Semi-blind signal detection for mimo and mimo-ofdm systems

Tài liệu tham khảo chuyên ngành viễn thông Semi-blind signal detection for mimo and mimo-ofdm systems

SEMI-BLIND SIGNAL DETECTION FOR MIMO AND MIMO-OFDM SYSTEMS

MA SHAODAN Ph D THESIS

THE UNIVERSITY OF HONG KONG 2006

Abstract of thesis entitled

“Semi-Blind Signal Detection for MIMO and MIMO-OFDM Systems”

A three-step semi-blind Rake-based multi-user detection technique is proposed for quasi-synchronous MIMO systems The first step separates the multi-user multi-path signal vector into multi-user single-path signal vectors based on second-order statistics (SOS) of the received signals A simple estimation method is proposed in the second step to estimate the time delays with the aid of pilots The third step combines multiple multi-user single-path signal vectors for signal detection System performance is improved by time diversity and only the upper bounds of the channel length and the time delays are required Simulation results show that the proposed technique achieves good performance and is not sensitive to over-estimation of the maximum channel length and the maximum time delay

A MIMO-OFDM system with short CP is next considered for higher bandwidth efficiency and a time domain semi-blind signal detection algorithm is proposed A new system model in which the i th received OFDM symbol is left shifted by J

samples is introduced Based on some structural properties of the new system model, an equalizer is designed using SOS of the received signals to cancel most of the inter-symbol interference (ISI) The transmitted signals are then detected from the equalizer output In the proposed algorithm, only 2P ( P is the number of transmit antennas/users in MIMO-OFDM systems) columns of the channel matrix need to be estimated, and channel length estimation is unnecessary In addition, the proposed algorithm is applicable irrespective of whether the channel length is shorter than, equal to or longer than the CP length Simulation results verify the effectiveness of the proposed algorithm, and show that it outperforms the existing ones in all cases

Finally, in order to further improve bandwidth efficiency, a MIMO-OFDM system without CP is considered and a two-step semi-blind signal detection algorithm is proposed The algorithm is based on some structural properties derived from shifting the received OFDM symbols The first step cancels inter-carrier interference (ICI) and ISI with an equalizer designed using SOS of the shifted received OFDM symbols The second step involves signal detection from the equalizer output in which the signals are still corrupted with multi-antenna interference (MAI) In the proposed algorithm, precise knowledge of the channel length is unnecessary and only one pilot OFDM symbol is utilized to estimate the required channel state information Simulation results show that the proposed algorithm achieves comparable performance to algorithms for standard MIMO-OFDM systems and it is robust against channel length overestimation

The number of words: 460

Semi-Blind Signal Detection for MIMO and MIMO-OFDM Systems

by

Ma Shaodan

B Eng., M Eng., Nankai University, P R China

A thesis submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy

at The University of Hong Kong May 2006

Declaration

I declare that this thesis represents my own work, except where due acknowledgement is made, and that it has not been previously included in a thesis, dissertation or report submitted to this University or to any other institution for a degree, diploma or other qualifications

Signed _

Ma Shaodan

Acknowledgements

I would like to take this chance to express the deepest gratitude to my supervisor, Professor T S Ng, for his continuous guidance and constructive suggestions during the course of my Ph.D program I owe my gratitude to my dear husband, Mr Yang Guanghua, for his encouragement, support and helpful advices I would like to thank Dr K W Yip, Dr N Wong and Dr Yonghong Zeng for their helpful discussions and valuable suggestions I would also like to thank the members in my research group, Dr Zhou Yiqing, Mr Chen Jianwu, Mr Zheng gan, Mr Ng ChiuWa, Mr Wang Hongzheng, Ms Pan Xinyue, Ms Peng Wei, for their friendship and useful discussions I would express my thanks to all the staff in the Department of Electrical and Electronic Engineering for their supportive work I also want to thank the University of Hong Kong for the award of postgraduate studentship It supports my life in Hong Kong and makes me focus on my research Finally, I owe my deepest gratitude to my parents, for their trust and support all the time.

