1. Introduction
1.2 Thesis Outline
The research of this thesis investigates how to efficiently assign the subcarriers in order to enhance the coverage reliability for OFDM-based spatial multiplexing sys-tems. We first focus on the analysis of the link outage probability which could be used as an indicator of the system performance. Because it is hard to analyze the link outage probability in OFDM-based spatial multiplexing systems, there are no closed form expressions in the literature. We evaluate analytical expressions for the link outage probability, and provide another simple approximation of link outage proba-bility to further derive the cell coverage of OFDM-based spatial multiplexing systems over frequency-selective fading channels. Furthermore, we focus on the assignment of each resource dimension to only one user to avoid the complexity and the assignment requires only limited amount of feedback. Besides, we assume frequency selective qua-sistatic channels where channels do not vary within a block of transmission. We first extend the suboptimal subcarriers assigning algorithm from SISO OFDM to MIMO
OFDM systems, and we call it fairness-oriented subcarriers assignment (FOSA) in this thesis. Besides, we propose a low-complexity coverage-oriented subcarriers as-signment algorithm (COSA) which can achieve larger cell coverage than FOSA for OFDM-based spatial multiplexing systems. Furthermore, we derive an approximately analytical expression for link outage and cell coverage by using COSA, and show how the total transmit power, number of antennas, number of users and the pass loss exponent could affect the cell coverage under this subcarriers assignment algorithm over frequency-selective fading channels.
The remaining chapters of this thesis are organized as follows. Chapter 2 intro-duces the background of the scalable OFDMA physical layer in IEEE 802.16 wireless metropolitan area network (WMAN). Furthermore, we discuss the scheduling scheme in multi-user MIMO systems and subchannel allocation approaches in the OFDMA systems. The definition of fairness performance, link outage probability, and cell coverage reliability are also included. Chapter 3 provides an analytical expression of the link outage probility, and provide another simple analytical closed form ap-proximation of the link outage probability to further derive the cell coverage of the OFDM-based spatial multiplexing systems over frequency-selective fading channels.
Chapter 4 proposes a low-complexity coverage-oriented subcarriers assignment algo-rithm (COSA) which can efficiently assign the subchannels in order to enhance the coverage reliability for OFDM-based spatial multiplexing systems. At last, Chapter 5 gives the concluding remarks and suggestions for future work.
Chapter 2 Background
In this chapter, we introduce the background of the scalable OFDMA physical layer in IEEE 802.16 wireless metropolitan area network (WMAN), the concept of scheduling techniques, and some definitions of the performance metric about the thesis.
2.1 Scalable OFDMA Physical Layer in IEEE 802.16 WirelessMAN
The IEEE 802.16 WirelessMAN [1] specifies the standards of air interface and medium access control (MAC) protocols for fixed, portable, and mobile broadband wireless access systems. The standard includes requirements for high data rate line of sight (LOS) operation in the 10-66 GHz range for fixed wireless networks as well as require-ments for non line of sight (NLOS) fixed, portable, and mobile systems operating in sub 11 GHz licensed and licensed exempt bands. In a NLOS environment, WMAN in the IEEE 802.16a specification is recommended to operate in a multicarrier modula-tion mode. Each OFDMA symbol consists of various types of subcarriers, including data, pilot and null. The number of the total subcarriers is 2048, which is equal to the fast Fourier transform (FFT) size.
Because of its superior performance in multipath fading wireless channels, or-thogonal frequency division multiplexing (OFDM) signaling is recommended in Wire-lessMAN OFDMA Physical layer modes of the 802.16 standard for operation in sub 11 GHz NLOS applications. The OFDM technology has been recommended in other
wireless standards such as digital video broadcasting (DVB) and wireless local area networking (WLAN), and it has been successfully implemented in the compliant so-lutions.
IEEE 802.16 specifies two flavors of OFDM systems: one is OFDM, and the other OFDMA. The first aims at less challenging applications, quite short distance, eventually indoors. It employs fast Fourier transform (FFT) size 256, and all carriers are transmitted at once. The downstream data is time-division multiplexed (TDM).
The upstream time frame is time-division multiple access (TDMA).
In OFDMA the higher FFT space (2048 and 4096 carriers) is divided into sub-channels. They are used in downstream for separating the data into logical streams.
Those streams employ different modulation, coding, and amplitude to address sub-scribers with different channel characteristics. In upstream the subchannels are used for multiple access. The subscribers are assigned on subchannels through Media Ac-cess Protocol (MAP).
