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Wireless communication using multiple-input multiple-output (MIMO) systems enables increased spectral efficiency for a given total transmit power. Increased capacity is achieved by introducing additional spatial channels that are exploited by using space-time coding. In this article, we survey the environmental factors that affect MIMO capacity. These factors include channel complexity, external interference, and channel estimation error. We discuss examples of space-time codes, including space-time low-densityparity-check codes and space- time turbo codes, and we investigate receiver approaches, including multichannel multiuser detection (MCMUD). The ‘multichannel’ term indicates that the receiver incorporates multiple antennas by using space-time-frequency adaptive processing. The article reports the experimental performance of these codes and receivers.
M - multiple-output (MIMO) sys- tems are a natural extension of developments in antenna array communication. While the
advantages of multiple receive antennas, such as gain andspatialdiversity,havebeenknownandexploitedfor some time [1, 2, 3], the use of transmit diversity has only been investigated recently [4, 5]. The advantages of MIMO communication, which exploits the physi- cal channel between many transmit and receive anten- nas, are currently receiving significant attention [6–9]. While the channel can be so nonstationary that it can- not be estimated in any useful sense [10], in this article we assume the channel is quasistatic.
MIMO systems provide a number of advantages over single-antenna-to-single-antennacommunication. Sensitivity to fading is reduced by the spatial diversity provided by multiple spatial paths. Under certain envi- ronmental conditions, the power requirements associ- ated with highspectral-efficiency communication can be significantly reduced by avoiding the compressive re-gionoftheinformation-theoreticcapacitybound.Here,spectral efficiency is defined as the total number of in- formation bits per second per Hertz transmitted from one array to the other.
After an introductory section, we describe the con- cept of MIMO information-theoretic capacity bounds. Because the phenomenology of the channel is impor- tant for capacity, we discuss this phenomenology and associated parameterization techniques, followed by ex-amplesofspace-timecodesandtheirrespectivereceiversand decoders. We performed experiments to investigate channelphenomenologyandtotestcodingandreceiver techniques.
Capacity
We discuss MIMO information-theoretic performance bounds in more detail in the next section. Capacity in- creases linearly with signal-to-noise ratio (SNR) at low SNR, but increases logarithmically with SNR at high SNR. In a MIMO system, a given total transmit power canbedividedamongmultiplespatialpaths(ormodes), driving the capacity closer to the linear regime for each mode, thus increasing the aggregate spectral efficiency. As seen in Figure 1, which assumes an optimal high spectral-efficiency MIMO channel (a channel matrix with a flat singular-value distribution), MIMO systems enable high spectral efficiency at much lower required energy per information bi
MIMO Wireless Communication
The information-theoretic bound on the spectral ef- ficiency is a function of the total transmit power and the channel phenomenology. In implementing MIMO systems, we must decide whether channel estimation information will be fed back to the transmitter so that the transmitter can adapt. Most MIMO communica- tion research has focused on systems without feedback. A MIMO system with an uninformed transmitter (without feedback) is simpler to implement, and at highSNRitsspectral-efficiencyboundapproachesthatofaninformed transmitter (with feedback).
One of the environmental issues with which com- munication systems must contend is interference, ei- ther unintentional or intentional. Because MIMO sys- tems use antenna arrays, localized interference can be mitigated naturally. The benefits extend beyond those achieved bysingle-input multiple-output systems, that is, a single transmitter and a multiple-antenna receiver, because the transmit diversity nearly guarantees that nulling an interferer cannot unintentionally null a large fraction of the transmit signal energy.
Phenomenology
We discuss channel phenomenology and channel pa- rameterization techniques in more detail in a later sec- tion. Aspects of the channel that affect MIMO system capacity, namely, channel complexity and channel sta- tionarity, are addressed in this paper. The first aspect, channel complexity, is a function of the richness of scat- terers. In general, capacity at high spectral efficiency increases as the singular values of the channel matrix increase. The distribution of singular values is a mea- sure of the relative usefulness of various spatial paths through the channel.
Space-Time Coding and Receivers
Experimental Results
Because information-theoretic capacity and practical performance are dependent upon the channel phenom- enology, a variety of experiments were performed. Both channel phenomenology and experimental procedures are discussed in later sections. Experiments were per-
98 LINCOLN LABORATORY JOURNAL VOLUME 15, NUMBER 1, 2005
MIMO Wireless Communication
TOY 2 × 2 CHANNEL MODEL
B of channel matrix eigenvalues is essential to the effectiveness of multiple-input, multiple-output(MIMO) commu- nication, we employ a toy example for the purposes of introduction, and we discuss the eigenvalue dis- tribution of a 2 × 2 narrowband MIMO system in the absence of environmental scatterers. To visualize the example, we can imagine two receive and two transmit antennas located at the corners of a rect- angle. The ratio of channel matrix eigenvalues can be changed by varying the shape of the rectangle. The columns of the channel matrix H(in Equation 1 in the main article) can be viewed as the receiver- array response vectors, one vector for each transmit
antenna,
H = 2(a1v1 a2v2),
where a1 and a2 are constants of proportionality (equal to the root-mean-squared transmit-to-receiveattenuation for transmit antennas 1 and 2 respec- tively) that take into account geometric attenuation and antenna gain effects, and v1 and v2 are unit- norm array response vectors. For the purpose of this discussion, we assume a = a1 = a2, which is valid if the rectangle deformation does not significantly af- fect overall transmitter-to-receiver distances.
The capacity of the 2 × 2 MIMO system is a functionofthechannelsingularvaluesandthetotal transmit power. Eigenvalues of HH† are given by
µ , = 2a2 (1± v†v ),
12 1 2
where the absolute value is denoted by . The separation between receive array responses can be described in a convenient form in terms of general- ized beamwidths [40],
b12 = 2arccos{ v1†v2 }.
For small angular separations, this definition of
beamwidths closely approximates many ad hocdefinitions for physical arrays. Figure A displays the eigenvalues µ1 and µ2 as a function of generalized beamwidth separation. When the transmit and re- ceive arrays are small, indicated by a small separa- tion in beamwidths, one eigenvalue is dominant. As the array apertures become larger, indicated by a larger separation, one array’s individual elements can be resolved by the other array. Consequently, the smaller eigenvalue increases. Conversely, the larger eigenvalue decreases slightly.
Equations 6 and 7 in the main article are em- ployed to determine the capacity for the 2 × 2 sys- tem. The “water-filling” technique (explained in a previoussidebar)mustfirstdetermineifbothmodes in the channel are employed. Both modes are used if the following condition is satisfied,
µ2 > Po + µ211 + µ12 ,