1.1 MIMO ……… 1

1.2 MIMO-OFDM ……….3

1.3 Semi-blind signal detection ……….4

1.4 Motivation and organization of the thesis ……… 6

Chapter 2 Semi-Blind Rake-Based Multi-User Detection for Quasi-Synchronous MIMO Systems ……… 9

2.1 Introduction ……….9

2.2 System model ………12

2.3 Semi-blind Rake-based multi-user detection technique ………14

2.3.1 Multi-user single-path signal separation ……….15

2.3.2 Time delay estimation ……….17

2.3.3 Multi-path combining ……….19

2.3.4 Channel noise consideration ……… 21

2.3.5 Performance analysis ……… 22

2.4 Examples and simulation results ……… 25

2.4.1 Time delay estimation ……….25

2.4.2 Semi-blind Rake-based multi-user detection technique … 27

2.4.2.1 Example 1 ……….27

2.4.2.2 Example 2 ……….30

2.5 Summary ………33

Chapter 3 Time Domain Semi-blind Signal Detection for MIMO-OFDM Systems with Short Cyclic Prefix ……….35

3.4.4 Data length effect ………57

3.5 Summary ………58

Chapter 4

Two-Step Semi-Blind Signal Detection for MIMO-OFDM

Systems without Cyclic Prefix ……… 60

4.1 Introduction ……… 60

4.2 System Model ………62

4.3 Two-Step Semi-blind Signal Detection ………66

4.3.1 Blind ICI and ISI cancellation ………67

4.3.2 Signal detection in the presence of MAI ……….70

4.3.3 Effect of channel noise ………71

4.3.4 Implementation ……… 72

4.4 Simulation Results ………73

4.4.1 Effect of SNR ……….…73

4.4.2 Effect of the parameter K ……… 76

4.4.3 Effect of channel length overestimation ……….78

4.5 Summary ………79

Chapter 5 Conclusions and suggestions for future research …………80

Reference ………83

Publications ……….89

List of Figures

1.1 MIMO system ……….2

1.2 MIMO-OFDM system ……… 4

1.3 Semi-blind technique ……….6

2.1 Quasi-synchronous transmission scheme ……….12

2.2 Block diagram of semi-blind Rake-based multi-user detection technique ……….15

2.3 Rake-based receiver ……….20

2.4 Time delay estimation (d1 = 2, d2 =4 and d3=1) ………26

2.5 BER versus SNR (synchronous MIMO system) ……… 29

2.6 BER versus the estimated maximum channel length ˆL (SNR = 18dB; synchronous MIMO systems) ………30

2.7 BER versus SNR (quasi-synchronous MIMO system) …………31

2.8 BER versus the estimated maximum channel length ˆL (SNR = 20dB; quasi-synchronous MIMO systems) ……… 32

2.9 BER versus the estimated maximum delay dˆPU (SNR = 20dB; quasi-synchronous MIMO system) ……….33

3.1 Block diagram of time domain signal detection algorithm for MIMO-OFDM system with short CP ……… 42

3.2The case where the channel length is 14 (L=14) ……… 53

3.3The case where the channel length is 16 (L=16) ……… 54 3.4The case where the channel length is 18 (L=18) ………… 55 3.5The case where the channel length is 20 (L=20) ……….56 3.6 Proposed algorithm for L =14, 16, 18, 20 (D=16) …….…… 57 3.7Data length effect on the proposed algorithm (L=20 and

SNR=dB)……….58 4.1Block diagram of MIMO-OFDM-WCP system ………62 4.2Block diagram of the receiver structure ………67 4.3BER versus SNR when the channel length is 6 (L=6) ……… 75 4.4BER versus SNR when the channel length is 8 (L=8) ……… 76 4.5Effect of K when the channel length is 6 (L=6) … ………… 77 4.6Effect of K when the channel length is 8 (L=8) ……… 78

List of Abbreviations

FDMA Frequency Division Multiple Access TDMA Time Division Multiple Access CDMA Code Division Multiple Access SDMA Spatial Division Multiple Access MIMO Multiple Input Multiple Output

HSDPAHigh Speed Downlink Packet Access

OFDM Orthogonal Frequency Division Multiplexing OFDMA Orthogonal Frequency Division Multiple Access DAB Digital Audio Broadcasting

DVB Digital Video Broadcasting WLAN Wireless Local Area Network

GSM Global System of Mobile communication HOS Higher Order Statistics

SOS Second Order Statistics

MAI Multiple Antenna Interference ISI Inter-Symbol Interference ICI Inter-Carrier Interference i.i.d independently identically distributed BER Bit Error Rate

SNR Signal-to-Noise Ratio

LS Least Squares

MMSE Minimum Mean Square Error

QPSK Quadrature Phase Shift Keying QoS Quality of Service

AWGN Additive White Gaussian Noise CP Cyclic Prefix

Chapter 1 Introduction

With the growth of broadband internet access and the development of multimedia services in cellular mobile wireless communications, an ever-increasing demand for high capacity and high speed transmission with good Quality-of-Service (QOS) has been created To meet this demand, various techniques have been proposed

