Chapter 3 Joint Beamforming and Subcarrier Allocation for
4.3 Complexity Analysis
In this section, we analyze the complexity of the proposed bit and power loading algorithm. This results are compared with the bit-filling and bit-removal algorithm adopted in [50], [53], and [54]. For these two methods, they require one logarithmic operation and three multiplications for initialization and one exponential operation and two multiplications for each iteration. The proposed algorithm requires one logarithmic operation, one exponential operation and two multiplications for initialization of each subcarrier; subsequently it no longer requires any complex operations in each iteration.
The detail description is shown in Table 4.1.
An example is given to make the complexity easy to compare. Consider that the rate requirement is 512 bits per OFDM symbol and the total number of subcarriers is 128; maximal number of bits can be assigned is 6. The results are shown in Table 4.2 where we observe the total number of logarithmic and exponential operations of the proposed algorithm is fewer than that of other algorithms. Besides, the proposed algorithm requires considerably fewer number of multiplications.
Table 4.1: Complexity of proposed bit and power loading algorithm compared with other conventional algorithms
Logarithm Exponent Multiplier
Bit-filling 1 B req 2Breq+ 3
Bit-removal 1 Nb−Breq 2(Nb−Breq) 3+
Proposed N N 2N+3
Table 4.2: Example of complexity analysis logarithm exponent multiplier
Bit filling 1 512 1027
Bit removal 1 256 515
Proposed 128 128 259
4.4 Computer Simulations
The simulation results are shown in the following figures. Figure 4.8 compares the BER performance of adaptive modulation with fixed modulation where the bits requirement per OFDM symbol is 128 bits and the number of subcarriers is 32. Hence the fixed modulation order is 4 in order to compare on a fair basis. It is observed that the performance of adaptive modulation has enormous improvement compared with that of nonadaptive modulation.
Figure 4.9 shows the BER curve with different bit requirements. Because the gap approximation is tighter while for BER≤10−2, we only show the performance in this range. From the figure, we find that the effect of different bit requirement on BER
curve is just a horizontal shift. The gap between two adjacent curves is about 2 dB.
Figure 4.10 gives the BER curves with different BER constraints with the understanding that gap approximation is an approximated equation describing the relation between BER and power. The results show that the average BER is always lower than the original BER constraint.
7 8 9 10 11 12 13
10-5 10-4 10-3 10-2 10-1
Eb/No
BER
64 subcarriers
fix modulation with 4 QAM
adaptive modulation with bit requiremenet = 128
Figure 4.8: BER performance of adaptive bit and power allocation compared with fixed modulation
4 6 8 10 12 14 16 18 20 10-5
10-4 10-3 10-2 10-1
Eb/No
BER
bit requirement = 64 bit requirement = 128 bit requirement = 192 bit requirement = 256 bit requirement = 320
Figure 4.9: BER performances of proposed bit loading algorithm with different bits requirements
0 1 2 3 4 5 6 7 8 9 10
10-6 10-5 10-4 10-3 10-2 10-1 100
CNR(dB)
BER
number of subcarrier =32, rate requirement = 128
BER constraint = 10 -3 BER constraint = 10 -4 BER constraint = 10 -5
Figure 4.10: BER performances of proposed bit loading algorithm with different BER constraints
4.5 Summary
The new bit-loading algorithm proposed in this chapter provides the optimal discrete solution to the power minimization problem under QoS constraints including BER and rate requirements. It also takes into account that bupper bounds the system.
In addition, it requires less computational complexity compared to the optimal bit-filling and bit-removal algorithms. The proposed algorithm exploits the subchannel gain-to-noise ratio levels in order to calculate a loop representative bit-allocation profile and then uses a multiple-bits insertion that results in faster convergence to the target rate. Finally, simulation results confirm the efficiency of the proposed algorithm.
Chapter 5
Beamforming Aided Multiuser Adaptive Radio Resource
Management
In Chapter 5, an adaptive radio resource-management algorithm for multiuser transmission in MIMO-OFDM systems is proposed. The objective of this algorithm is to: 1) exploit the inherent system diversities including time, frequency, space, and multiuser diversities; 2) minimize the overall transmit power; 3) instantaneously guarantee the fulfillment of each user’s QoS requirements including BER and rate requirements. To be more specific, the proposed algorithm optimizes transmit and receive beamforming, subcarrier allocation, power and bit distribution for all users jointly according to the instantaneous CSI and QoS requirements.
