# Performance of Layered Steered Space---Time Codes in Wireless Systems

TL;DR: The error performance and capacity of a single-user LSSTC system is derived and recursive expressions for the probability of error are given which showed nearly perfect match to the simulation results.

Abstract: Layered Steered Space---Time Codes (LSSTC) is a recently proposed multiple-input multiple-output (MIMO) system that combines the benefits of vertical Bell Labs space---time (VBLAST) scheme, space---time block codes (STBC) and beamforming. In this paper, we derive the error performance and capacity of a single-user LSSTC system. The analysis is general enough to any layer ordering and modulation schemes used. In addition, the derived analysis is general for any LSSTC structure in which layers may have different number of antenna arrays and may be assigned power according to any power allocation. Furthermore, we analytically investigate the tradeoff between the main parameters of the LSSTC system, i.e., diversity, multiplexing and beamforming. Our results give recursive expressions for the probability of error for LSSTC which showed nearly perfect match to the simulation results. Results have also revealed the possibility of designing an adaptive system in which it was shown that combining beamforming, STBC, and VBLAST has better performance than VBLAST at high SNR range.

## Summary (5 min read)

Jump to: [Introduction] – [1.1.1 Propagation Characteristics of Wireless Channels] – [Attenuation] – [The Doppler Effect] – [Fading Distributions] – [1.1.2 Diversity] – [1.2.1 Multi-Antenna Systems] – [Diversity-Based Systems] – [Multiplexing-Based Systems] – [Beamforming-Based Systems] – [Hybrid Systems] – [1.2.2 Scheduling] – [1.3 Thesis Contributions] – [1.4 Thesis Outline] – [Multi-Antenna Systems] – [2.1 Space-Time Block Codes (STBC)] – [Alamouti’s Transmit Technique] – [2.2 Vertical Bell Labs Layered Space-Time Architec-] – [2.3 Adaptive Antenna Arrays] and [2.4 Chapter Conclusions]

### Introduction

- Wireless devices such as mobile phones have been gaining more and more popularity mainly because of their mobility.
- At the same time wireless networks still have to compete with their wired counterparts mainly because of their high data rates.
- In Section 1.3, the authors list the thesis contributions.

### 1.1.1 Propagation Characteristics of Wireless Channels

- In a real environment radio waves from mobile devices travel through the air, buildings and other obstacles.
- Reflections from different objects cause the waves to travel via multiple paths to the receiver.
- A reliable communication system tries to overcome or take advantage of these channel perturbations.

### Attenuation

- Attenuation is the loss of the average received signal power [10].
- The presence of very large obstacles such as buildings, hills, etc. causes another type of attenuation known as log-normal shadowing [11].
- Geometric models have been proposed to explain these large-scale power losses but statistical models are often used because of their accurate description of particular real environments.
- A common formula used to model attenuation is [3] PL(d)[dB] = PL(d0)+10n log ( d d0 ) +Xσ (1.1) where Xσ is a zero mean Gaussian distributed random variable (in dB) with standard deviation σ (also in dB) and accounts for the log normal shadowing effect.
- The exponent n can have values from 1.6 (in indoor line of sight) up to 6 (in highly builtup cites).

### The Doppler Effect

- When there is a relative movement between the transmitter and receiver, the carrier frequency, as perceived by the receiver, gets shifted by some amount; this is known as the Doppler effect [3].
- The amount of frequency shift depends on the relative mobility, the direction of movement and the frequency of the carrier.
- Another parameter, often used to characterize the time varying nature of the channels is the coherence time which is related to the Doppler shift [3].

### Fading Distributions

- The fading effect is usually described statistically using the Rayleigh distribution.
- The amplitude of the sum of two quadrature Gaussian signals follows the Rayleigh distribution whereas the phase follows a uniform distribution.
- Figure 1.1 shows the PDFs of Rayleigh and Ricean distributions.

### 1.1.2 Diversity

- Diversity is a powerful technique that provides link improvement at low cost.
- This is done by providing multiple independently faded versions of the transmitted signal (diversity branches) at the receiver in order to produce a better version of the transmitted signal, thus ensuring more reliable communication as long as one of the received versions is not in a deep fade.
- There are many ways of combining the diversity branches [3].
- In maximal ratio combining (MRC), the signals from each diversity branch are aligned in phase, and weighted by their channel gains before adding them coherently.
- This time interval must be longer than the coherence time of the channel [3].

