3 Multiuser OFDM Systems and Subcarrier Allocation
3.4 Dynamic Subcarrier Allocation Algorithms for Multiuser OFDM Systems
3.4.3 Two-Stage Subcarrier Allocation Algorithm
_ (
_ ( ,
( , );
_ ( , );
}
c
c
u c
CALC WEIGHT N u CALC RATIO
SORT N
ASSIGN BEST k N
=
=
u
u
u
w
r T
r
, );
u wu);
3.4.3 Two-Stage Subcarrier Allocation Algorithm
In the above allocation algorithms, the number of allocated subcarriers for each user is assumed already known. In fact, it has to be estimated due to the limit of
available subcarriers. In the following, the two-stage allocation algorithm [32] will be introduced including the estimation of the number of allocated subcarriers for each user and the determination of which subcarriers are given to which user. The two-stage allocation algorithm involves two stages based on the following reasons:
1. The resources for one user, i.e., the number of subcarriers and the transmit power, mainly depend on the mean CNR of its channel.
2. Which subcarrier is assigned to one user depends on the CNR according to Equations (3.14) and (3.16).
In the first stage, the number of allocated subcarriers for each user has to be estimated. It takes into account the users’ mean CNRs, the desired minimum data rate Bmin(u), and the total transmit power Pt. The mean CNR of the user u can be defined as
1 ,
1 Nc
u c v
T = N
∑
= Tu v (3.20)where Tu v, = Hu v, 2/Γu nu v, 2is the CNR value of the user u and subcarrier v. Each user is assigned a number of subcarriers ku such that the desired data rate Bmin(u) can be achieved. The corresponding energy for the user u with the number of allocated subcarriers ku can be defined as
1 min( ) /
( ) (2B u ku 1)
tot u u
E u =k T − − (3.21)
Besides, the sum of total required energy for all users must be smaller than the total transmit power. At the beginning, ku can be calculated as if the maximum number of bits per symbol bmax could be applied to all subcarriers:
min max
[ ( )
u B u ]
k = b (3.22)
Normally, in this step much more subcarriers are assigned than available. Then, a subcarrier will be removed form the user who has to increase the smallest amount of transmit power without this subcarrier. This procedure is repeated until exactly Nc
subcarriers are granted. On the contrary, if there are much less subcarriers assigned than available, new subcarriers will be assigned for each user until the total required
energy does not exceed the total transmit power Pt. This procedure repeats until no subcarriers are left. Fig. 3.9 presents the flow chart of the estimation of the number of allocated subcarriers for each user. It can be stated as follows:
Initialization:
In the second stage, which subcarriers are given to which user has to be determined. The idea for the subcarrier assignment is that the users choose alternatively the subcarrier with the best CNR. Therefore, the order in which the users choose their subcarriers is important. A procedure based on priorities controls the order. The reference priority can be defined as the number of subcarriers of the user u over the total number of subcarriers.
0( ) u
c
p u k
= N (3.23)
After the user u has chosen one subcarrier, ku is subtracted by one. Afterwards, ku
stands for the number of subcarriers that are still to be assigned. Then, the actual priority of the user u can be defined as
1
The user with the most subcarriers begins the subcarrier assignment, then after each step the user with the greatest difference between the reference and actual priority is picked out for the next turn. The subcarrier allocation matrix can be defined as
, with c if the subcarrier v is assigned to the user u, and zero otherwise. Fig. 3.10 presents the flow chart of subcarrier assignment which can be stated as follows:
(cu v,
3.5 Computer Simulations
Computer simulations are conducted to evaluate the performance of above mentioned dynamic subcarrier allocation algorithms employed in multiuser OFDM systems, including the proposed one presented in Section 3.4.3. Two assumptions are made in the following simulations: perfect CSI is available at the transmitter side and the tap gains are constant over an OFDM symbol (quasi-static fading). The standard wireless exponential decay channel model with delay profile illustrated in Fig. 3.11 is employed in the simulations [40]. The corresponding channel impulse response can be expressed as:
where Tsample is the sampling period and τrms is the root mean square delay spread of the channel. The variance σ02 is chosen to normalize the average receive power to one, i.e. . The number of samples taken in the impulse response should ensure sufficient decay of the impulse response tail, such that i
2 1
In the first simulation, the fading effect of a system with the subcarrier number varied is examined. Figs. 3.13-14 show the subcarrier channel gains and corresponding number of bits for two users and thirty users, respectively. Owing to the channel gain variations associated with one specific subcarrier for different users, the subcarrier with poor channel quality for one user may experience good channel qualities for other users.