This chapter is organized as follows. Section 5.1 formulates the problem of beamforming aid multiuser adaptive radio resource management and proposes an algorithm to solve it, subsequently signaling model in practical wireless communication system is described in Section 5.2. Finally simulation results of the proposed algorithm are shown in Section 5.3.
5.1 Proposed Beamforming Aided Multiuser Radio Resource Management Algorithm
The problem we consider about in multiuser MIMO-OFDM systems where each user and base station are equipped with the same number of antennas; it try to decide how many users can occupy the same subcarrier at the same time. Our objective is to minimize the total transmit power while satisfying each user’s QoS constraints including rate and BER requirements. This problem can be formulated as follows:
, , the subcarrier indicator whose value is defined as
,
In order to achieve our objective, the proposed algorithm optimizes transmit and receive beamforming, subcarrier allocation, power distribution, and bit distribution for all users jointly according to the instantaneous CSI and QoS requirements.
Based on the beamforming aided subcarrier allocation algorithm proposed in Chapter 3, we assign each user subcarriers to transmit data and decide the transmit and receive beamformers on each subcarrier in order to null the interference between users.
After the procedure of beamforming and subcarrier assignment, the bit and power
each user in order to minimize the total transmit power with each user’s QoS constraints met. The detail procedure of the algorithm is described in the following steps:
Beamforming Aided Multiuser Adaptive Radio Resource Management Algorithm Step 1) Choose any N users from K total users. For each selection,
1 N
H k k k k
α
=
=
∑
H u v is
the channel matrix composed of allowed users’ channel matrices, transmit weight vector is calculated by
Tk = k
w v and receive weight vector is
calculated by 1
k
T H
R k k
⎡ − ⎤
=⎣ ⋅ ⎦
w e u ; then calculate 2 2
1( / )
k
N
k T
k= α
∏
w as themetric for choosing which users could occupy this subcarrier.
Step 2) Choose the maximal one and let selected users transmit data on this subcarrier.
Step 3) Do the above two steps for each subcarrier. Finally, the result of subcarrier allocation indicates which users can occupy each subcarrier. On the other hand, it also shows which subcarriers can be used by one user.
Step 4) For each user, implement the bit and power loading algorithm proposed in Chapter 4 with the assigned subcarriers and QoS.
The transceiver block diagram of beamforming aided multiuser radio resource management algorithm is shown in Figure 5.1; the detail description of the transmitter architecture is illustrated in Figure 5.2.
Channel
Adaptive Modulator Nc
IFFT and
Adaptive Demodulator Nc
Beamforming, Bit and Subcarrier Allocation Information
Adaptive Modulator Nc
IFFT and
Adaptive Demodulator Nc
Beamforming, Bit and Subcarrier Allocation Information
Figure 5.1: Block diagram of downlink multiuser adaptive MIMO-OFDM systems
Subcarrier allocaiton
BPSKQPSK8QAM16QAM 32QAM 64QAM Power S/P
BPSKQPSK8QAM16QAM 32QAM 64QAM Power S/P
BPSKQPSK8QAM16QAM 32QAM 64QAM Power S/P
b1[n,k] Allocate subcarriers to
each user according to the channel state information
Assign different modulation orders to each subcarrier for each user
Assign different power to each subcarrier for each user
BPSKQPSK8QAM16QAM 32QAM 64QAM Power S/P
BPSKQPSK8QAM16QAM 32QAM 64QAM Power S/P
BPSKQPSK8QAM16QAM 32QAM 64QAM Power S/P
b1[n,k] Allocate subcarriers to
each user according to the channel state information
Assign different modulation orders to each subcarrier for each user
Assign different power to each subcarrier for each user
Figure 5.2: Transmitter architecture of beamforming aided radio resource management algorithm
5.2 Signaling Model in Adaptive Scenario
Because the parameters of the proposed algorithm are based on the instantaneous channel state information of all users, obtaining the instantaneous channel state information becomes the most important issue. In this section, we discuss the signaling model in the adaptive scenario. Figure 5.3 illustrates the signaling model for which the system is based upon a time-division duplex (TDD) operation, assuming that the durations of the uplink and downlink timeslots are the same, and are denoted by to. Consider the downlink transmission at time t, for example. Assuming that the channel is reciprocal, the BS first predicts the downlink channel of time t based on the uplink frame received at time t-t0 and then the BS adapts the bit and power allocation accordingly; subsequently the resultant parameters are sent to the mobiles via the control channels. Likewise, the mobile predicts the downlink channel of time t based on the downlink frame received at time t-2t0 and then the mobile adapts the receive beamforming vector. The quality of channel prediction suffers from the changes of the CSI between successive timeslots due to the presence of Doppler spread. Fortunately, in most cases, the channel varies relatively slowly compared with the frame rate.