### 1.2.1 Multi-Antenna Systems

- Recent research on wireless communication systems has shown that using multiple antennas at both the transmitter and the receiver offers the possibility of higher data rates compared to single antenna-systems.
- The information-theoretic capacity of MIMO channels was shown to grow linearly with the minimum of the numbers of transmit and receiver antennas in rich scattering environments, and at sufficiently high signal-to-noise (SNR) ratios [15].
- For singleinput single-output (SISO) channels, the capacity increases logarithmically with SNR.
- Thus, a significant capacity increase can be achieved using MIMO systems without any increase in transmit power or expansion in the bandwidth [16].
- In the following, the authors will review some of the major contributions in multi-antenna systems.

### Diversity-Based Systems

- In 1998, Alamouti designed a simple transmission diversity technique for systems having two transmit antennas called space-time block codes (STBC) [4].
- This method provides full diversity and requires simple linear operations at both transmission and reception side.
- The encoding and decoding processes are performed with blocks of transmission symbols.
- The Alamouti’s simple transmit diversity scheme was extended in [17] and [18] with aid of the theory of orthogonal designs to larger number of transmit antennas.
- These codes are referred to in the literature as orthogonal space-time block codes .

### Multiplexing-Based Systems

- The Bell Labs Layered Space-Time Architecture is a narrowband pointto-point communication architecture for achieving high spectral efficiency.
- To achieve this capacity, diagonal BLAST was proposed by Foschini in [19], which utilizes multi-element antenna arrays at both ends of wireless link.
- Two nulling 13 criteria, namely zero-forcing (ZF) [21] and minimum mean squared error (MMSE) are utilized as detection algorithms.
- Originally, the BLAST detection scheme was based on a successive interference cancellation (SIC) [2, 21, 22], and later on, a parallel interference cancellation (PIC) scheme was proposed in [23].
- In [6], decoding algorithms for multi-layered space time block codes were compared.

### Beamforming-Based Systems

- In adaptive antenna systems multiple antennas are used to receive (or transmit) the same information.
- Instead of using only one antenna to receive (or transmit) the radio signal, combinations of multiple antennas output (or input) are used to focus the energy towards one direction.
- The same concept of adaptive antennas can be found under different names such as smart antennas, or adaptive beamforming [27].
- Actual figures are always lower than that, but for the case of three sectors of 120◦-sectors and uniformly distributed users the actual capacity gain is quite close to the upper bound [26].
- One of the earliest forms of quasi-adaptive generic arrays is the side lobe canceller (SLC) presented in [38].

### Hybrid Systems

- Several systems that combine two or more MIMO schemes have been proposed in order to satisfy certain tradeoffs.
- The performance is analyzed through a comparison to that of pre-ordered decoding with and without power allocation.
- Also, exploiting the orthogonal nature of STBC, the number of received antennas can be reduced compared to traditional VBLAST.
- The transmitted signal is encoded by STBC and precoded by beamforming weights independently before transmitting on different antenna arrays [27].
- Similar work but with different approach has been conducted in [58].

### 1.2.2 Scheduling

- In systems with a single base station antenna, it was shown in [59] that transmitting to the user with the strongest channel at any given time achieves the sum rate capacity, which is the sum-of rates of all the users [59].
- In [9], multiuser diversity resulting from independence of fading among users in multi-user environments was shown to be capable of increasing the system capacity.
- In order to exploit the multi-user diversity and at the same time maintain fairness across the users, two other scheduling schemes have been proposed.
- In situations where minimal channel variation is experienced, opportunistic beamforming (OBF) has been proposed in [63] to create artificial channel variation where it might not otherwise exist.
- The PF scheduler assigns a user for transmission when its 22 instantaneous channel capacity is high relative to its average channel condition.