1.1 MIMO

In the 1st generation (1G) mobile communication system, frequency domain is exploited to achieve the desired system capacity by FDM (Frequency Division Multiplexing), while time domain is exploited by TDM (Time Division Multiplexing) in the 2nd generation (2G) mobile communication system To improve the system capacity, code domain is exploited by CDM (Code Division Multiplexing) in some 2G and current 3rd generation (3G) mobile communication systems However, the data rate which can be achieved in the current and extended 3G systems is only as high as 14.4Mbps

To further improve the system capacity, space domain, which is regarded as the "last frontier" that can substantially improve the capacity, is exploited in the 3.5G such as HSDPA (High Speed Downlink Packet Access) system and being considered for the next generation mobile communication systems As a capacity boosting

technique, MIMO (Multiple Input Multiple Output) utilizes multiple antennas at both ends of a wireless link as shown in Fig 1.1 A number of signals are simultaneously transmitted from different transmit antennas onto the same physical channel and then separated by multiple receive antennas and signal processing techniques at the receiver Independent studies have shown that the capacity of MIMO systems can grow linearly with the number of transmit and receive antennas [Winters, Salz and Gitlin, 1994; Foschini and Gans, 1998; Paulraj, Gore, Nabar and Bolcskei, 2004] A lot of research interest has thus been attracted to MIMO systems due to their high capacity and spectral efficiency in recent years [Dai, Molisch and Poor, 2004; Chizhik, Ling, Wolniansky, Valenzuela, Costa and Huber, 2003; Chizhik, Foschini, Gans and Valenzuela, 2002]

Fig 1.1 MIMO system

Generally, MIMO systems can be classified into two categories One is space time coding system where correlated data streams are transmitted through different antennas and the transmission quality (bit-error-rate) is improved due to spatial diversity [Tarokh, Seshadri and Calderbank, 1998] The other is spatial multiplexing

RX MRX 1

TX PTX 2TX 1

Data stream

Space Time Coding

or Spatial Demux

Frequency selective

fading channels

system where independent data streams are transmitted over different antennas, thus increasing the transmission rate or improving the system capacity [Gesbert, Shafi, Shiu, Smith and Naguib, 2003] In this thesis, the focus is on spatial multiplexing as the goal is to increase the data transmission rate

1.2 MIMO-OFDM

OFDM (Orthogonal Frequency Division Multiplexing) was first proposed by Chang [1966] The basic operational principle is that the high-rate data stream is split and modulated into a number of parallel orthogonal subcarriers using a bank of sinusoidal generators In 1971, Weinstein and Ebert [1971] suggested the employment of discrete Fourier transform (DFT) to replace the bank of sinusoidal generators and demodulators, which significantly reduces the implementation complexity of OFDM Afterwards, a lot of studies on OFDM were presented, e.g., [Cimini, 1985; Hirosaki, 1981; Kalet, 1989; Hirosaki, 1980; Muquet, Wang, Giannakis, de Courville and Duhamel, 2002; Speth, Fechtel, Fock and Meyr, 1999; Muquet, de Courville and Duhamel, 2002; Heath, and Giannakis, 1999; Lei and Ng, 2004; Luise, Reggiannini and Vitetta, 1998]

As a special case of multi-carrier modulation, OFDM has high spectral efficiency and is robust against frequency selective fading which is accomplished by inserting a cyclic prefix at the beginning of each OFDM symbol The high spectral efficiency and robustness have justified the adoption of OFDM as a standard transmission technique in a host of applications such as satellite and terrestrial digital audio broadcasting (DAB), digital video broadcasting (DVB) and wireless local area network (WLAN, e.g IEEE 802.11a/g)

As mentioned before, MIMO is a promising system to achieve high system capacity for multimedia applications in wireless communications In practice, multipath propagation usually occurs and causes frequency selective fading in MIMO channels It is therefore desirable to combine MIMO with OFDM technique as

illustrated in Fig 1.2 to combat the effect of frequency selective fading Currently, MIMO-OFDM technique with high system capacity as well as robustness against frequency selective fading is attracting considerable research interests all over the world [Sampath, Talwar, Tellado, Erceg and Paulraj, 2002; Stuber, Barry, Mclaughlin, Li, Ingram and Pratt, 2004; Bolcskei, Gesbert and Paulraj, 2002; Bolcskei, Borgmann and Paulraj, 2003; Dubuc, Starks, Creasy and Hou, 2004] It is being adopted in the coming WLAN standard (IEEE 802.11n) and is recognized as a strong candidate for the future 4th generation (4G) mobile communications standards