Therefore, the channel can be considered as a quasi-static one, and the channel variation within successive timeslots can be neglected [46].
Base Station Channel Mobile Station
Estimate receive vector for the next downlink frame
Base Station Channel Mobile Station
Estimate receive vector for the next downlink frame
Base Station Channel Mobile Station
Estimate receive vector for the next downlink frame
Figure 5.3: Signaling model in adaptive scenario
5.3 Computer Simulations
In this section, computer simulation results are conducted to evaluate the performance of the beamforming aided radio resource management algorithm.
Throughout the simulation, we only deal with discrete time signal processing in the baseband; hence pulse-shaping and matched-filtering are not considered for the sake of simulation simplicity. Also, channel estimation and timing synchronization are assumed to be perfect. Table 5.1 lists all parameters used in our simulation. There are 64 subcarriers in the OFDM system and each link in MIMO is modeled as an i.i.d Rayleigh fading channel. The set of QAM constellation used in the simulation is {0, 2, 4, 8, 16, 32, and 64}. There are four users in one cell, and each user and base station are equipped with two antennas.
The BER performances of the beamforming aided multiuser adaptive radio resource management with different rate requirements are shown in Figure 5.4. We
algorithm in this chapter are almost the same, equal to about 1.2 dB, whereas the gaps between the different rate requirements in the single user case is about 1.7 dB.
Moreover, as the rate requirement increases, the gap between the four user case and single user case becomes larger.
Now, we consider the operations under the situation that only partial CSI is available at the transmitter, but full CSI is available at the receiver. The transmitter acquires channel knowledge either via a feedback channel, or, by channel estimation in a time division duplex (TDD) operation. The partial CSI includes the perfect CSI H plus a perturbation term ∆H with known probability density function (pdf). Figure 5.5 shows BER performances with channel estimation error, where H H ∆H = + represents the estimated channel at the transmitter. It is assumed that each element in
∆H is an i.i.d Gaussian distribution with zero mean and variance σe2 [52]. As seen in the figure, we observe that the performance degradation is acceptable when the variance of channel estimation error is less than 0.01.
Table 5.1: Simulation parameters of beamforming aided multiuser adaptive radio resource management algorithm
Number of subcarriers 64 Maximum number of bits
can be assigned 6
Channel model Rayleigh fading
Number of users 4
Number of transmit
antennas 2
Number of receive antennas 2
4 6 8 10 12 14 16 18 10-7
10-6 10-5 10-4 10-3 10-2 10-1
Eb/No
BER
4 users bit requirement = 32
4 users, bit req = 32 4 users, bit req = 48 4 users, bit req = 64 signal user, bit req = 128 signal user, bit req = 192 signal user, bit req = 256
Figure 5.4: BER performances of beamforming aided multiuser resource allocation compared to single user case
4 5 6 7 8 9 10 11 12
10-6 10-5 10-4 10-3 10-2 10-1
Eb/No
BER
4 user, bit requirement per user = 32
variance of error = 0.1 variance of error = 0.05 variance of error = 0.01 without estimation error
Figure 5.5: BER performances of beamforming aided multiuser resource allocation with channel estimation error
5.4 Summary
In this chapter we combine the two algorithms introduced in Chapter 3 and Chapter 4 in order to adaptively adjust our physical layer parameters including transmit and receive beamforming vectors, subcarriers, modulation orders and power. The algorithm is called beamforming aided multiuser adaptive radio resource management while frequency, time, space and multiuser diversities are used to enhance the overall system performance. The objective of the algorithm is to minimize the total transmit power while satisfying each users’ QoS constraints. In multiuser adaptive MIMO-OFDM system, perfect CSI is essentially known in the transmitter. Therefore we introduce a signaling model for TDD based system in Section 5.2 and then BER performances with or without channel estimation error are shown in Section 5.3. It can be demonstrated that the results of beamforming aided multiuser radio resource management perform well in power efficiency.
