In this section, we simulate the V-BLAST performance both for the ideal and realistic case. We define the relation between SNR and E N at each receive b 0 antenna as follows:
( )
0 0
0
signal power
SNR noise power 1
s b t
s s b
t
s
E E N M
T T E
N B N N N M
T
⋅ ⋅
= = = = ⋅ ⋅ (2.46)
where E is the symbol energy, s T is the symbol duration, B is the system bandwidth s and M is the modulation order. Throughout the following simulations, the system transmit power is normalized to 1, and hence the noise power corresponding to a specific E N is generated by b 0
noise power 0
b t
N E N M
= ⋅ ⋅ (2.47)
Figure 2.10 shows the BER performance of the (Nt, Nr) = (4, 4) ZF V-BLAST system with ideal detection and cancellation. It is obvious that in the ideal case, the diversity gain increases as the number of effective transmit antennas decreases.
However, as shown in Figure 2.11, the realistic V-BLAST system suffers from error propagation and hence the diversity gain degrades. In Figure 2.12, we compare two equal rate V-BLAST systems. It is interesting to see that the system with fewer transmit antennas will outperform the one with more transmit antennas in the BER performance.
This phenomenon hints that given a MIMO channel and some transmit power budget, we can improve the MIMO system performance by simply adjusting transmission parameters at no cost of transmission rate. So, it strongly motivates us involve the concept of adaptive modulation in MIMO, which will be described in Chapter 3.
Figure 2.1: Diagram of a MIMO wireless transmission system.
Figure 2.2: An illustration of a spatial multiplexing system.
Transmitter Receiver
"
Figure 2.4: Diagonal and Vertical Layered Space-Time encoding with Nt = . 3
Figure 2.5: Diagonal Layered Space-Time decoding with Nt = . 3
Figure 2.6: Vertical Layered Space-Time decoding with Nt = . 3
Figure 2.7: V-BLAST based MIMO-OFDM transmitter architecture.
Suppressed
Encoder Bit Æ M-QAM DEMUX 1ÆNt
Encoder Bit Æ M-QAM DEMUX 1ÆNt
Figure 2.8: V-BLAST based MIMO-OFDM receiver architecture.
RX Antenna 1 Remove
CP FFT
RX Antenna 1 Remove
CP FFT
-5 0 5 10 15 10-6
10-5 10-4 10-3 10-2 10-1 100
Eb/No (dB)
BER
1st detected layer 2nd detected layer 3th detected layer 4th detected layer
Figure 2.10: ZF V-BLAST performance with ideal detection and cancellation. QPSK modulation is used. (Nt, Nr) = (4, 4).
-5 0 5 10 15 20 10-4
10-3 10-2 10-1 100
Eb/No (dB)
BER
1st detected layer 2nd detected layer 3th detected layer 4th detected layer
Figure 2.11: ZF V-BLAST performance with error propagation. (Nt, Nr ) = (4, 4). QPSK modulation is used.
-5 0 5 10 15 20 25 10-5
10-4 10-3 10-2 10-1 100
(4Tx, 4Rx) QPSK (2Tx, 4Rx) 16-QAM
Eb/No (dB) BER
Figure 2.12: Comparison of ZF V-BLAST (Nt, Nr) = (4, 4) with QPSK modulation and (Nt, Nr) = (2, 4) with 16-QAM modulation.
Chapter 3
Adaptive Modulation Assisted MIMO-OFDM Systems
The combined application of MIMO and OFDM (MIMO-OFDM) yields a noticeable physical layer capable of meeting the requirements for 4G broadband wireless systems [17]. Thanks to OFDM, which is characterized by possessing multi-channels over frequencies, the signal processing techniques involved in MIMO-OFDM could be borrowed from the sophisticated space-time ones by admitting the virtual equivalence between time and frequency in some particular scenarios.
From the analysis of MIMO channel capacity, we figure out that the waterfilling distribution of power over channels with different SNR values achieves the optimal transmission scheme [34]. However, while the waterfilling distribution will indeed yield the optimal solution, it is difficult to compute, and also assumes infinite granularity in the constellation size, which is not practically realizable.
In this chapter, we introduce a practical adaptive loading procedure for MIMO-OFDM that uses the V-BLAST as both its channel quality indicator and detection algorithm. Bit and power are allocated in a manner to fix the total transmission power while maximizing the data rate and yet still maintaining a target system performance.