### 1.3 Thesis Contributions

- The authors investigate the analytical error performance of single user LSSTC, and recursive expressions for the probability of error is obtained starting from previously obtained results for VBLAST; their work extends that work to the LSSTC case where beamforming and STBC are involved.
- The analytical results are supported by simulation results.
- This curve relates these three extremes, where increasing one parameter causes the other parameters to decrease and vice versa.
- The authors propose a multi-configuration transmission scheme based on LSSTC and VBLAST systems.
- Also the authors derive a formula for the PDF of the maximum pre-processing SNR for a Greedy-based multi-user LSSTC.

### 1.4 Thesis Outline

- The system model of each of those systems is introduced with necessary details.
- Chapter 3 introduces the system model of single-user LSSTC, where the authors show in detailed mathematical steps the benefit of combining STBC, VBLAST, and beamforming.
- The authors investigate the performance of this scheme for different modulation schemes, namely, BPSK, M-ary PSK and M-ary QAM.
- Also, the authors use numerical methods for finding the optimum power conditions.

### Multi-Antenna Systems

- These systems are the components that constitute the LSSTC.
- Section 2.1 gives a description of STBC and presents the system model of Alamouti’s transmit technique.
- The system model of VBLAST is presented in Section 2.2, where the vertical encoding process of VBLAST is also discussed.
- Finally, Section 2.3 introduces the system model of adaptive antenna arrays.

### 2.1 Space-Time Block Codes (STBC)

- The challenge of communication over Rayleigh fading channels is that the error probability decays only inversely with SNR, compared with the exponential de- 26 27 cay observed on AWGN channels.
- STBC [4] is a simple method that enhances the reliablility by increasing the decay of error probability through diversity.
- The symbols (x1,x2, . . . ,xn) arrive at the encoder which are mapped to an m× l orthogonal transmission matrix, where the ith row represents the transmitted symbols from the ith antenna and the jth column represents the transmitted symbols in the jth time slot.
- (2.1) The maximum transmission rate of STBC is equal to one symbol/time slot.
- For orthogonal STBC, the maximum rate is achieved only for the two transmit antennas case which is Alamouti’s scheme [17].

### Alamouti’s Transmit Technique

- Historically, the transmit diversity technique proposed by Alamouti was the first STBC.
- The following notation will be used throughout this thesis.
- The decoding operation assumes that the fading channel coefficients during the two consecutive transmission time periods, t1 and t2, are to remain constant.
- The receiver observes the received signals for the whole block length l.

### 2.2 Vertical Bell Labs Layered Space-Time Architec-

- Ture A high-level block diagram of a single user VBLAST system is shown in Figure 2.2 where the number of transmit antennas is NT and the number of receive antennas is NR.
- As shown above, is essentially a single-user system which uses multiple transmitters, it was shown in [2] that it differs from traditional multiple-access techniques.
- Second, unlike frequency division multiple access (FDMA), each transmitted signal occupies the entire system bandwidth.
- A single data stream is demultiplexed into 4 sub-streams, and each sub-stream is then encoded into symbols and fed to its respective transmitter.
- No inter-layer coding, or coding of any kind, is required, though conventional coding of the individual layers may certainly be applied.

### 2.3 Adaptive Antenna Arrays

- According to Sections 2.1 and 2.2, it becomes clear that multiple antennas can be used for the sake of attaining either spatial diversity or spatial multiplexing gains.
- Because of this implementation, AAs are also named adaptive antenna arrays and the elementary antennas composing the array are called antenna elements.
- Beamforming is an effective technique for reducing the multiple-access interference, where the antenna gain is increased in the direction of the desired user, whilst reducing the gain towards the interfering users [68].
- On the transmitter side, when the DOA of the dominant paths at the receiver is known for the transmitter, then the transmit power is concentrated in the direction of the target user, and less power is wasted in the other directions.
- Basic block diagram for the AA architecture is depicted in Figure 2.4.

### 2.4 Chapter Conclusions

- These systems are the components of LSSTC, therefore, understanding the system model of each of those systems is essential in this thesis.
- It was shown that STBC introduces diversity by providing redundancy in both time and space.
- VBLAST can increase the data rate by providing spatially-multiplexed channels that operates with same frequency.
- On the other hand, beamforming can provide a direct SNR gain by steering the radiation pattern toward the desired user.