Fig 1.2 MIMO-OFDM system

1.3 Semi-blind signal detection

Traditional signal detection techniques use training sequences to estimate the channel as the first step Signal detection then follows equalization Most mobile communication standards such as GSM (Global System of Mobile communication) include training sequence to estimate the channels These techniques are robust and yield accurate channel estimation but the bandwidth efficiency is inevitably reduced For example, in GSM, 20% of the bits in a burst are used as training sequences

RX MRX 1

TX PTX 2TX 1

Spatial Demux

Frequency selective

fading channels

CP insertion

CP insertion

CP insertion

To eliminate this bandwidth efficiency reduction when the wireless system is operating on slow fading channels, blind signal detection techniques based on only the received signals without any training sequence are proposed in [Inouye and Hirano, 1997; Tugnait, 1997; Thirion-Moreau and Moreau, 2002; Tugnait, 1998; Giannakis, Inouye and Mendel, 1989; Shen and Ding, 2000; Zhu, Ding and Cao, 1999; Tugnait and Huang, 2000; Tugnait, 1998; Abed-Meraim and Hua, 1997; Abed-Meraim, Loubaton and Moulines, 1997; Xavier, Barroso and Moura, 2001] Generally, blind techniques are based on the higher-order statistics (HOS) or the second-order statistics (SOS) of the received signal SOS methods are particularly attractive since they have lower computation complexity and require shorter data records to accurately estimate the statistics However, the SOS methods suffer from the lack of robustness: many blind SOS methods fail when the channel length is overestimated In addition, the SOS methods usually leave an indeterminacy in the symbols This suggests that the SOS methods should not be utilized alone It requires some form of additional information

To overcome the above problem, semi-blind techniques are proposed [Zeng and Ng, 2004] as shown in Fig 1.3 It exploits the information used by blind methods as well as the information coming from known symbols As it incorporates the information of known symbols, the possible pitfalls of blind methods are avoided On the other hand, exploiting the blind information in addition to the known symbols allows the detection of the signals with the use of shorter training sequence for a desired detection quality Apart from the robustness consideration, semi-blind techniques also appear very interesting from a performance point of view, as it can offer better performance than the training sequence methods or the blind methods when the wireless system is operating on slow fading channels

Fig 1.3 Semi-blind technique

1.4 Motivation and organization of the thesis

In MIMO and MIMO-OFDM systems, a number of signals from multiple antennas are transmitted through multi-path channels They may suffer from a deep fading and be corrupted by interference and noise at the receiver Signal detection is therefore an important component in these systems

Most of the works done on signal detection for MIMO systems consider synchronous case It means that all signals transmitted from different users must be time-aligned at the receiver Perfect synchronization among all users is thus required However, when applying MIMO to the uplink of a cellular mobile communication system, it is generally difficult to achieve perfect synchronization due to different locations of mobiles and multi-path propagations A quasi-synchronous MIMO system operating in multi-path channels, in which signals of all users are time-aligned at the receiver to within a synchronization window, is more consistent with real situations as different users are likely to have slightly different time delays However, there are few signal detection algorithms, if any, proposed for quasi-synchronous MIMO systems due to the difficulties in time delay estimation and intersymbol interference cancellation

As a promising candidate for the future 4G mobile communication standards, MIMO-OFDM has high system capacity and is robust against frequency selective fading However, in most of the works for MIMO-OFDM system, a cyclic prefix is required at the beginning of each OFDM symbol [Sampath, Talwar, Tellado, Erceg

Training sequence methods

Blind methods

Training sequence

All symbols are considered as unknown

Combines training sequence and blind information

Semi-blind methods

and Paulraj, 2002; Stuber, Barry, Mclaughlin, Li, Ingram and Pratt, 2004; Bolcskei, Gesbert and Paulraj, 2002; Bolcskei, Borgmann and Paulraj, 2003; van Zelst and Schenk, 2004] The length of the CP is chosen longer than the channel length to eliminate the inter-carrier interference (ICI) and inter-symbol interference (ISI) For example, in the wireless local area network (IEEE 802.11a) standard, the length of CP is 25% of an OFDM symbol duration, resulting in a significant loss in bandwidth efficiency It is apparent that if the CP is shortened or removed, substantial gain in bandwidth efficiency can be achieved A MIMO-OFDM system with short CP or without CP is therefore desirable As the CP is shortened or removed, ICI and ISI may be introduced in the received signals Their presence destroys the orthogonal property of the subcarriers, making signal detection very difficult So far, only few published works are available in the literature