3.1 Adaptive Modulation
Wireless communication channels typically exhibit time-variant quality fluctuations and hence conventional fixed-mode modems usually suffer from bursts of error (see Figure 3.4 to get the idea). This defect could be somewhat mitigated if the system was designed to provide a high link margin, that is, determine transmission parameters based on the worst-case channel conditions to render the immunity against channel impairments. However, it results in insufficient utilization of the full channel capacity. An efficient approach of avoiding these detrimental effects is to dynamically adjust transmission parameters based on the near instantaneous channel quality information. In general, the following steps have to be taken to react to the change in channel condition for an adaptive wireless transceiver.
1. Channel quality estimation: If the communication between the two stations is bi-directional and the channel can be considered reciprocal, then each station can estimate the channel quality on the basis of received symbols, and adapt the parameters of the local transmitter to this estimation in an open-loop manner.
2. Choice of the appropriate parameters for the next transmission: The transmitter has to select the appropriate modulation mode for each sub-channel based on the prediction of the channel quality for the next timeslot.
3. Signaling of the employed parameters: The receiver has to be informed, as to which demodulator parameters to employ for the received packet. This information can be either conveyed by the transmitted signal itself, at the cost of a loss of effective data throughput, or estimated by a blind detection mechanism at the receiver.
3.2 SNR Based Switching Levels
In [7], several metrics that may be used as CSI were surveyed. Among those, SNR-based and Error-based CSI are the most commonly used ones. Typically, SNR or SINR could be available from the physical layer by exploiting power measurement in slots without intended transmit data. Approximate BERs are sometimes available via packet error rates (PERs), which are normally extracted from the cyclic redundancy check (CRC) at the link layer. These two types of CSI come with their pros and cons.
SNR-based CSI offers the flexibility to adapt the modes on a very fast basis; however, it relies on the computation of switching thresholds that may be inaccurate. The accuracy of the threshold mechanism increases by taking into account higher order statistics of the SNR than just the mean. Error based CSI captures accurate performance of the modes; however, this accuracy is reached only after a substantial amount of traffic is observed. An important topic of current research is to combine all types of CSI together to yield accuracy and robustness over a wide range of channels, adaptation rates, and traffic conditions [7].
The first attempt to finding optimum switching levels that are capable of satisfying various transmission integrity requirements was mad by Webb and Steele [10]. They used the BER curves of each constituent modulation mode, obtained from simulations over an AWGN channel, to find the SNR value, where each modulation mode satisfies the target BER requirement. This intuitive concept of determining the switching levels has been widely used since then. By using this regime, the instantaneous BER always remains below a certain threshold BERεerror. In order to satisfy this constraint, the first modulation mode should be “no transmission”. In this case, the set of switching levels T (in dB) is given by
T
={
t0 = −∞, |tk εm ( )tk =εerror, ∀ ≥k 1}
(3.1)where ε γmk( ) is the BER of the mk-ary constituent modulation mode over the AWGN channel when the instantaneous SNR, used as the channel quality measure, is γ . We use 7-mode AQAM, i.e. No TX, BPSK, QPSK, 8-QAM, 16-QAM, 32-QAM, and 64-QAM as constituent modulation modes. Their signal constellation diagrams and BER curves are depicted in Figure 3.5 and Figure 3.6. Throughout the following discussions, we will follow this method and concentrate on the case of εerror =0.0001, which is commonly required for low-BER data transmission systems. A set of switching thresholds according to Figure 3.6 is given in Table 3.2, which is independent of the underlying fading and the average SNR.
3.3 Adaptive MIMO-OFDM Systems
In a system with multiple antennas at the transmitter and/or receiver, the SNR not only varies over time and frequency but also depends on a number of parameters including the way the transmitting signals are mapped and weighted onto the transmit antennas, the processing techniques used at the receiver, and some propagation related parameters such as the pairwise antenna correlation. In this section, we consider a space-time-frequency scheme, that is V-BLAST based MIMO-OFDM as describe before, and develop a practical LA procedure that integrate temporal, spatial, and spectral components together.
Our problem is to assign bits and power to each sub-channel to maximize data rate for some given power budget and a target BER. The main feature of our approach is to separate the joint space-frequency problem into two separated ones by treating each OFDM tone as a narrow band MIMO. We demonstrate by computer simulations that the V-BLAST based MIMO-OFDM system works well to satisfy the system target BER even in the low SNR scenarios at the cost of degrading transmission rate.
Seeing that a discrete rate set should be used in a practical communication system, a loading criterion for discrete rate is required instead of using the water-filling solution derived by maximizing Shannon capacity. However, a close form solution for optimal discrete rate and power control could not be found and an exhaustive search over the set of rates and powers is too complicated to be conducted in a real time. Hence, some bit loading algorithms were proposed to obtain an optimal (or near optimal) solution [25]-[27]. On account of simplicity and capability, when applying bit loading in the MIMO-OFDM system, we promote that Campllo’s loading criteria [27] could be somewhat modified and extended to the V-BLAST based adaptive MIMO-OFDM system with reasonable computation complexity.
