Introduction to Multiple Antenna Systems

Regarded as a breakthrough in wireless communication system design, multiple antenna systems fuel the ever increasing data rate requirements of advanced technologies like UMTS, LTE, WLAN etc. Multiple antenna systems come in different flavors and are generally referred as Multiple Input Multiple Output systems (MIMO). In a series of articles, I intend to cover various aspects of multiple antenna systems – specifically the diversity techniques.

This article is part of the book ● Wireless Communication Systems in Matlab (second edition), ISBN: 979-8648350779 available in ebook (PDF) format and Paperback (hardcopy) format.

Diversity techniques:

Diversity techniques are employed to make a communication system robust and reliable even over varying channel conditions. Diversity techniques exploit the channel variations rather than mitigating it. Diversity techniques combat fading and interference by presenting the receiver with multiple uncorrelated copies of the same information bearing signal. Essentially, diversity techniques are aimed at creating uncorrelated random channels -uncorrelated copies of the same signal (may also be in combined form) at the receiver front end. Combining techniques are employed at the receiver to exploit multipath propagation characteristics of a channel.

Broadly speaking, the term diversity broadly categorized as

● Time diversity:
—-Multiple copies of information sent on different time slots. The time slots are designed in such a way that the delay between the signal replicas should be greater than the Coherence Time () of the channel. This condition will create uncorrelated channels over those time slots. Coding and interleaving are also equivalent techniques that break the channel memory into multiple chunks there by spreading and minimizing the effect of deep fades. This technique consumes extra transmission time.
● Frequency diversity:
—-Signal replicas are sent across different frequency bands that are separated by at-least the Coherence Bandwidth () of the channel – thereby creating uncorrelated channels for the transmission. By this method, the level of fading experienced by each frequency bands are different and at-least one of the frequency bands may experience the lowest level of fading – strongest signal in this band. This technique requires extra bandwidth. Example : Orthogonal Frequency Division Multiplexing (OFDM) and spread spectrum.
● Multiuser diversity [1-6]:
—-Employing adaptive modulation and user scheduling techniques to improve the performance of a multiuser system. In such systems, the channel quality information for each user is utilized by a scheduler to select the number of users, coding and modulation such that an objective function (throughput and fairness of scheduling) is optimized. Example: OFDMA and access scheme used in latest wireless systems such as IEEE 802.16e (Mobile WiMAX)
● Spatial diversity (antenna diversity):
—Aimed at creating uncorrelated propagation paths for a signal, spatial diversity is effected by usage of multiple antennas in the transmitter and/or the receiver. Employing multiple antennas at the transmitter is called “Transmit Diversity” and multiple antennas at the receiver is called “Reception Diversity“. Diversity combining techniques like Selection Combining (SC), Feedback or Scanning Combining (FC or SC), Maximum Ratio Combining (MRC) can be employed by the receiver to exploit the multiplath effects. Spatial diversity techniques can also be used to increase the data rates (spatial multiplexing) rather than improving the reliability of the channel. Example: MIMO, beamforming and Space-Time Coding (STC)
● Polarization diversity (antenna diversity):
—-Multiple copies of the same signal are transmitter and received by antennas of different polarization. Used the mitigate polarization mismatches of transmit and receiver antennas.
● Pattern diversity (antenna diversity):
—-Multiple versions of the signal are transmitted via two or more antenna with different radiation patterns. The antennas are spaced such that they collectively act as a single entity aimed at providing more directional gain compared to an omni-directional antenna.
● Adaptive arrays (antenna diversity):
—-Ability to control the radiation pattern of a single antenna with active elements or an array of antennas. The radiation pattern is adapted based on the existing channel conditions.

The above is just a broad classification. There exists more advanced diversity techniques (example : cooperative diversity↗) that can be a combination of one or more techniques listed above.

The following text concentrates on Spatial Diversity or the MIMO systems.

Single Input Single Output (conventional system)

The conventional radio communication systems contain one antenna at the transmitter and one at the receiver.  In MIMO jargon, this is called Single Input and Single Output system (SISO). The channel capacity (C)) is constrained by Signal to Noise Ratio (S/N)) and the bandwidth (B) as given by the well-known Shannon Hartley theorem for a Continuous Input Continuous Output Memoryless AWGN channel (CCMC) ^[7].

Multiple Antenna Systems or MIMO:

Here, the system configuration typically contains M antennas at the transmitter and N antennas at the receiver front end as illustrated in the next figure. Here, each receiver antenna receives not only the direct signal intended for it, but also receives a fraction of signal from other propagation paths. Thus, the channel response is expressed as a transmission matrix . The direct path formed between antenna 1 at the transmitter and the antenna 1 at the receiver is represented by the channel response . The channel response of the path formed between antenna 1 in the transmitter and antenna 2 in the receiver is expressed as and so on. Thus, the channel matrix is of dimension .

The received vector is expressed in terms of the channel transmission matrix , the input vector and noise vector  as

where the various symbols are

For asymmetrical antenna configuration (), the number of data streams (or the number of uncoupled equivalent channels) in the system is always less than equal to the minimum of the number of transmitter and receiver antennas – .

For a single user system, the capacity scales linearly with    relative to a SISO system^[8].

More on the classification of multiple antenna systems and their capacity in subsequent posts.

Jump to next article in this series: MIMO – Diversity and Spatial Multiplexing

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References:

[1] M Torabi, D Haccoun, Performance analysis of joint user scheduling and antenna selection over MIMO fading channels. IEEE Signal Process Lett 18(4), 235–238 (2011).↗
[2] L Jin, X Gu, Z Hu, Low-complexity scheduling strategy for wireless multiuser multiple-input multiple-output downlink system, IET Commun 5(7), 990–995 (2011).↗
[3] B Makki, T Eriksson, Efficient channel quality feedback signaling using transform coding and bit allocation, Vehicular Technology Conference, VTC (Ottawa, ON, 2010), pp. 1–5.↗
[4] T Eriksson, T Ottosson, Compression of feedback for adaptive transmission and scheduling. Proc IEEE 95(12), 2314–2321 (2007).↗
[5] G Dimic, ND Sidiropoulos, On downlink beamforming with greedy user selection: performance analysis and a simple new algorithm, IEEE Trans Signal Process 53(10), 3857–3868 (2005).↗
[6] VKN Lau, Proportional fair space-time scheduling for wireless communications. IEEE Trans Commun 53(8), 1353–1360 (2005).↗
[7] J. G. Proakis, Digital Communications, Mc-Graw Hill International, Editions, 3rd ed., 1995.↗
[8] Torlak, M.; Duman, T.M., MIMO communication theory, algorithms, and prototyping, Signal Processing and Communications Applications Conference (SIU), 2012 20th , vol., no., pp.1,2, 18-20 April 2012.↗

Articles in this series
[1] Introduction to Multiple Antenna Systems
[2] MIMO - Diversity and Spatial Multiplexing
[3] Characterizing a MIMO channel - Channel State Information (CSI) and Condition number
[4] Capacity of a SISO system over a fading channel
[5] Ergodic Capacity of a SISO system over a Rayleigh Fading channel - Simulation in Matlab
[6] Capacity of a MIMO system over Fading Channels
[7] Single Input Multiple Output (SIMO) models for receive diversity
[8] Receiver diversity - Selection Combining
[9] Receiver diversity – Maximum Ratio Combining (MRC)

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