Motivated by practical situation in mobile communication systems and for higher bandwidth efficiency, this thesis addresses the signal detection problem for three systems in the following three chapters In Chapter 2, a quasi-synchronous MIMO system is considered and a semi-blind Rake-based multi-user detection technique is proposed It consists of three steps: multi-user single-path signal separation, time delay estimation and multi-path combination It is proved that better BER performance is achieved by time diversity and the proposed technique is not sensitive to over-estimation of the maximum channel length and the maximum time delay In Chapter 3, a MIMO-OFDM system with short CP is considered for higher bandwidth efficiency and a time domain semi-blind signal detection algorithm is proposed An equalizer is designed using SOS of the received signals to cancel most of the ISI The transmitted signals are then detected from the equalizer output The proposed algorithm has its own advantages as compared to the existing ones and its effectiveness is verified by computer simulation In Chapter 4, a MIMO-OFDM system without CP is considered to further improve the bandwidth efficiency and a two-step semi-blind signal detection algorithm is proposed The first step cancels ICI and ISI with an equalizer The second step is signal detection from the equalizer

output in which the signals are still corrupted with multi-antenna interference (MAI) In the proposed algorithm, precise knowledge of the channel length is unnecessary and only one pilot OFDM symbol is utilized By computer simulations, it is shown that the proposed algorithm achieves comparable performance to algorithms for standard MIMO-OFDM systems and it is robust against channel length overestimation Finally, the thesis is concluded in Chapter 5

Chapter 2

Semi-Blind Rake-Based Multi-User Detection for Quasi-Synchronous MIMO Systems

2.1 Introduction

As introduced in Chapter 1, when applying MIMO to the uplink of a cellular mobile communication system, perfect synchronization among all users is generally difficult to achieve due to different locations of mobiles and multi-path propagations It is therefore more reasonable to model the system under consideration as a quasi-synchronous MIMO system where different users are likely to have slightly different time delays However, there are few algorithms, if any, proposed for quasi-synchronous MIMO systems due to the difficulties in time delay estimation and intersymbol interference cancellation

In wireless communications, multi-path signals have been exploited to achieve diversity gain to improve the system performance Rake receiver technique is widely used in CDMA systems for single-user detection as multi-path signals transmitted from a desired user can be easily separated from other users utilizing the orthogonal property of spreading codes between different users and the low cross correlation property of the desired user’s spreading code [Bottomley, Ottosson and Wang, 2000;

Tjhung, Xue, Dai, Wong and He, 2002; Singh, Kumari, Mallik and Jamuar, 2002; Mallik, Singh and Kumari, 2003; Liu and Li, 1999] It is not used in TDMA and FDMA as signal detection is relatively simple and the performance gain cannot be justified by the added complexity MIMO with spatial multiple access is analogous to CDMA in the sense that multiple users transmit simultaneously into the same physical channel The fact that Rake receiver has not been utilized in MIMO so far can be attributed to the difficulty in multi-user detection which requires separating multi-user multi-path signals as well as estimating the time delay for each user

In this chapter, a semi-blind Rake-based multi-user detection technique which incorporates a new simple time delay estimation method is proposed for quasi-synchronous MIMO systems operating in multi-path channels The proposed technique consists of three steps The first step separates the multi-user multi-path signal vector into multi-user single-path signal vectors based on second order statistics (SOS) of the received signals without knowledge of the channel state information The second step is time delay estimation which is essential for signal detection The third step combines multiple multi-user single-path signals and detects the multi-user signals

The first step in the proposed technique is to model the received signals of all users as synchronous so that many of the existing signal detection algorithms [Zhu, Ding and Cao, 1999; Lopez-Valcarce and Dasgupta, 2001; Moulines, Duhamel, Cardoso and Mayrargue, 1995; Tugnait, 2001; Miller, Taylor and Gough, 2001; Abed-Meraim, Loubaton and Moulines, 1997; Liu and Xu, 1997; Hua, An and Xiang, 2003] for synchronous MIMO systems can be used to separate the users’ signals into multi-user single-path signals Unlike CDMA systems where the orthogonal property of spreading codes is utilized to separate multi-path signals, SOS of the received signals is generally utilized to separate the multi-path signals in MIMO systems One SOS-based method, the column-anchored zeroforcing method [Zhu, Ding and Cao, 1999], is chosen in the proposed technique as it is not sensitive to channel length overestimation so that perfect channel length estimation is not required For the

second step, as the time delay information of all users are embedded in each of the multi-user single-path signal vector after step one, the strongest signal vector is selected for time delay estimation To the best of the authors' knowledge, only two pilot-based time delay estimation methods have been proposed [Nishimura, Tanabe, Ohgane, Ogawa, Doi and Kitakado, 2000] The first one uses the sliding correlator, which has the limitation that when the difference between any two delays is less than two symbol periods, accurate estimation cannot be achieved The second one is the vector orthogonalization method, which is computationally complex as it requires estimating the noise subspace of the received-signal matrix Since the time delay information can be modeled in either the user signal vector or the channel matrix, a simple pilot-based method is proposed for the latter model using the structural properties of the channel matrix It is relatively simple compared with the methods in [Nishimura, Tanabe, Ohgane, Ogawa, Doi and Kitakado, 2000] and it also has the added advantage that it does not require the actual maximum time delay Only the upper bound is needed