Chapter 6 Conclusion
In this thesis, the multiuser adaptive MIMO-OFDM system incorporating beamforming aided multiuser adaptive radio resource management algorithm is proposed. This algorithm can be divided into two parts. The first part is the beamforming aided subcarrier allocation algorithm which designs transmit and receive beamforming to let each subcarrier be occupied by more than one user without interference and solves the subcarrier assignment problem which chooses the users with better channel gain to transmit signal. The second part is a new bit and power allocation algorithm which obtains the optimum bit distribution with less computational complexity.
In Chapter 3, the ZF beamforming design algorithm is presented first. This algorithm uses the channel state information and SVD to jointly design transmit and receive beamformers. The transmit beamforming vector tries to match independent subchannels that are produced from the channel composed of allowed users’ channel matrices. The function of the receive beamforming vector is to null interference from other users. Based on the beamforming design, we can calculate the output SNR of for each user. In order to maximize the total system performance, a beamforming aided subcarrier allocation algorithm is proposed. By some derivations, we find that the
throughput of the single carrier system is proportional to the product of the SNRs of all allowed users if each user’s BER constraint is the same. Consequently, we choose the product of SNRs as the metric while selecting users to transmit data in one subcarrier.
The group of users can utilize this subcarrier only if the product of SNRs for these users is the largest. As soon as which users can occupy each subcarrier is decided, which subcarriers can be used by one user also can be decided. Through judiciously assigning subcarriers to users, the overall transmission rate of the multiuser MIMO-OFDM system can be increased.
After the beamforming aided subcarrier allocation algorithm is introduced, the two-stage optimal bit and power loading algorithm is presented in Chapter 4. Under the QoS constraints including rate and BER requirements, this algorithm aims to minimize the total transmit power. For instance, the subcarriers with good channel qualities are more likely to employ a higher modulation order to reduce the overall transmit power of the system, while the subcarriers with poor channel qualities are more likely to employ a lower modulation order to maintain the target BER. The algorithm can find the optimal bit distribution with lower computational power compared with other algorithms. This algorithm is divided into two stages. The core idea of the first stage is to utilize the difference of CNRs between subcarriers to calculate an initial bit allocation. The result shows it has no more than a single bit difference per subcarrier compared with the optimal distribution. In the second stage, a bit-removal algorithm with fewer candidates is used to achieve the target rate bit distribution. It can be demonstrated that this algorithm works well in saving total transmit power with users’
rate constraints satisfied. Finally, the complexity analysis shows that the proposed algorithm needs less computational operations compared with other conventional algorithms.
In Chapter 5, we combine the two algorithms introduced in Chapter 3 and Chapter
4 to adaptively adjust physical layer parameters including transmit and receive beamforming vectors, subcarriers, modulation orders and transmit power. The ultimate goal is to minimize the total transmit power in the system while satisfying each user’s QoS. The algorithm is called beamforming aided multiuser adaptive radio resource management; it can fully use frequency, time, space and multiuser diversity to enhance the overall system performance. In multiuser adaptive MIMO-OFDM systems, perfect channel state information is essentially known in the transmitter. Therefore a signaling model for TDD based system is given. However, in practice it is impossible to obtain perfect CSI due to noisy channel estimation and unavoidable delay between performing channel estimation and using estimation result for actual transmission.
Hence we show BER performances with channel estimation error and observe that the performance degradation is acceptable when the error variance is less than 0.01.
Furthermore, if we design the problem without perfect CSI but with partial state information, the results may be more suited for practical systems. In recent research, partial CSI issue has been considered important. Based on the partial CSI, the future work can be directed toward the re-design of beamforming aided subcarrier allocation and adaptive bit and power loading algorithms suited to multiuser MIMO-OFDM systems.