Unlike many other OFDM-based systems such as WLAN, the 802.16 standard supports variable bandwidth between 1.25 and 20 MHz for NLOS operations. This feature, along with the requirement for support of combined fixed and mobile usage models, makes the need for a scalable design of OFDM signaling inevitable. The con-cept of scalable OFDMA is introduced to the IEEE 802.16 WirelessMAN OFDMA mode by the 802.16 Task Group e (TGe) and has been the subject of many contribu-tions to the standards committee. Other features such as AMC subchannels, Hybrid Automatic Repeat Request (H-ARQ), high-efficiency Uplink (UL) subchannel struc-tures, multiple-input-multiple-output (MIMO) diversity, enhanced advanced antenna system (AAS), and coverage enhanceing safety channels were introduced simultane-ously to enhance coverage and capacity of mobile systems while providing the tools to trade off mobility with capacity.
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2.2 Scheduling in OFDMA Systems
Successful deployment of wireless voice communication system promises a bright fu-ture for wireless high data rate services such as the internet access or multimedia applications. In order to provide high data rate services, orthogonal frequency divi-sion multiplexing access (OFDMA) is being considered as a viable candidate because of its ability to overcome multipath fading.
If the channel is static and is perfectly known to the transmitter and its receiver, water-filling with adaptive modulation is known to be optimal. Water-filling also applies if the channel is slowly fading as in fixed wireless systems of if the channel estimation and feedback can be performed in a short time span. Because the technique of adaptive loading has been hardly included in actual implementation due to the time varying nature of wireless channels, it starts to receive more attention as the spectral efficiency and the low complexity become more important.
However, the water-filling solution can only be used for single-user systems or multiuser systems with fixed resource assignment. For example, in Time Division Multiple Access (TDMA) or Frequency Division Multiple Access (FDMA) systems with non-adaptive fixed resource allocation, an independent dimension such as time slot or frequency band is assigned to each user regardless of channel response. Here each user effectively becomes a single user who is independent of all other users. In this case, the water-filling solution can be used for each user to maximize its throughput.
However, the maximized rate is far below the rate that can be achieved by adaptive resource allocation, and a set of users suffers from poor channel gains of assigned dimensions. If we assign a dimension to users whose channel gains are good for it, larger throughput can be achieved.
The characterization of information theoretic channel capacity for a multiuser system is a complex optimization problem. In order to achieve the channel
capac-ity, highly complex coding and decoding such as maximum likelihood detection or multiuser detection with successive decoding is needed. [2] focused on exclusive as-signment of each resource dimension to only one user to avoid the complexity and the error propagation problems. That is to say, it allows only one user to occupy a dimension related to a specific frequency at a specific time.
2.3 Scheduling in MU-MIMO Systems
In multi-user MIMO (MU-MIMO) systems, all users are coordinated for commu-nications by using scheduling algorithms and considering quality of service (QoS) requirements of each user. When multiple antennas are used on the transmitter and receiver side, the scheduling algorithm is significant in determining the system ca-pacity in a multi-user MIMO environment, where different transmit antennas can be assigned for data transmissions of specific users, simultaneously. When the instanta-neous knowledge of the received signal-to-noise ratio (SNR) is exploited to schedule a user, we can extract the multi-user diversity. As more transmit and receive antennas are used and more users are considered in cellular networks, scheduling algorithms become more important in complicated system environment.
In a multiuser MIMO system over flat fading channels, multiuser diversity can be exploited to improve downlink capacity. [3] proposed a fair scheduling scheme called strongest-weakest-normalized-subchannel-first (SWNSF) which can significantly in-crease the coverage of the multiuser MIMO system while further improving system capacity. Furthermore, this scheduling algorithm requires only scalar feedback, be-cause each user only needs to send back a scalar value to inform the channel condition without considering the number of transmit and receive antennas.
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2.4 Scheduling in Multi-user MIMO-OFDM Systems
In principle, OFDM and MIMO can be integrated to offer the benefits in terms of both simplicity and high performance. MIMO OFDM is a special case of the general multiuser multicarrier MIMO system. Such is indeed an active topic within the IEEE 802.16/20 standardization bodies. In [4], it extend the study on OFDMA/SISO to multiuser multicarrier MIMO systems. Also, [4] proved that OFDMA/MIMO is the optimal (in terms of total capacity) downlink scheme under the independent decoding constraint.
However, unlike OFDMA/SISO where the optimal solution can be found with linear complexity (with respect to the number of users and number of the subcarriers), the OFDMA/MIMO problem has no explicit solution due to the tangled effects of subcarrier allocation and power loading. To sum up, in order to obtain the optimal subcarrier allocation and the optimal power loading, and exhaustive search needs to be performed, and the cost of exhaustive search is exponentially increased with respect to the number of subcarriers and is polynomially increased with respect to the number of users.