Once the time delays for different users have been estimated, the different path signals are combined using the Rake receiver principle for multi-user detection It is shown that the output of the combiner yields the estimated transmitted signals It follows that the multi-user signals can easily be detected after the time delays are estimated The advantages of the proposed technique are: 1) perfect synchronization of all users is not required; 2) time diversity is achieved by Rake-based receiver for performance enhancement; 3) only the upper bounds of the channel length and the time delay are needed Simulation results show that the proposed technique achieves good performance and is robust against over-estimation of both the maximum channel length and the maximum time delay These results indicate that the proposed technique can readily be implemented because perfect estimation of the maximum channel length and the maximum time delay, tasks that are difficult in practice, are not required

The rest of this chapter is organized as follows In Section 2.2, the

quasi-synchronous MIMO system model is introduced The semi-blind Rake-based user detection technique with time delay estimation is presented in Section 2.3 In Section 2.4, the performance of the proposed technique is demonstrated by simulation Finally, a summary of this chapter is given in Section 2.5

multi-2.2 System model

A MIMO system with P users sharing the same physical channel, each transmitting a

signal via a single antenna to the receiver having M receive antennas, is considered

The communication channel for each user is a multi-path fading channel This situation arises in the uplink of a mobile communication system in which a mobile station is usually equipped with one antenna and multi-path propagation usually

occurs The channel between the transmit antenna of the i th user and the j th receive

antenna at the receiver, denoted by h n , is modeled as an ij( ) L th-order FIR filter In ij

quasi-synchronous systems, the signals of all users are time-aligned at the receiver within a small synchronization window as shown in Fig 2.1

Fig 2.1 Quasi-synchronous transmission scheme

Transmitted signalUser 1

User 2

d

Let the time delay of the i th-user signal bed , i i ∈ {1, 2, , P } In digital

communication systems, it takes on an integer value and satisfies d i ≥ 0 The synchronization window of the system is dPU, representing the maximum time delay in the system Assume that all the time delays are not greater than the synchronization window, di ≤dPU, i ∈ {1, 2, , P } The received signal at the j th receive

antenna at time n can be expressed as

independently identically distributed (i.i.d.) AWGN noise at the j th antenna, which

is generally uncorrelated with the input signals of all users Let ( )x ni =x n di( − i)and L = max1≤ ≤i P,1≤ ≤j M(Lij) denotes the maximum channel length, y n can be j( )modeled as

and ( )⋅ represents matrix transpose T

Suppose N + 1 sampled received-signal vectors are collected The observation vector is given by

Here we make a general assumption that the channel convolution matrix H is of full

column rank after removing all-zero columns This is a sufficient condition for detecting the signals based on SOS [Gorokhov and Loubaton, 1997] In order to meet this condition, the number of receive antennas must be chosen to be larger than the number of users, i.e., M > , and PN must be chosen to satisfy N >(P L× ) /(M −P), so that the matrix H has more rows than columns

2.3 Semi-blind Rake-based multi-user detection technique

In this section, a semi-blind Rake-based multi-user detection technique is proposed as illustrated in Fig 2.2

Fig 2.2 Block diagram of semi-blind Rake-based multi-user detection technique

To simplify the derivation of the algorithm, zero noise is first assumed The effect of noise on the developed technique is then examined In the absence of noise, yN+1 can be expressed as

N+ n = N+ n

2.3.1 Multi-user single-path signal separation

The observation vector yN+1 in (2-13) can also be rewritten as

Multi-path combining (Rake-based

(lP+ th column and the ( 1)1) l+ Pth column of H It is obvious that the received

signal vector yN+1 is a multi-user multi-path signal vector which is a superposition of (N+ + path multi-user signals To improve the system performance by time L 1)diversity, single-path signals of all users must be separated from yN+1 Here, the idea for single-path signal separation is to design an equalizer G so that the output vector k

of the equalizer G ykN+1( )n contains only one path signal of each user

Based on the statistically independent assumption of the input signals, the correlation matrix of xN+1( )n is given by

where {}E ⋅ is the expectation operator, *

( )⋅ denotes the conjugate transposition, and

J is a (P N+ + L 1) × (P N+ + matrix with zero entries except along the lower L 1)(kP)th subdiagonal, in which the entries are one The auto-correlation matrix of the received signal vector yN+1( )n is therefore