For instance, the 20th subcarrier has a low channel gain for the 20th user, but it has a high channel gain for the 30th user. It appears that the 30th user is more suitable to use the 20th subcarrier than the 20th user. In fact, it’s quite improbable that a subcarrier is unsuitable to use for all users.
In the second simulation, the data rate is evaluated as a function of input SNR
0
E N . The corresponding results obtained with different numbers of users are shown s
in Fig. 3.15. The data rate increases when more users are simultaneously considered.
This is because the multiuser diversity possesses a great chance for subcarriers to have
good channel qualities when more users are considered.
In the third simulation, the efficacy of three dynamic subcarrier allocation algorithms is investigated as a function of user number. The results shown in Fig. 3.16 indicate that the two-stage subcarrier allocation algorithm outperforms other two subcarrier allocation algorithms. This is because that the two-stage subcarrier allocation algorithm allocates one subcarrier to one user at a time according to the order, while the basic and advanced subcarrier allocation algorithms allocate a group of subcarriers to one user at a time. Therefore, the two-stage subcarrier allocation algorithm will allocate to each user the most appropriate subcarriers and possesses better performance as compared with other methods.
In the final simulation, the computational complexity in terms of execution time is examined as a function of user number. The results shown in Fig. 3.17 obviously indicate that the execution time increases when the user number increases. The basic subcarrier allocation algorithm requires the lowest execution time because it assigns the best ku subcarriers to the current target user in each iteration step without computing coefficients such as wu,v, p0(u), and p(u) used in the advanced and two-stage subcarrier allocation algorithms. Besides, the advanced subcarrier allocation algorithm requires the most execution time because it needs to recompute the weights for all unassigned subcarriers and sort with respect to the next user to be assigned after an assignment of subcarriers to one user. Although, the advanced and two-stage subcarrier allocation algorithms require higher execution time, they are still computationally efficient algorithms.
3.6 Summary
Orthogonal frequency division multiplexing (OFDM) has gained wide acceptance in wireless communications as an appropriate broadband modulation scheme. OFDM systems have desirable immunity to intersymbol interference (ISI) caused by delay spread of wireless channels. Therefore, it is a promising technique for high data rate transmission over frequency-selective fading channels. In Section 3.1, OFDM systems are introduced.
Since multiple access technique plays an important role in multiuser systems, different multiple access schemes for OFDM systems are developed. Time division multiple access (TDMA) and frequency division multiple access (FDMA) assign an independent dimension, e.g. time slot or subchannel, to each user which are introduced in Sections 3.2 and 3.3. However, TDMA and FDMA are not optimal because they are fixed regardless of the current channel quality. Therefore, the two-stage dynamic subcarrier allocation algorithm is proposed in Section 3.4.3 to allocate subcariers adaptively to each user based on users’ channel qualities and quality of service (QoS) requirements. The simulation results show that the two-stage dynamic subcarrier allocation algorithm can indeed enhance the overall data rate of multiuser OFDM systems.
XN-Ncp XN-1 X0 X1 XN-1
Cyclic Prefix Useful Part
Ncp N
Complete OFDM Signal
N+Ncp
XN-Ncp XN-1 X0 X1 XN-1
Cyclic Prefix Useful Part
Ncp N
Complete OFDM Signal
N+Ncp
Figure 3.1: OFDM signal with cyclic prefix extension.
Serial to parallel converter Input data
Symbols
IDFT
2 1
dNc−
2 2
dNc−
Nc2
d−
2 1
d Nc
− +
......
x0
x1
c 1
xN −
Parallel to serial converter
D/A OFDM
signal
...
c cp
N N
x −
.........
Figure 3.2: A digital implementation of appending cyclic prefix into OFDM signal in the transmitter.
Binary Input Timing and Frequency
Synchronization Timing and Frequency
Synchronization
Figure 3.3: Black diagrams of an OFDM transceiver.
