The wireless communication environment is very hostile. The signal transmitted over a wireless communication link is susceptible to fading (severe fluctuations in signal level), co-channel interference, dispersion effects in time and frequency, path loss effect, etc. On top of these woes, the limited availability of bandwidth posses a significant challenge to a designer in designing a system that provides higher spectral efficiency and higher quality of link availability at low cost.
Previous article in this series : Introduction to Multiple Antenna Systems
Multiple antenna systems are the current trend in many of the wireless technologies that is essential for their performance (you will even see it in your future hard disk drives as Two Dimensional Magnetic Recording (TDMR) technology). Multiple Input Multiple Output systems (MIMO) improve the spectral efficiency and offers high quality links when compared to traditional Single Input Single Output (SISO) systems. Many theoretical studies [1-2] and communication system design experimentations [3-5] on MIMO systems demonstrated a great improvement in performance of such systems.
Techniques for improving performance
Spatial Multiplexing techniques [6], example – BLAST[7] yields increased data rates in wireless communication links. Fading can be mitigated by employing receiver and transmit diversity (Alamouti Scheme [8] , Tarokh et. al[9]) , there by improving the reliability of the transmission link. Improved coverage can be effected by employing coherent combining techniques – which gives array gain and increases the signal to noise ratio of the system. The goals of a wireless communication system are conflicting and a clear balance of the goals is needed for maximizing the performance of the system.
The following text concentrates on two of the above mentioned techniques – diversity and spatial multiplexing.
MIMO classification with respect to antenna configuration
In MIMO jargon, communication systems are broadly categorized into four categories with respect to number of antennas in the transmitter and the receiver, as listed below.
● SISO – Single Input Single Output system – 1 Tx antenna , 1 Rx antenna
● SIMO – Single Input Multiple Output system – 1 Tx antenna, 
Rx antennas (
)
● MISO – Multiple Input Single Output system – 
Tx antennas, 1 Rx antenna (
)
● MIMO – Multiple Input Multiple Output system – Tx antennas, Rx antennas (
)
Diversity and Spatial-Multiplexing
Apart from the antenna configurations, there are two flavors of MIMO with respect to how data is transmitted across the given channel. Existence of multiple antennas in a system, means existence of different propagation paths. Aiming at improving the reliability of the system, we may choose to send same data across the different propagation (spatial) paths. This is called spatial diversity or simply diversity. Aiming at improving the data rate of the system, we may choose to place different portions of the data on different propagation paths (spatial-multiplexing). These two systems are listed below.
● MIMO – implemented using diversity techniques – provides diversity gain – Aimed at improving the reliability
● MIMO – implemented using spatial-multiplexing techniques – provides degrees of freedom or multiplexing gain – Aimed at improving the data rate of the system.
Diversity:
As indicated, two fundamental resources available for a MIMO system are diversity and degrees of freedom. Let’s see what these terms mean
In diversity techniques, same information is sent across independent fading channels to combat fading. When multiple copies of the same data are sent across independently fading channels, the amount of fade suffered by each copy of the data will be different. This guarantees that at-least one of the copy will suffer less fading compared to rest of the copies. Thus, the chance of properly receiving the transmitted data increases. In effect, this improves the reliability of the entire system. This also reduces the co-channel interference significantly. This technique is referred as inducing a “spatial diversity” in the communication system.
Consider a SISO system where a data stream [1, 0, 1, 1, 1] is transmitted through a channel with deep fades. Due to the variations in the channel quality, the data stream may get lost or severely corrupted that the receiver cannot recover.The solution to combat the rapid channel variations is to add independent fading channel by increasing the number of transmitter antennas or receiver antennas or the both.
The SISO antenna configuration will not provide any diversity as there is no parallel link. Thus the diversity is indicated as (0).
Instead of transmitting with single antenna and receiving with single antenna (as in SISO), let’s increase the number of receiving antennas by one more count. In this Single Input Multiple Output (SIMO) antenna system, two copies of the same data are put on two different channels having independent fading characteristics. Even if one of the link fails to deliver the data, the chances of proper delivery of the data across the other link is very high. Thus, additional fading channels increase the reliability of the overall transmission – this improvement in reliability translates into performance improvement – measured as diversity gain. For a system with transmitter antennas and receiver antennas, the maximum number of diversity paths is 
. In the following configuration, the total number of diversity path created is 
.
In this way, more diversity paths can be created by adding multiple antennas at transmitter or receiver or both. The following figure illustrates a 
MIMO system with number of diversity paths equal to 
.