( )= { + ( + ) + ( ) }= kPYkENnkNn

As x ni( )=x n di( − i), the delay information is embedded in ( )x n and the system i

model (2-13) is similar to that of [Zhu, Ding and Cao, 1999] The ISI (intersymbol interference) cancellation method for synchronous systems in [Zhu, Ding and Cao, 1999], which is insensitive to the channel length overestimation, can be applied to (2-13) It follows that an equalizer G for ISI cancellation can be designed as k

where N ′ = N + L + 1, and 0a b× is an a b× zero matrix

Applying the equalizer G to the received signal vector k yN+1( )n , one obtains

columns of H are retained in the multi-user single-path signal vector ( )okn As the middle columns of H defined in (2-12) have large norms, their selection should

provide the strongest signal components [Zhu, Ding and Cao, 1999] Therefore k is set as

in which k equals to o ⎢⎣(N+ +L 1) / 2⎥⎦ where ⎢ ⎥i denotes truncation of the enclosed parameter It follows that the multi-user single-path signal vector with the strongest signal components is first generated by the equalizer G with the parameter kk= ko

Then the other multi-user single-path signal vectors are generated by setting k =ko± , 12

k=k ± , Note that k satisfies 0 ≤ k ≤ N+ −L dPU

2.3.2 Time delay estimation

In order to detect all users’ signals, time delay estimation is absolutely necessary The time delay information is embedded in each multi-user single-path signal vector

modeled the delay information in the user signal vector (x n−ko) However, the sliding correlation method cannot accurately estimate the time delays when the difference between any two delays is less than two symbol periods and the vector orthogonalization method is rather complicated As the time delay information can be modeled either in the user signal vector or in the channel matrix, a simple method to estimate the delay information is proposed here using the structural property of the latter case

Rewrite the multi-user single-path signal vector ( )

columns Namely, the matrix HRE( )ko has only P non-zero columns on the position

(d P ii+ , i ) ∈ {1, 2, , P } Time delay information is now embedded in the

channel matrix HRE( )ko Suppose HRE( )ko is known, it follows that for each i , the

norm of the (d P ii + th column of ) HRE( )ko must be the largest among the (m P ii + )th columns, m i ∈ { 0, 1, , dPU }, because other columns among these (dPU +1)columns are all-zero columns With this special structural property, the (m P ii + )th columns, m i ∈ { 0, 1, , dPU}, are grouped together to form P different groups

The column with the largest norm in each group is selected and its position in the matrix HRE( )ko is denoted by K , i i∈ {1, 2, , P } The estimated time delays ˆ

for i=2, the {2, 4, 6} th columns form the second group and dˆ2 =(4 2) / 2 1− =

It is clear that in order to estimate the time delays, knowledge of the matrix ( )

H is required Obviously there is no restriction on how HRE( )ko is to be estimated However, as the accuracy of the time delay estimation has a profound effect on the performance of multi-user detection, it is preferred to use some pilots embedded in the signals so that the estimation accuracy can be guaranteed In order to estimate the M N( + × (1) dPU +1)P matrix HRE( )ko from the multi-user single-path signal vector ( )

The proposed Rake-based receiver is illustrated in Fig 2.3 It consists of 2m+1

fingers, each corresponding to a different delay of yN+1( )n equalized by a different

equalizer The q th finger output is given by

o is the (ko− + th path multi-user signal The q 1) 2m+1

path multi-user signals are combined by the combining weights

Fig 2.3 Rake-based receiver

Recall that HP( )ko is an M N( + × matrix, each column of which is a non-1) P

zero column of H ( )HPko is of full column rank follows the assumption that H has

full column rank after removing all-zero columns in Section 2.2 Therefore, the matrix

In order to compute the combining weights in (2-35), the channel gain matrices

Pko +q

H , {0, 1, 2,q∈ ± ± ,±m} are required We recall that (dPU +1)P+dPU pilots have been inserted into each user’s signal to estimate the time delays Using some of these pilots, the least-square estimate [Kay, 1993] of HP(ko+q) using (2-29) can be obtained as

2.3.4 Channel noise consideration

In the presence of noise, yN+1( )n is given by (2-8) Let the variance of noise be σ2 The auto-correlation matrix of yN+1( )n is

weight matrix V can be designed based on the MMSE criterion as [Liu and Li, 1999] m