(a)
Power
Time
Frequency
FDMA
Power
Time
Frequency
FDMA
(b)
Power
Frequency
Time TDMA
Power
Frequency
Time TDMA
Figure 3.4: Illustration of different multiple access techniques (a) FDMA and
(b) TDMA.
f0
T=1/f0
Time
OFDM Symbol Carrier Data
f0
T=1/f0
Time
OFDM Symbol Carrier Data
Figure 3.5: OFDM time-frequency grid.
User 1 User 2 User 3 User 4 User 5
Time
Frequency
User 1 User 2 User 3 User 4 User 5
Time
Frequency
Figure 3.6: Illustration of block FDMA.
User 1 User 2 User 3 User 4 User 5
Time
Frequency
User 1 User 2 User 3 User 4 User 5
Time
Frequency
Figure 3.7: Illustration of interleaved FDMA.
User 1 User 2 User 3 User 4 User 5
Time
Frequency
User 1 User 2 User 3 User 4 User 5
Time
Frequency
Time
Frequency
Figure 3.8: Illustration of OFDM-TDMA.
Start
Assign each user new subcarriers until the required energy doesn’t exceed the total transmit power
Assigned subcarriers
< Total subcarriers ?
Remove a subcarrier from the user which has to increase its transmit
power by the smallest amount without this subcarrier
Exactly total subcarriers ?
Yes No
Yes
No
Get the number of subcarriers for each user
Start
Assign each user new subcarriers until the required energy doesn’t exceed the total transmit power
Assigned subcarriers
< Total subcarriers ?
Remove a subcarrier from the user which has to increase its transmit
power by the smallest amount without this subcarrier
Exactly total subcarriers ?
Yes No
Yes
No
Get the number of subcarriers for each user
Assign each user new subcarriers until the required energy doesn’t exceed the total transmit power
Assigned subcarriers
< Total subcarriers ?
Remove a subcarrier from the user which has to increase its transmit
power by the smallest amount without this subcarrier
Exactly total subcarriers ?
Yes No
Yes
No
Get the number of subcarriers for each user
Figure 3.9: Flow chart of the estimation of the number of allocated subcarriers for each user.
>>0 ?
uKu
∑
Start
Calculate each user's P0(u)
The user with most subcarriers begins subcarrier assignment
The user with the greatest difference between P0(u) and P(u) is picked out
for subcarrier assignment
Calculate each user's P(u) Get the subcarriers assigned to each user
Yes No
Assigned the subcarrier with the best CNR
Assigned the subcarrier with the best CNR
u 0 ?
uK
∑
Start
Calculate each user's P0(u)
The user with most subcarriers begins subcarrier assignment
The user with the greatest difference between P0(u) and P(u) is picked out
for subcarrier assignment
Calculate each user's P(u) Get the subcarriers assigned to each user
Yes No
Assigned the subcarrier with the best CNR
Assigned the subcarrier with the best CNR
Figure 3.10: Flow chart of the subcarrier assignment.
10Ts 9Ts
8Ts 7Ts 6Ts 5Ts 4Ts 3Ts 2Ts Ts
0 Magnitude
10Ts Time 9Ts
8Ts 7Ts 6Ts 5Ts 4Ts 3Ts 2Ts Ts
0 Magnitude
Time
Figure 3.11: Channel impulse response for IEEE 802.11a.
Fig. 3.12: A typical time-selective and frequency-selective fading channel (assuming an exponential decay channel model with τrms =50 sn and a speed of 60 m/s at 5 GHz).
(a)
0 10 20 30 40 50 60
3 4 5 6 7 8 9
Subcarrier Index
Subcarrier Channel Gain (dB)
User 1 User 2
(b)
10 20 30 40 50 60
1
2 0
0.5 1 1.5 2 2.5 3
Subcarrier Index User Index
Number of Bits
Figure 3.13: Subcarrier channel gains and corresponding number of bits for two uses under the exponential decay Rayleigh fading channel with τrms=50 ns, and fd =0 Hz. Other parameters are listed in Table 3.1.
0
20
40
60
80
0 10
20 300
2 4 6 8
Subcarrier Index User Index
Subcarrier Channel Gain (dB)
Figure 3.14: Subcarrier channel gains for thirty users under the exponential decay Rayleigh fading channel with τrms=50 ns, and fd =0 Hz. Other parameters are listed in Table 3.1.