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Dedicated to

My Late Father, Mother, Brothers, Sisters

and

Teachers

ACKNOWLEDGEMENTS

In the name of Allah, the Most Gracious and the Most Merciful

All praise is due to Allah (Subhanahu wa-ta’ala) who gave me the knowledge,

courage and patience to accomplish this research, and I ask Him to accept it as

an act of worship. I ask for His blessings, mercy, and forgiveness. May the peace

and blessings of Allah be upon Prophet Muhammad (Peace Be upon Him).

My deep appreciation goes to my advisor Dr. Salam Zummo. He was always

there when I needed him, and even with his tight schedule, he has always found

time for me. I am extremely grateful to him for his prompt replies and his numer-

ous proofreads. Also, I acknowledge, with deep gratitude the guidance of Dr.

Samir Al-Ghadhban, my co-advisor. His support and guidance were very impor-

tant, especially in Matlab. Dr. Samir has provided me with many subroutines

that were essential to my work. I am also very grateful to my thesis committee

members, Dr. Maan Kousa, Dr. Wajih Abu-Al-Saud, and Dr. Yahya Al-Harthi, for

their care, cooperation and constructive advice.

i

I would like to express my deepest indebtedness to my late father, and to my

mother, sisters and brothers for their constant prayers, guidance, encouragement

and support throughout my career. They are the source of power, inspiration,

and conﬁdence in me. I also like to thank my colleagues and friends for their

concern and help.

Acknowledgement is due to the King Fahd University of Petroleum and Min-

erals and the Department of Electrical Engineering, for the support and the ex-

cellent facilities given for this research, and for granting me the opportunity to

pursue my graduate studies with ﬁnancial support.

ii

##### Citations

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01 Dec 2010TL;DR: This paper derives a formula for the PDF of the maximum preprocessing SNR for a Greedy-based multi-user LSSTC and shows that many of the scheduling criteria derived in literature does not perform well with the LS STC system.

Abstract: In this paper we evaluate a recently proposed multiple-input multiple-output (MIMO) system called the Layered Steered Space-Time Codes (LSSTC). The LSSTC system is evaluated for multi-user environments where scheduling can be used to increase the system capacity by harnessing the multi-user diversity. This evaluation is done by comparing the capacity and the probability of error for several combinations of algorithms and criteria for scheduling users' data. The results obtained show that many of the scheduling criteria derived in literature does not perform well with the LSSTC system. Instead, a scheduling criterion that directly coincides with the detection mechanism of the LSSTC receiver is derived. This scheduling criterion can jointly maximize the capacity and minimize the error probability. Also we derive a formula for the PDF of the maximum preprocessing SNR for a Greedy-based multi-user LSSTC.

2 citations

••

17 Dec 2010TL;DR: The aim of this research is to investigate the analytical error performance of single user LSSTC, and the tradeoff between several parameters of LS STC is analyzed.

Abstract: In this work we study a recently proposed multiple-input multiple-output (MIMO) system called the Layered Steered Space-Time Codes (LSSTC) that combines the benefits of vertical Bell Labs space-time (VBLAST) scheme, space-time block codes (STBC) and beamforming. The aim of this research is to investigate the analytical error performance of single user LSSTC. In addition, the tradeoff between several parameters of LSSTC is analyzed.

2 citations

••

TL;DR: A new downlink scheme employing LSSTC with asymmetric power allocation, by assuming that the user feeds the BS with the average signal-to-noise ratio per VBLAST layer through the uplink feedback channel.

Abstract: Layered Steered Space-Time Codes (LSSTC) is a recently proposed multiple-input multiple-output system that combines the benefits of vertical Bell Labs space-time (VBLAST) scheme, space-time block codes and beamforming. We suggest a new downlink scheme employing LSSTC with asymmetric power allocation, by assuming that the user feeds the BS with the average signal-to-noise ratio per VBLAST layer through the uplink feedback channel. The motivation behind proposing such a system is to enhance the error performance by assigning power to the layers in an optimal manner. We refer to the system proposed as the optimal power allocation LSSTC (OPA-LSSTC). Our analysis is general such that it includes asymmetric layered systems in which each layer may have different number of antennas and also the power can be assigned to layers asymmetrically.

##### References

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AT&T

^{1}TL;DR: This paper presents a simple two-branch transmit diversity scheme that provides the same diversity order as maximal-ratio receiver combining (MRRC) with one transmit antenna, and two receive antennas.

