Ant 1

TX

Ant 2

Ant N_t

h

h

RX

Nr

( )

²

( )



%

( ) ⁿ

η

Figure 2.7: Schematic of the generic MIMO system

The schematic of a generic single-user MIMO system is illustrated in Figure 2.7, where Nt transmit antennas and Nr receive antennas are equipped at the transmitter and re-ceiver, respectively. The following are conditions assumed for the MIMO system in Figure 2.7:

• The channel maintains invariant during the transmission of one frame, which means that channel is block or slow fading.

• The channel is frequency-flat fading, which means that spectrum of channel is con-stant over the whole bandwidth such that channel gain can be represented by a

2.2 MIMO-OFDM Systems Model 14

Chapter 2: Chapter

complex number.

Under the above assumptions, the input/output relation of a narrowband, single-user MIMO system can be written as

x[n] = Hu[n] + η[n], Nr× Nt channel matrix, and η[n] is the Nr× 1 channel noise vector. The channel matrix is given as transmit antenna to the i^th receive antenna. αij and βij are the real part and imaginary part of hij, respectively. φij is the phase angle of hij and |hij| is the magnitude. If αij

and βij are independent and Gaussian distributed random variables, then |hij| is Rayleigh distributed, which leads to a Rayleigh flat-fading channel.

While the transmission bandwidth is larger than the coherent bandwidth of channels, the channel is considered to be frequency selective. Denoting a frequency selective fading channel impulse response from the j^th transmit antenna to the i^th receive antenna as hij = [hij[0] hij[1] . . . hij[q]]^T, where q is the channel order. The Nr × Nt MIMO

2.2 MIMO-OFDM Systems Model 15

matrix can then be written as

where ℓ = 0, 1, . . . , q. The input/output relation of the frequency selective fading channel can then be written as

x[n] = Xq

ℓ=0

Hℓu[n − ℓ] + η[n]. (2.1)

Compared with frequency flat fading attenuation, (2.1) is a linear superposition of the product of Hℓ and the transmit signal vector due to convolution. (2.1) can be rewritten more compactly if we further define

H, number of the received signal vector. Using these definitions, the input/output relation in (2.1) can be written as

ˇ

x[n] = Hˇu[n] + ˇη[n].

2.2 MIMO-OFDM Systems Model 16

Chapter 2: Chapter