-5 0 5 10 15 20 25 30 35 0
10 20 30 40 50 60 70 80 90 100
Es/No (dB)
Data Rate (Mbps)
40 Users 20 Users 10 Users
Figure 3.15: Data rate versus E Ns 0
rms
for the OFDM system with the two-stage subcarrier allocation algorithm under the exponential decay Rayleigh fading channel with τ =50 ns, and fd =0 Hz. The number of users is 10, 20, and 40. Other parameters are listed in Table 3.1.
5 10 15 20 25 30 35 40 45 50 28
30 32 34 36 38 40 42 44
Uesr Number
Data Rate (Mbps)
Two-Stage Advanced Basic Static
Figure 3.16: Data rate versus number of users for the OFDM system with different subcarrier allocation algorithms under the exponential decay Rayleigh fading channel with τrms=50 ns, and fd =0 Hz. Other parameters are listed in Table 3.1.
5 10 15 20 25 30 35 40 45 50 0
0.5 1 1.5 2 2.5 3
User Number
Execution Time (sec)
Advanced Two-Stage Basic
Figure 3.17: Execution time versus number of users for the OFDM system with different subcarrier allocation algorithms under the exponential decay Rayleigh fading channel with τrms=50 ns, and fd =0 Hz. Other parameters are listed in Table 3.1.
Table 3.1: Simulation parameters for the OFDM system.
Number of transmit/receive antennas 1/1
Carrier frequency 5 GHz
Channel bandwidth 20 MHz
Number of carriers 64
OFDM symbol duration 3.2µs
Guard interval 0.8µs
M-QAM available 0, 1, 2, 3, 4, 5, 6 Number of OFDM symbols in a packet 100
Number of users 10, 20, 40
Doppler spread 0 Hz
Channel model Exponential delay profile, τrms= 50 ns
Chapter 4
Multiuser Adaptive MIMO-OFDM Systems
In Chapter 3, different subcarrier allocation schemes are presented to make users choose the most appropriate subcarriers for them according to their QoS requirements and the channel condition. Besides choosing the subcarriers with large channel gains, adaptive modulation is also an important technique to increase data rates. Assuming the transmitter knows the instantaneous channel transfer functions of all users, significant performance improvement can be achieved if adaptive modulation is used in multiuser MIMO-OFDM systems.
In this chapter, a practical adaptive loading algorithm will be introduced in multiuser MIMO-OFDM systems. It uses the V-BLAST as both its channel quality indicator and detection algorithm. Under the total transmit power constraint, this algorithm aims to maximize the data rates and still maintain a target system
erformance.
p
4.1 V-BLAST Based OFDM Systems
The OFDM systems combined with the V-BLAST algorithm can dramatically increase the capacity of wireless radio links with no additional power and bandwidth consumption. It can achieve high spectral efficiency to ease the scarcity of radio spectrum. The core idea in such scheme is that with the aid of OFDM, the whole detection problem in MIMO-OFDM systems would be translated into Nc parallel
sub-problems. In addition, the V-BLAST algorithm implements a non-linear detection technique, which is somewhat analogous to the decision feedback equalization to decouple co-channel interference and makes the spatial multiplexing possible. In this scheme, flat fading in the channel bandwidth is required.
Fig. 4.1 illustrates the V-BLAST based MIMO-OFDM transmitter architecture. A traditional 1-D channel encoder is used to encode the information bits. Then these coded bits are mapped on the symbols of constellation adopted for each subcarrier.
bit streams{
Nc×Nt c n k ki[ , ]: =0,1,…Nc} for i 1, 2 ,= … Nt are fed to the IFFT at the ith transmit antenna on the kth subcarrier to generate the nth transmitted OFDM symbols from the ith transmit antenna at a given time slot n.
Fig. 4.2 illustrates the V-BLAST based MIMO-OFDM receiver architecture.
Receive antennas 1~Nr will receive the radiate signal from transmit antennas 1~Nt, where the V-BLAST requires Nr≥ Nt to ensure its proper working. The received data at each receive antenna will then pass through a FFT with the removal of the CP. The FFT output at the receive antenna j is a set of Nc signals. The output for each frequency subcarrier can be expressed as
, 1
[ , ] t [ , ] [ , ] [ , ] 1, 2,...,
N
j j i i j
i
r n k H n k c n k η n k k N
=
=
∑
+ ∀ = c (4.1)where is the flat fading coefficient representing the channel gain form the transmit antenna i to the receive antenna j at frequency k, and
, [ , ] Hi j n k
[ , ]
j n k
η denotes the additive complex Gaussian noise at the receiver antenna j and frequency k with two-sided power spectral density per dimension and uncorrelated for different n’s, k’s, and j’s.