2.5 Some Definitions of Performance Metrics
Here we define the performance metrics used in this thesis.
2.5.1 Fairness performance
We first define a fairness index F in the multiuser systems as follows
F =
where Ti is the number of times the subchannels allocated to ith user. For F = 1, it is the fairest condition between users, and it is not fair as F ¿ 1.
2.5.2 Link outage probability
To begin with, we first define the link outage probability which reflects how reliable a system can support the corresponding link quality. For a single-input single-output (SISO) system in a flat fading channel, link outage is usually defined as the probability that the received SNR is less than a predetermined value γth, i.e. Pout = Pr{γ < γth} [5]. The link outage for the spatial multiplexing MIMO system in a flat fading channel is defined as the event when the receive SNR of any substream is less than γth [6] [3].
When all the degrees of freedom in the spatial domain of a MIMO system are used for the transmission of parallel and independent data streams to exploit the spatial multiplexing gain, the data stream with the lowest SNR in the MIMO system will dominate the link reliability performance especially when the high-percentile link reliability, such as 90% or even higher, is concerned.
The OFDM-based spatial multiplexing system in a frequency selective fading channel can be viewed as the sum of flat fading MIMO channels. As discussed before, the high-percentile link reliability performance of each MIMO flat-fading channel is dominated by the weakest substream. Considering the average weakest eigen-mode over a series of N’s MIMO flat-fading subchannels, we define the link outage
13 probability of the spatial-multiplexing-based MIMO OFDM system for user k as follows:
Poutk = Pr Ã1
N XN n=1
γk,n,M ≤ γth
!
, (2.2)
where γk,n,M represents the receive SNRs of the weakest substream corresponding to the kth user in subchannel n for n = 1, . . . , N .
2.5.3 Cell Coverage Reliability
With Poutk being the link outage probability for user k, we define the cell coverage for all the users in a cell is the farthest distance at which the link quality suffices for maintaining a required receive SNR γth with cell coverage reliability (1 − Poutk ). Our focus is on the farthest user in the boundary of the cell coverage. In other words, if the farthest user maintains the link quality, the other (K − 1) users will maintains it too.
Analysis for Coverage Performance for OFDM-based Spatial Multiplexing
Systems
Combining multi-input multi-output (MIMO) antenna techniques with orthogonal frequency division multiplexing (OFDM) modulation (MIMO-OFDM) becomes an attractive air-interface solution for the next generation high speed wireless systems.
Nevertheless, because the total available transmit power is split uniformly across transmit antennas in MIMO-OFDM systems, increasing the number of transmit an-tennas leads to a smaller signal-to-noise ratio (SNR) per degree of freedom. Thus the coverage performance of this kind of MIMO-OFDM system becomes an essential issue. In this chapter by means of order statistics and Glivenko- Cantelli theorem, we develop an analytical expressions for the link outage probability and cell coverage re-liability of OFDM-based spatial multiplexing systems in a frequency selective fading channel, respectively.
3.1 Introduction
Orthogonal frequency division multiplexing (OFDM) modulation has become a pop-ular modulation technique for transmission of broadband signals. OFDM can convert a frequency selective fading channel into a parallel collection of frequency flat
fad-15 ing sub-channels and thus can overcome inter-symbol interference (ISI) [7] [8]. In the meanwhile, multi-input multi-output (MIMO) antenna techniques can provide spatial multiplexing gain and diversity gain to increase spectrum efficiency and link reliabil-ity, respectively [9] [10] [11] [12]. Combining MIMO with OFDM (MIMO-OFDM) becomes an attractive air-interface solution for the next generation high speed wireless systems.
Generally, there are three categories of MIMO-OFDM techniques.
• The first aims to realize spatial diversity and frequency diversity gain without the need for channel state information (CSI) at the transmitter. In the first category, the results in [13] proposed a transmit diversity scheme in a frequency selective fading channel. A space-time code across space and frequency (rather than time) was shown in [14] to yield spatial diversity. In [15, 16], a low-density parity-check (LDPC)-based space time code was proposed to exploit both spatial diversity and selective fading diversity for MIMO-OFDM system in correlated. [17] presented the space-frequency code that can achieve full diversity in space and frequency for MIMO-OFDM systems, where neither transmitter and receiver has perfect CSI. [18] investigated the performance of space-frequency coded MIMO OFDM as a function of Riciean K-factor, angle spread, antenna spacing and power delay profile. In [19], a code design framework for achieving full rate and full diversity in MIMO frequency-selected fading channels was proposed.