Spatial Multiplexing:
In spatial multiplexing, each spatial channel carries independent information, there by increasing the data rate of the system. This can be compared to Orthogonal Frequency Division Multiplexing (OFDM) technique, where, different frequency subchannels carry different parts of the modulated data. But in spatial multiplexing, if the scattering by the environment is rich enough, several independent subchannels are created in the same allocated bandwidth. Thus the multiplexing gain comes at no additional cost on bandwidth or power. The multiplexing gain is also referred as degrees of freedom with reference to signal space constellation [2]. The number of degrees of freedom in a multiple antenna configuration is equal to 
, where is the number of transmit antennas and is the number of receive antennas. The degrees of freedom in a MIMO configuration governs the overall capacity of the system.
Following figure illustrates the difference between diversity and spatial multiplexing. In the transmit diversity technique shown below, same information is sent across different independent spatial channels by placing them on three different transmit antennas. Here, the diversity gain is 3 (assuming 
MISO configuration) and multiplexing gain is 0.
In the spatial multiplexing technique, each bit of the data stream (independent information) is multiplexed on three different spatial channels thereby increasing the data rate. Here, the diversity gain is 0 and the multiplexing gain is 3 (assuming 
MIMO configuration).
Exploiting diversity and degree of freedom:
As seen above, in a MIMO system with rich scattering environment (independent uncorrelated spatial paths), space time codes are designed to exploit following two resources.
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References
[1] I. E. Telatar, “Capacity of multi-antenna gaussian channels,” European Transactions on Telecommunication, vol. 10, pp. 585–595, Nov./Dec. 1999.
[2] G. J. Foschini, “Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas,” Bell Labs Tech. J., vol. 1, no. 2, pp. 41–59, 1996.
[3] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-time block code from orthogonal designs,” IEEE Trans. Inform. Theory, vol. 45, pp. 1456–1467, July 1999.
[4] G. Foschini, G. Golden, R. Valenzuela, and P. Wolniansky, “Simplified processing for high spectal efficiency wireless communication employing multi-element arrays,” IEEE J. Select. Areas Commun., vol. 17, pp. 1841–1852, Nov. 1999.
[5] R. Heath, Jr. and A. Paulraj, “Switching between multiplexing and diversity based on constellation distance,” in Proc. Allerton Conf. Communication, Control and Computing, Oct. 2000.
[6] A. Paulraj and T. Kailath, Increasing capacity in wireless broadcast Systems using distributed transmission/directional reception (DTDR), US Patent No. 5,345,599, Issued 1993
[7] Gerard. J. Foschini, Layered Space-Time Architecture for Wireless Communication in a Fading Environment When Using Multi-Element Antennas”.Bell Laboratories Technical Journal: 41–59,(October 1996)
[8] S.M. Alamouti (October 1998). “A simple transmit diversity technique for wireless communications”. IEEE Journal on Selected Areas in Communications 16 (8): 1451–1458
[9] V. Tarokh, N. Seshadri, A. Calderbank, ‘Space-Time Codes for High Data Rate Wireless Communication: Performance Criterion and Code Construction,’ IEEE Trans. on. Information Theory, Vol. 44, No.2, pp.744-765, March 1998
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why did we need to predict SINR at the receiver ?
Hy
Greetings from Pakistan,
I am unable to understand that why the term degree of freedom and spatial multiplexing are used interchangeably. Please explain a bit.
Thanks
Degree of freedom is the number of independent channels that can be exploited by the transmitter for sending the data. In spatial multiplexing these independent channels carry different bits (multiplexing) of the information stream (see the image above).
Thank you very much for you response.
I am scratching my head and internet together to find out the reason to call TM6 as Spatial Multiplexing though there is only one Layer (Rank 1) and no spatial multiplexing gain can be achieved in LTE from that.
Am I missing anything here about definition of Spatial Multiplexing.
pleas help about massive mimo uplink
In the example you gave above, why are you comparing spatial multiplexing with 3 Rx antennas and spatial diversity with 1 antenna. Is it not that we require same N_t and N_r for fair comparison?
Does spatial mutliplexing require N_t = N_r?
As you define, degrees of freedom, multiplexing gain of the above transmit diversity scheme should be 1 (min(3,1)), but, why did you say it is zero?
Those two statements are separate. The statements are meant for neither fair comparison nor for deducing any meaningful gain.
The statements are just to illustrate the difference between the two techniques.
Again, it is a comparative statement. I say zero, since we are not gaining anything with transmit diversity in terms of multiplexing gain. It only improves the reliability.
Thank you. What about spatial multiplexing? will it require N_t = N_r?
There is no such requirement.