Abstract: This paper presents a simple two-branch transmit diversity scheme. Using two transmit antennas and one receive antenna the scheme provides the same diversity order as maximal-ratio receiver combining (MRRC) with one transmit antenna, and two receive antennas. It is also shown that the scheme may easily be generalized to two transmit antennas and M receive antennas to provide a diversity order of 2M. The new scheme does not require any bandwidth expansion or any feedback from the receiver to the transmitter and its computation complexity is similar to MRRC.

13,706 citations

### "Performance of Layered Steered Spac..." refers background in this paper

...Alamouti [2] has presented in a new scheme called STBC with two transmit and one receive antennas that provides the same diversity order as maximal-ratio receiver combining (MRRC) with one transmit and two receive antennas....

[...]

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TL;DR: A simple characterization of the optimal tradeoff curve is given and used to evaluate the performance of existing multiple antenna schemes for the richly scattered Rayleigh-fading channel.

Abstract: Multiple antennas can be used for increasing the amount of diversity or the number of degrees of freedom in wireless communication systems. We propose the point of view that both types of gains can be simultaneously obtained for a given multiple-antenna channel, but there is a fundamental tradeoff between how much of each any coding scheme can get. For the richly scattered Rayleigh-fading channel, we give a simple characterization of the optimal tradeoff curve and use it to evaluate the performance of existing multiple antenna schemes.

4,422 citations

••

Bell Labs

^{1}TL;DR: This paper describes a wireless communication architecture known as vertical BLAST (Bell Laboratories Layered Space-Time) or V-BLAST, which has been implemented in real-time in the laboratory and demonstrated spectral efficiencies of 20-40 bps/Hz in an indoor propagation environment at realistic SNRs and error rates.

Abstract: Information theory research has shown that the rich-scattering wireless channel is capable of enormous theoretical capacities if the multipath is properly exploited In this paper, we describe a wireless communication architecture known as vertical BLAST (Bell Laboratories Layered Space-Time) or V-BLAST, which has been implemented in real-time in the laboratory Using our laboratory prototype, we have demonstrated spectral efficiencies of 20-40 bps/Hz in an indoor propagation environment at realistic SNRs and error rates To the best of our knowledge, wireless spectral efficiencies of this magnitude are unprecedented and are furthermore unattainable using traditional techniques

3,925 citations

••

TL;DR: This paper dramatically reduces encoding and decoding complexity by partitioning antennas at the transmitter into small groups, and using individual space-time codes, called the component codes, to transmit information from each group of antennas.

Abstract: The information capacity of wireless communication systems may be increased dramatically by employing multiple transmit and receive antennas. The goal of system design is to exploit this capacity in a practical way. An effective approach to increasing data rate over wireless channels is to employ space-time coding techniques appropriate to multiple transmit antennas. These space-time codes introduce temporal and spatial correlation into signals transmitted from different antennas, so as to provide diversity at the receiver, and coding gain over an uncoded system. For large number of transmit antennas and at high bandwidth efficiencies, the receiver may become too complex whenever correlation across transmit antennas is introduced. This paper dramatically reduces encoding and decoding complexity by partitioning antennas at the transmitter into small groups, and using individual space-time codes, called the component codes, to transmit information from each group of antennas. At the receiver, an individual space-time code is decoded by a novel linear processing technique that suppresses signals transmitted by other groups of antennas by treating them as interference. A simple receiver structure is derived that provides diversity and coding gain over uncoded systems. This combination of array processing at the receiver and coding techniques for multiple transmit antennas can provide reliable and very high data rate communication over narrowband wireless channels. A refinement of this basic structure gives rise to a multilayered space-time architecture that both generalizes and improves upon the layered space-time architecture proposed by Foschini (see Bell Labs Tech. J., vol.1, no.2, 1996).

599 citations

### "Performance of Layered Steered Spac..." refers methods in this paper

...Similar work was considered in [3] where space time trellis codes (STTC) were used as the component codes....

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##### Frequently Asked Questions (2)

###### Q2. What are the contributions in this paper?

In this paper, the authors compared the performance of multiple-input multiple-output ( MIMO ) systems with a single-user MIMO system.