Information theory shows that multiple-input multiple-output (MIMO) communication systems can significantly increase the capacity of band-limited wireless channels by a factor of the minimum number of transmit and receive antennas, provided that a rich multipath scattering environment is utilized. In Sections 2.1 and 2.2, MIMO system model and MIMO channel capacity are introduced.
In order to achieve extraordinary data rate in MIMO systems, spatial multiplexing technique is presented in Section 2.3. Spatial multiplexing allows a data rate enhancement in a wireless radio link without additional power or bandwidth consumption. It is realized by transmitting independent data signals from the individual transmit antennas. Two typical spatial multiplexing schemes, D-BLAST and V-BLAST, are introduced in Sections 2.3.1 and 2.3.2.
( ) t = ( ) t + ( ) t
Figure 2.1: MIMO wireless transmission system model.
Transmitter Receiver
Figure 2.2: An illustration of a spatial multiplexing system.
1 : 3
Figure 2.3: Diagonal Bell Labs’ Layered Space-Time encoding procedure.
1.
Figure 2.4: Diagonal Bell Labs’ Layered Space-Time decoding procedure.
1 : 3
Figure 2.5: Vertical Bell Labs’ Layered Space-Time encoding procedure.
Decode
Figure 2.6: Vertical Bell Labs’ Layered Space-Time decoding procedure.
0 5 10 15 20 25 30 0
2 4 6 8 10 12 14 16 18 20
SNR (dB)
Channel Capacity (bits/sec/Hz)
(1,5) SIMO Channel (1,4) SIMO Channel (1,2) SIMO Channel SISO Channel
Figure 2.7: Capacity of a SISO channel compared to the ergodic capacity of Rayleigh fading SIMO channels with (Nt, Nr) = (1, 2), (1, 4), and (1, 5).
0 5 10 15 20 25 30 0
5 10 15
SNR (dB)
Channel Capacity (bits/sec/Hz)
(5,1) MISO Channel (4,1) MISO Channel (2,1) MISO Channel SISO Channel
Figure 2.8: Capacity of a SISO channel compared to the ergodic capacity of Rayleigh fading MISO channels with (Nt, Nr) = (2, 1), (4, 1), and (5, 1).
0 5 10 15 20 25 30 0
5 10 15 20 25 30
SNR (dB)
Channel Capacity (bits/sec/Hz)
(5,5) Rayleigh Fading MIMO Channel (4,4) Rayleigh Fading MIMO Channel (2,2) Rayleigh Fading MIMO Channel SISO Channel
Figure 2.9: Capacity of a SISO channel compared to the ergodic capacity of Rayleigh fading MIMO channels with (Nt, Nr) = (2, 2), (4, 4), and (5, 5).
-5 0 5 10 15 20 10-8
10-7 10-6 10-5 10-4 10-3 10-2 10-1 100
Es/No (dB)
BER
1st Detected Layer 2nd Detected Layer 3th Detected Layer 4th Detected Layer
Figure 2.10: ZF V-BLAST BER performance with ideal detection and cancellation.
QPSK modulation is used and (Nt, Nr) = (4, 4).
-5 0 5 10 15 20 10-4
10-3 10-2 10-1 100
Es/No (dB)
BER
1st Detected Layer 2nd Detected Layer 3th Detected Layer 4th Detected Layer
Figure 2.11: ZF V-BLAST BER performance with error propagation. QPSK modulation is used and (Nt, Nr) = (4, 4).
Chapter 3
Multiuser OFDM Systems and Subcarrier Allocation Schemes
In recent years, there has been substantial research interest in applying orthogonal frequency division multiplexing (OFDM) to high speed wireless communications due to its advantage in mitigating the severe effects of frequency-selective fading [18]-[19].
By allowing a number of users to share an OFDM symbol, the multiple access concepts are possible in OFDM systems. Owing to the multiple access concepts, there are two kinds of resource allocation schemes. One is fixed resource allocation scheme [25] and the other is dynamic resource allocation scheme [26]-[32]. Fixed resource allocation scheme including time division multiple access (TDMA) and frequency division multiple access (FDMA) assigns an independent dimension, such as time slot or subchannel, to each user regardless of the current channel quality. On the other hand, dynamic resource allocation scheme allocates a dimension adaptively to each user based on users’ channel qualities. Due to the time-varying nature of wireless channels, dynamic resource allocation scheme makes full use of the multiuser diversity to achieve better performance. In this chapter, the basic ideas and resource allocation schemes suited to the multiuser OFDM systems will be introduced.