Bibliography
[1] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-time codes for high data rate wireless communication: performance criterion and code construction,” IEEE Trans. Inf. Theory, vol. 44, no. 2, pp. 744–765, Mar.
1998.
[2] “Space-time block codes from orthogonal designs,” IEEE Trans. Inf. Theory, vol. 45, no. 5, pp. 1456–1467, Jul. 1999.
[3] S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Sel. Areas Comm., vol. 16, no. 10, pp. 1451–1458, Oct. 1998.
[4] D.P. Palomar, J. M. cioffi and M. A. Lagunas, ‘Joint Tx-Rx beamforming design for multicarrier MIMO channels: a unified framework for convex optimization,” IEEE Trans. Signal Processing., vol. 51, pp. 2381-2401, no 9, Sept. 2003
[5] D.P. Palomar and M. A. Lagunas, “Joint transmit-receive space-time equalization in spatially correlated MIMO channels: a beamforming approach,” IEEE J. Sel. Areas., vol 21, pp 730-743, no 5, June 2003
[6] P. A. Dighe, R. K. Mallik, and S. S. Jamuar, “Analysis of transmit-receive diversity in Rayleigh fading,” IEEE Trans. Comm., vol. 51, no. 4, pp.
694–703, Apr. 2003.
[7] S. Thoen, L. V. der Perre, B. Gyselinckx, and M. Engels, “Performance analysis of combined transmit-SC/receive-MRC,” IEEE Trans. Comm., vol.
49, no. 1, pp. 5–8, Jan. 2001.
[8] C.-H. Tse, K.-W. Yip, and T.-S. Ng, “Performance tradeoffs between maximum ratio transmission and switched-transmit diversity,” in Proc. IEEE PIMRC, vol. 2, Sept. 2000, pp. 1485–1489.
[9] R. W. Heath Jr. and A. Paulraj, “A simple scheme for transmit diversity using partial channel feedback,” in Proc. IEEE Asilomar Conf. Signals, Syst., Comput., vol. 2, Nov. 1998, pp. 1073–1078.
[10] M. Kang and M. S. Alouini, “Largest eigenvalue of complex wishart matrices and performance analysis of MIMO MRC systems,” IEEE J Sel. Areas Comm., vol. 21, no. 4, pp. 418–426, Apr. 2003.
[11] H. Shi, M. Katayama, T. Yamazato, H. Okada, and A. Ogawa, “An adaptive antenna selection scheme for transmit diversity in OFDM systems,” in Proc.
IEEE Veh. Technol. Conf. Fall, vol. 4, Oct. 2001, pp. 2168–2172.
[12] Xing Zhang; Wenbo Wang; Yuanan Liu; “Multiuser OFDM with adaptive frequency-time two-dimensional wireless resource allocation” IEEE J Sel.
Areas Comm., vol 2, Aug.-1 Sept. 2004 pp.824 - 828
[13] Zukang Shen; Andrews, J.G.; Evans, B.L., ”Adaptive resource allocation in multiuser OFDM systems with proportional rate constraints”, IEEE Trans.
Wireless Comm., vol. 4, issue 6, Nov. 2005 pp. 2726 – 2737
[14] Ying Jun Zhang; Letaief, K.B.;, “Multiuser adaptive subcarrier-and-bit allocation with adaptive cell selection for OFDM systems” IEEE Trans.
Wireless Comm,. vol. 3, Issue 5, Sept. 2004 pp.1566 - 1575
[15] S. Catreux, D. Gesbert, V. Ercge and R. W. Heath JR, “Adaptive modulation and MIMO coding for broadband wireless data networks,” IEEE Comm.
Mag.., Jun. 2002.
[16] G. G. Raleigh and J. M. Cioffi, “Spatio-temporal coding for wireless communication,” IEEE Trans. Comm., vol. 46, pp. 357-366, Mar. 1998.
[16] G. G. Raleigh and J. M. Cioffi, “Spatio-temporal coding for wireless communication,” IEEE Trans. Comm., vol. 46, pp. 357-366, Mar. 1998.