0/ 2 N
The use of OFDM allows considering flat fading in the channel bandwidth which is true in each sub-band. Hence at time n, the Nr outputs for the frequency k,
{
r n kj[ , ]: j=1, 2,...,Nr}
, are fed to a V-BLAST component to detect the Nt transmitted signals at the kth subcarrier. This detecting process is repeated for subcarriers 1~Nc, and produces NtNc estimated symbols,{
c n k iˆ [ , ]:i =1, 2,...,N kt; =1, 2,...,Nc}
in the end.These symbols are then multiplexed to the demodulator to complete the traditional 1-D channel decoding.
4.2 Adaptive Modulation for OFDM Systems
Adaptive modulation is a promising technique to increase data rate that can be reliably transmitted over fading channels. The basic idea behind adaptive modulation technique is to adapt the transmission parameters to take advantage of prevailing channel conditions. It aims to exploit the variations of the wireless channel (over time, frequency, and space) by dynamically adjusting certain transmission parameters to the changing environmental and interference conditions observed between the base station and the subscriber. Many parameters are provided that can be adjusted relative to the channel fading, including data rate, transmit power, instantaneous BER, symbol rate, and channel code rate. In practical implementations, the values for the transmission parameters are quantized and grouped together in what referred to as a set of modes.
The goal of an adaptive modulation algorithm is to ensure that the most efficient mode is always used, over varying channel conditions, based on a mode selection criterion (minimum transmit power, maximum data rate, etc). Making modes available that enable communication even in poor channel conditions renders the system robust.
Under good channel conditions, spectrally efficient modes are alternatively used to increase throughput. In contrast, systems with no adaptive modulation are constrained to use a single mode that is often designed to maintain acceptable performance when the channel quality is poor to get maximum coverage. In other words, these systems are effectively designed for the worst case channel conditions, resulting in insufficient utilization of the full channel capacity. In the following, the general steps of an adaptive modulation system can be presented to react to the change of channel conditions.
1. Channel quality estimation: If the channel is reciprocal and the communication between two stations is bi-directional, then the two stations can estimate the channel quality on the basis of received symbols, and adapt the transmission parameters of the local transmitter to this estimation in an open-loop manner. On the other hand, if the channel is not reciprocal, the receiver has to estimate the channel quality and signal explicitly this perceived channel quality to the transmitter via the uplink in a close-loop manner.
2. Choosing the appropriate transmission parameters for the next transmission:
According to the prediction of the channel quality for the next time slot, the transmitter has to choose the most appropriate modulation mode for each subchannel.
3. Signaling of the used parameters: The information that demodulator parameters to employ for the received packet can be either estimated by a blind detection mechanism at the receiver or conveyed by the transmitted signal itself.
The practical challenges of adaptive modulation technique can be described as follows:
1. Adaptation rate: In the slow varying channels, a low adaptation rate adaptive modulation algorithm is required to track the large variations influenced by user location within the cell, seasons, road traffic, and cell deployment. On the other hand, a high adaptation rate adaptive modulation algorithm applied in the fast varying channels is required to track the small variations influenced by the time-frequency selective fading channels. It is easily understand that faster adaptation leads to larger capacity gain, since the channel variations are exploited in a more accurate manner. However, fast adaptation has practical limitations, in both time and frequency. Fast adaptation increases the number of mode change messages that must be sent over the air, consuming bandwidth and time resources.
1. Adaptation rate: In the slow varying channels, a low adaptation rate adaptive modulation algorithm is required to track the large variations influenced by user location within the cell, seasons, road traffic, and cell deployment. On the other hand, a high adaptation rate adaptive modulation algorithm applied in the fast varying channels is required to track the small variations influenced by the time-frequency selective fading channels. It is easily understand that faster adaptation leads to larger capacity gain, since the channel variations are exploited in a more accurate manner. However, fast adaptation has practical limitations, in both time and frequency. Fast adaptation increases the number of mode change messages that must be sent over the air, consuming bandwidth and time resources.