3.1 Review of OFDM
OFDM is a special case of multicarrier transmission, where a single data stream is transmitted over a number of low data rate subcarriers. OFDM can be thought of as a
hybrid of multicarrier modulation (MCM) and frequency shift keying (FSK) modulation scheme. The principle of MCM is to transmit data by dividing the data stream into several parallel data streams and modulate each of these data streams onto individual subcarriers. FSK modulation is a technique whereby data is transmitted on one subcarrier from a set of orthogonal subcarriers in symbol duration. Orthogonality between these subcarriers is achieved by separating these subcarriers by an integer multiples of the inverse of symbol duration of the parallel data streams. With the OFDM technique used, all orthogonal subcarriers are transmitted simultaneously. In other words, the entire allocated channel is occupied through the aggregated sum of the narrow orthogonal subbands.
The main reason to use OFDM systems is to increase the robustness against frequency-selective fading or narrowband interference. In a single carrier system, a single fade or interference can cause the entire link fail, but in a multicarrier system, only a small amount of subcarriers will be affected. Then the error correction coding techniques can be used to correct errors. The equivalent complex baseband OFDM signal can be expressed as
2 1 1
where Nc is the number of subcarriers, T is the symbol duration, dk is the transmitted subsymbol (M-PSK or M-QAM), φk( )t =ej2πf tk / T is the kth subcarrier with the frequency /fk =k T , and uT(t) is the time windowing function. Using the correlator-based OFDM demodulator, the output of the jth branch can be presented as
2 1 2
By sampling x(t) with the sampling period Td=T/Nc, the discrete time signal xn can be expressed as
2 1 2
Note that xn is the inverse fast Fourier transform (IFFT) output of the N input data subsymbols. Similarly, the output of the jth branch can also be presented in the digital form
In theory, the orthogonality of subcarriers in OFDM systems can be maintained and individual subcarriers can be completely separated by the fast Fourier transform (FFT) at the receiver when there are no intersymbol interference (ISI) and intercarrier interference (ICI) introduced by transmission channel distortions. However, it is impossible to obtain these conditions in practice. In order to eliminate ISI completely, a guard interval is imposed into each OFDM symbol. The guard interval is chosen larger than the expected delay spread, such that the multipath from one symbol cannot interfere with the next symbol. The guard interval can consist of no signals at all.
However, the effect of ICI would arise in that case due to the loss of orthogonality between subcarriers. To eliminate ICI, the OFDM symbol is cyclically extended in the guard interval to introduce cyclic prefix (CP) as shown in Figs. 3.1-2. This ensures that delayed replicas of the OFDM symbol always have an integer number of cycles within the FFT interval, as long as the delay is smaller than the guard interval. As a result, the delayed multipath signals which are smaller than the guard interval will not cause ICI.
The complete OFDM signal with CP is given by
2 1 2 ( )
where N is the number of samples in CP. Due to CP, the transmitted OFDM symbol
becomes periodic, and the linear convolution process of the transmitted OFDM symbols with the channel impulse responses will become a circular convolution one.
Assuming the value of Ncp is larger than the channel length, the received data vector can be expressed as
= +
Applying SVD on the channel response, we have
= H
H UΣV (3.7) where U and V are unitary matrices, and is a diagonal matrix. Substituting
Equation (3.7) and the equalities of
Σ
= V and =UH
x X Y y into Equation (3.6), the received data vector can be written as
( )
This means that the output Y can be expressed in terms of the product of and X plus noise. When
Σ
transform (DFT) matrix with the lth entry as 1 j2 Nlc
l
c
N e
− π
=
Q (3.10)
As in Equation (3.8), the received data y can be transformed into Y
( )
H H H H
= = + = +
= +
Σ N
Y Q y Q Hx η Q HQ X Q η ΣX N
H
(3.11)
According to Equation (3.11), by adding CP to the OFDM symbol, the modulation in OFDM is equivalent to multiplying the frequency domain signals of the OFDM symbol with the channel’s frequency response Σ.
The block diagrams of the OFDM transceiver is shown in Fig. 3.3, where the upper path is the transmitter chain and lower path corresponds to the receiver chain. In the center, IFFT modulates a block of input values onto a number of subcarriers. In the receiver, the subcarriers are demodulated by the FFT, which performs the reverse operation of the IFFT. In fact, the IFFT can be made using the FFT by conjugating input and output of the FFT and dividing the output by the FFT size. This makes it possible to use the same hardware for both transmitter and receiver. This complexity saving is only possible when the transceiver doesn’t have to transmit and receive simultaneously. The functions before the IFFT can be discussed as follows. Binary input data is first encoded by a forward error correction code. The encoded data is then interleaved and mapped onto QAM values. In the receiver path, after passing the radio frequency (RF) part and the analog-to-digital conversion (ADC), the digital signal processing starts with a training sequence to determine symbol timing and frequency offset. The FFT is used to demodulate all subcarriers. The FFT outputs are mapped onto binary values and decoded to produce binary output data. In order to successfully map the QAM values onto binary values, the reference phases and amplitudes of all subcarriers have to be acquired first.