R where RY(0) = HH + * σ2I Since some error generally exists in the

estimation of σ2 and this error will degrade the performance, we prefer not to subtract the noise contribution from RY( )k Instead, the equalizers G are k

constructed based on RY( )k as if it were noiseless Denote the perturbation of G k

due to noise contribution as Gk noise, The multi-user single-path signal vector ok( )n is

Lemma 1: If A and B are positive definite Hermitian matrices, it satisfies that

Proof: In fact,

Since A A−1( −1+B−1)−1A is positive definite, its eigenvalues are real numbers and −1

greater than zero and therefore trace(A A−1( −1+B−1)−1A−1)>0 Hence,

traceA B+ − <traceA− and the lemma is proved

For the noisy case with knowledge of the noise variance σ2, the output of the Rake-based receiver with the parameter m is obtained based on (2-30) and (2-39)

P mP mP mP mP mP moo

P mP m

trace EnknkSNR

trace Enknktrace

− ≤ ≤ , is an (M N+ × matrix, each column of which is a non-zero column 1) P

of H , it is apparent that the matrices HP(ko −q) and HP m, in (2-32) have full column rank Therefore the square matrices HP(ko−q)*HP(ko−q) and H H*P m, P m, are positive definite Hermitian matrices and their eigenvalues are real numbers and greater than zero From (2-32), we get

signal vector in the receiver It is obvious that the output SNR of the Rake-based receiver is increased by multi-path combining Consequently, based on the relation between the average BER and the output SNR, the average BER satisfies

Rake mRake mRake

The average BER is reduced by multi-path combining It means that the performance is improved by time diversity

2.4 Examples and simulation results

2.4.1 Time delay estimation

A quasi-synchronous MIMO system with P=3 users and M =3 receive antennas operating in single-path channels is used as an example to illustrate the proposed time delay estimation method In the simulation, QPSK modulation was used The synchronization window dPU was set to 8 and the time delays of the users were assumed as follows: d1= , 2 d2 = , and 4 d3 = (arbitrarily selected for illustration 1purpose) The single-path channel response matrix h(0) was randomly generated with Rayleigh probability distribution The received signal vector y( )n was therefore

( )n = (0) ( )n + ( ),n

For single-path channels, the time delay estimation method in Step 2 can be directly applied by remodeling the channel matrix as hRE(0), which is an M×(dPU +1)P

matrix where the (d P ii+ th column, i ∈ {1, 2, , P }, is the i th column of (0)) h

and other columns are all-zero columns In this example, (dPU +1)P+dPU randomly generated pilots were exploited

In Fig 2.4, the solid line shows the normalized norms of the (m Pi + th columns, 1)

m ∈ { 0, 1, , dPU}, in the estimated matrix hˆRE(0) The dashed line indicates the normalized norms of the (m Pi + th, 2) m i ∈ { 0, 1, , dPU}, columns and the dot line corresponds to the normalized norms of (m Pi + th, 3) m i ∈ { 0, 1, , dPU}, columns Each group norms are normalized by the maximum norm in the group The

simulation is performed under the condition that SNR=20dB, where

( )

Eh l x n ldSNR

Fig 2.4 Time delay estimation (d1 = , 2 d2 = , and 4 d3 = ) 1

2.4.2 Semi-blind Rake-based multi-user detection technique

Computer simulations have been conducted to investigate the performance of the proposed semi-blind Rake-based technique In the following two examples,

(dPU +1)P+dPU randomly generated pilots were inserted into each user’s signal and the pilot matrix XRE(n k− o) in (2-26) containing the pilots was selected to have full rank The auto-correlation of the received signal vector was computed from some finite number of received signal vector as

where N was the number of received signal vectors used In our simulations, sN was s

chosen as 500 The performance measure, BER, was computed by averaging the results among all users over 1000 simulation runs Each simulation run had a data length of 500 symbols

2.4.2.1Example 1

A synchronous MIMO mobile communication system with P = 2 users and M = 4

receive antennas was considered All users’ signals were modulated with QPSK scheme For synchronous systems, the time delays of all users were zero (d = 1 d = 0) 2

and the maximum time delay dPU was equal to zero The maximum channel length

L was set as 4 and the channel responses were generated randomly with Rayleigh

probability distribution The parameter N was set as ˆ

P LPMN

where ˆL is the estimated maximum channel length and ⎢ ⎥a truncates the parameter

a to the nearest integer Two Rake-based receivers were designed with the parameter

m= (corresponding to single-path receiver) and m=2 (arbitrarily selected for illustration purpose) For comparison purpose, the MMSE multi-user detector with