• The main goal of the second class of MIMO-OFDM techniques is to increase ca-pacity by exploiting multiplexing gain in the spatial domain, i.e., transmitting independent data streams across antennas and tones. The V-BLAST system sug-gested in [11] is a well-known layered approach to achieve spatial multiplexing gain in multi-antenna systems. [20] showed that a MIMO delay spread channel can provide both higher diversity gain and multiplexing gain than MIMO
flat-fading channels. However, increasing the number of transmit antennas results in a smaller signal-to-noise ratio (SNR) per degree of freedom because the total available transmit power is split uniformly across transmit antennas. This leads to link outage or coverage issue of the spatial multiplexing MIMO system. This issue has been investigated originally in [6] and a multiuser scheduling solution to ad-dress this issue in MIMO flat-fading channels was proposed in [3]. Nevertheless, the coverage performance for spatial-multiplexing-based MIMO-OFDM systems in frequency-selective fading channels has not been widely discussed so far.
• The third type of MIMO-OFDM technique is to decompose the channel coeffi-cient matrix by singular value decomposition (SVD) and construct pre-filter and post-filters at the transmitter and the receiver to achieve the capacity [21]. This technique requires perfect CSI available at both the transmitter and receiver.
In this chapter, we focus on the second type of MIMO-OFDM systems and aim to derive the closed form expressions for link outage and cell coverage cell cover-age of the OFDM-based spatial multiplexing systems over frequency-selective fading channels. The rest of this chapter is organized as follows. In Section II, we describe the system model. In Section III, we define the link outage for MIMO-OFDM sys-tems. In Section IV, we derive the exact analytical expression form of link outage of MIMO-OFDM systems, and provide an approximation analytical form of link out-age of MIMO-OFDM systems in Section V. In Section VI, we discuss the coverout-age performance of MIMO system. In Section VII, we show numerical results and give concluding remarks in Section VIII.
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3.2 System model
We consider a point-to-point MIMO system with M transmit antennas and M receive antennas. In the meanwhile, we adopt OFDM modulation with total NT sub-carriers and let a group of adjacent NT/N subcarriers form a subchannel. The total bandwidth of each subchannel is assumed to be smaller than the channel coherent bandwidth.
Figure 3.1 shows the considered structure of the OFDM-based spatial multiplexing systems, where MN independent data streams are multiplexed in M transmit an-tennas and N subchannels. The transmit power is uniformly split to M transmit antennas. It is assumed that the length of the cyclic prefix (CP) in the OFDM sys-tem is greater than the length of the discrete-time baseband channel impulse response so that the frequency-selective fading channel indeed decouples into a set of parallel frequency-flat fading channels [22]. With xnand yn denoting the M × 1 transmit and receive signal vectors, respectively, we can write
yn =√
gnHnxn+ nn , (3.1)
where n is the sub-channel index and Hnrepresents the M ×M MIMO channel matrix of the nth subchannel and each entry of Hn is an i.i.d. circular-symmetric complex Gaussian variable [18]. Represent nn the M × 1 spatially white noise vector with E[nnn∗n] = σ2nI where (·)∗ is the transpose conjugate operation. At last gn depicts the large-scale behavior of the channel gain. For a user at a distance of r from the base station, gn can be written as [23]
10 log10(gn) = −10µ log10(r) + g0 [dB] , (3.2) where µ is the path loss exponent and g0 is a constant subject to certain path loss models.
Fig. 3.1: OFDM-based Spatial Multiplexing Systems.
3.3 Definitions
3.3.1 Link Outage Probability
To begin with, we first define the link outage probability which reflects how reliable a system can support the corresponding link quality. For a single-input single-output (SISO) system in flat fading channel, link outage is usually defined as the probability that the received SNR is less than a predetermined value γth, i.e. Pout = Pr{γ < γth} [5]. The link outage for the spatial multiplexing MIMO system in a flat fading channel is defined as the event when the receive SNR of any substream is less than γth [6] [3].
When all the degrees of freedom in the spatial domain of a MIMO system are used for the transmission of parallel and independent data streams to exploit the spatial multiplexing gain, the data stream with the lowest SNR in the MIMO system will dominate the link reliability performance especially when the link reliability likely of high percentile, such as 90% or even higher, is concerned.
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Fig. 3.2: The Eigenvalues in Each Subchannel.
The OFDM-based spatial multiplexing system in a frequency selective fading channel can be viewed as the sum of flat fading MIMO channels as shown in Fig. 3.2.
As discussed before, the high-percentile link reliability performance of each MIMO
As discussed before, the high-percentile link reliability performance of each MIMO