In conclusion, OFDM is a powerful modulation technique that simplifies the removal of distortion due to the multipath channel and increases bandwidth efficiency.
The key advantages of OFDM transmission scheme can be summarized as follows:
1. OFDM is an efficient way to deal with multipath. For a given delay spread, the implementation complexity is significantly lower than that of a single carrier system with an equalizer.
2. In relatively slow time-varying channels, it is possible to significantly enhance the capacity by adapting the data rate per subcarrier according to the signal-to-noise ratio (SNR) of that particular subcarrier.
3. OFDM is robust against narrowband interference because such interference affects only a small amount of subcarriers.
4. OFDM makes single-frequency networks possible, which is especially attractive for broadcasting applications.
3.2 Multiple Access Techniques
Multiple access concepts can be defined as the sharing of a fixed communication resource by a group of users. For wireless communications, the communication resource can be thought of as a hyperplane in frequency and time dimensions. The goal of multiple access techniques is to allow users to share the communication resource without creating unmanageable interference with each other. In the following, two of the most basic multiple access techniques for wireless communications will be reviewed: one is frequency division multiple access (FDMA) and the other is time division multiple access (TDMA).
In FDMA systems, the frequency-time plane is partitioned into non-overlapping frequency bands. Each of them serves a single user. Every user is therefore equipped with a transmitter for a given, predetermined, frequency band, and a receiver for each band which can be implemented as a single receiver for the entire range with a bank of bandpass filters for the individual bands. The graph in Fig. 3.4 (a) illustrates the FDMA concept. The spectral regions between adjacent channels are called guard bands, which help reduce the interference between channels. FDMA is used exclusively for analog cellular systems, even though FDMA can be used for digital systems in theory.
Essentially, FDMA splits the allocated spectrum into many subchannels. In current analog cell systems, each subchannel is 30 kHz. The main advantage of FDMA is its simplicity. It doesn’t require any coordination or synchronization among users since
each user can use its own frequency band without interference. However, this is also the cause of waste especially when the load is momentarily uneven since when one user is idle his share of bandwidth can’t be used by other users. It should be noted that if the users have uneven long term demands, it is possible to divide the frequency range unevenly, i.e., proportional to the demands. However, FDMA is not flexible when adds a new user to the network requiring equipment modification, such as additional filters, in every other user. As a result, FDMA is considered the least efficient way of mobile communications. It is being replaced by the new digital networks such as TDMA.
In TDMA systems, sharing of the communication resource is accomplished by dividing the frequency-time plane into non-overlapping time slots which are transmitted in periodic bursts. Every user is allowed to transmit freely during the time slot assigned to him, that is, the entire system resources are devoted to that user during the assigned time slot. The graph in Fig. 3.4 (b) illustrates the TDMA concept. Time is segmented into intervals called frames. Each frame is further partitioned into user assignable time slots. An integer number of time slots constitutes a burst time or burst.
Guard times are allocated between bursts to prevent overlapping of bursts. Each burst is comprised of a preamble and the message portion. The preamble is the initial portion of a burst used for carrier and clock recovery, station identification, and other housekeeping tasks. The message portion of a burst contains the coded information sequence. In some systems, a training sequence is inserted in the middle of the coded information sequence. The advantage of this scheme is that it can aid the receiver in mitigating the effects of the channel and interference. The disadvantage is that it lowers the frame efficiency; that is, the ratio of the bit available for messages to the total frames length.
The TDMA systems are designed for use in a range of environments and situations, form hand portable using in a downtown office to a mobile user traveling at high speed on the freeway. It also supports a variety of services for the end user, such as voice, data, fax, short message services, and broadcast messages. TDMA offers a flexible air interface, providing high performances in capacity, coverage, mobility, and capability to handle different types of user needs. While TDMA is a good digital system, it is still somewhat inefficient since it has no flexibility for varying data rates and has no
accommodations for silence in telephone conservation. TDMA also requires strict signaling and timeslot synchronization. A point worth noting is that both FDMA and TDMA system performances degrade in the presence of the multipath fading. More specifically, due to the high data rates of TDMA systems, the time dispersive channel (a consequence of delay spread phenomenon) causes intersymbol interference (ISI). This is a serious problem in TDMA systems thus requiring adaptive techniques to maintain system performance. The key advantages of TDMA can be summarized as follows:
1. Sharing single carrier frequency with multiple users.
2. Non-continuous transmission makes handoff simpler. It means that mobile assisted handoff is possible.
3. Less stringent power control due to the reduced interuser interference.
4. Slots can be assigned on demand (concatenation and reassignment). It means that bandwidth can be supplied on demand.
The disadvantages of TDMA can also be summarized as follows:
1. High synchronization overhead is needed.
2. Equalization is necessary for high data rates.
3. Power envelop will pulsate. It is caused by interfering with other devices.
4. High frequency/slot allocation complexity is needed.
3.3 Multiple Access in OFDM Systems
In one OFDM symbol, the data is modulated using Nc subcarriers and when there are multiple users, each user may be allocated a set of subcarriers, i.e., the data transmission to a particular user can take place using the allotted set of subcarriers. This is illustrated using the OFDM time and frequency grid shown in Fig. 3.5. Each rectangle in the grid can be considered as a resource and it can be allocated to any particular user in an OFDM symbol time. The user can employ a specific type of modulation depending on the quality of service (QoS) requirements and the channel quality allocated to him. Therefore, OFDM systems can offer flexibility in modulation order and multiple access. In addition, the base station must send the signaling information to each user indicating the subcarriers and time slots allotted to the user.
In general, it can be said that uncertainties concerning OFDM as a multiple access
concept concerns the system uplink. The main issue is to keep the mobile synchronized to the base station in time and frequency grid. This means that the mobiles must transmit the information with some timing advance due to the different propagation delay of the radio channels. The mobiles need to be synchronized to preserve the system orthogonality and avoid intercarrier interference (ICI). On the contrary, the downlink follows the same paths as the broadcast concepts and has already proven functional. All users are always orthogonal to each other because they are multiplexed in the base station. If a mobile loses the synchronization on the downlink, the only thing that happens is that the connection is lost. No other user will suffer from this type of failure. In the following, the OFDM transmission technique combining with multiple access techniques, such as FDMA and TDMA will be introduced.
3.3.1 Frequency Division Multiple Access (FDMA)
In OFDM-FDMA systems, each user is allocated a predetermined band of subcarriers and each user’s data is transmitted using only the subcarriers allotted to the user. This scheme can also be defined as OFDMA systems. In each allocated subcarrier, adaptive bit loading can be performed depending on the subchannel SNR to achieve the user’s requirements. By allocating distinct sets of subcarriers to different users, the available bandwidth can be flexibly shared between different users while avoiding any multiple access interferences (MAI) between them. There are variations possible in OFDM-FDMA systems, such as block FDMA and interleaved FDMA, which are stated below.
In the block FDMA scheme, each user is allocated a group of adjacent subcarriers as illustrated in Fig. 3.6. The different shades in Fig. 3.6 represent different users and the subcarriers allocated to them. The allocation of blocks to users can be accomplished by using the greedy algorithm. Assuming that each user is allocated only one block, the first block is allocated to the user with the best SNR of the block in the first step. Then, this particular user and the allotted block are removed from the search and the procedure is continued for the next block until all blocks are allocated. In most cases, the adjacent subcarrier gains are highly correlated and consequently, the bit loading of the block can be considered together. It means that the same modulation mode can be
used for all subcarriers in the block. The main advantage of the block FDMA scheme is easy allocation of subcarriers with less computational complexity but it lacks in robustness. There is a high probability that all subcarriers allocated to a user will fade at the same time. As a remedy, an improvement called interleaved FDMA will be introduced in the following.
In the interleaved FDMA scheme, the subcarriers assigned to a particular user are interlaced with other users’ subcarriers in the frequency domain. If a deep fade occurs, only a single subcarrier of a particular user is affected and the data can be recovered by using coding techniques across many OFDM symbols. Fig. 3.7 illustrates the interleaved FDMA concept.
The key advantages of OFDM-FDMA can be summarized as follows:
1. No multiple access interferences (MAI).
2. Incoherent or coherent modulation.
3. Adaptation to channel characteristics 4. Robustness against estimation errors.
3.3.2 Time Division Multiple Access (TDMA)
In OFDM-TDMA systems, each user is assigned a time slot during which all the subcarriers can be used for the particular user. This is illustrated in Fig. 3.8. The duration of each slot is assumed equal to the OFDM symbol. Due to the variations of the subcarrier channel gains for users, channel gains for some subcarriers may be quite low, while they are quite high for other subcarriers. Owing to the channel gain variations regarding one specific subcarrier for different users, the subcarrier with a low channel gain for one user may experience a high channel gain for some other users.
In OFDM-TDMA systems, each user is assigned a time slot during which all the subcarriers can be used for the particular user. This is illustrated in Fig. 3.8. The duration of each slot is assumed equal to the OFDM symbol. Due to the variations of the subcarrier channel gains for users, channel gains for some subcarriers may be quite low, while they are quite high for other subcarriers. Owing to the channel gain variations regarding one specific subcarrier for different users, the subcarrier with a low channel gain for one user may experience a high channel gain for some other users.