The joint space-frequency bit loading problem should be taken apart into two separated sub-problems for the following reasons:
1. The active sub-channels should be predetermined before a full search over Nc×Nt
sub-channels to avoid the unpredictable manner introduced by the V-BLAST detection algorithm.
2. By taking the joint loading problems apart into two smaller ones, the sorting complexity is significantly reduced.
Hence, at the first stage, the loading algorithm is applied to each subcarrier to obtain an optimal bit and power allocation over its Nt spatial channels. At the second stage, the same loading algorithm is processed over those active sub-channels surviving from the first stage (at mostNt×Nc). The two-stages procedure are described as follows:
Stage 1:
For each sub-band k (containing Nt spatial channels), our allocation problem could be stated as follows:
1 probability, respectively, of the ith transmit antenna at the kth subcarrier, εerror is the target BER, and Pbudget is the total power constraint (Pbudget is normalized to 1 in our simulation to guarantee a fair comparison between systems equipped with different transmit antennas). In general, b should be restricted to an integer number when the practicability is under consideration. However, if we define b as information rate, a system using a specified channel encoder along with different puncturing rate will make b equivalent to some fraction numbers. For example, if we use a convolution encoder to encode a sequence of source bits and puncture output bits to rate 3/4, and then modulate them by using QPSK, b will be equivalent to 3/2. To facilitate our descriptions, we start with the case without channel coding.
A. Initialization
1. Set q, defined as the state of the Nt transmit antennas according to their active modes, to be 2Nt − at the first iteration. To realize what q denotes, we give an 1 example. Assuming that four antennas are available at the transmitter side, if we select three of them, e.g. the 1st, 2nd, and 4th antennas to be active, the state q will become 13, which is the result of converting the corresponding active-mode vector [1, 1, 0, 1] to a decimal number. Let Rate 0= and Presidual final_ =Pbudget.
i active t active
t active
P k P i active N
N k
= ∀ ≤ ≤ (3.3)
3. Calculate the post-processing SNR of each active layer
_ 2 _ 2
4. Clip the power of each layer and thereby reduce its SNR to fit the nearest threshold below it (assumed to be tk in Equation 3.1) by consulting the threshold table, and collect the residual power
residual budget i active
i
P k P P k
=
= −
∑
(3.6)B. Power-Tighten
1. Since this step is valid for all subcarriers, we drop the index k for the following expressions. Let ∆p bi( )i be the power required for ith layer to increase rate from transmission mode into the next higher-rate mode.
2. Following the principle: A bit distribution is said to be Power-tighten if
(a) (Pm ←Pm+ ∆p bm m+ 1)
1. Following the principle: A distribution is said to be efficient if max[ i( )] min[i i( i 1)]
Since it makes no sense to add and remove one bit in the same channel at the same time, the case n m= should be discarded in (e) to avoid this contradiction.
D. Comparing and Recording
1. If (all the predetermined active layers remain surviving)
If
1
Rate
Nt
i i
b
=
∑
≥If Presidual >Presidual final_
1
Rate t
N i i
b
=
=
∑
; Presidual final_ =Presidualelse q← − q 1 else q← − q 1 else q← − q 1
In this stage, we do an exhaustive search to determine which transmit antennas should be active to support the optimal bit and power allocation for every subcarrier.
Therefore, given a subcarrier, we should examine 2Nt − possible combinations, which 1 seem to be a time-consuming task. Fortunately, the needed effort can be eased due to the causality between every possible combination. For example, given a subcarrier, if we assume that the procedure starts with searching the antenna state [1, 1, 1, 1] and finally converges to the state [1, 0, 1, 0], then the following search starts with the antenna state [1, 0, 1, 0] will lead to the same result, thus can be omitted.
Stage 2:
In this stage, the algorithms B and C are reused for those sub-channels (both frequency and spatial channels) surviving from the first stage to further exhaust the total residual power, that is
1
c [ ]
N
residual k
P k
∑
= , to get a rate enhancement.B. Power-Tighten
1 ;1
1 1
0 t c [ ] min [ [ ]( [ ] 1)]
t c
N N
c budget i i N k N i i
i k
N P P k p k b k
≤ ≤ ≤ ≤
= =
≤ ⋅ −
∑∑
≤ ∆ + (3.10)C. Power-Efficientizing
; ;
max[ [ ]( [ ])] min[ [ ]( [ ] 1)]i i i i
i k p k b k ≤ i k p k b k + (3.11)
3.4 Computer Simulations
In this section, computer simulations are conducted to evaluate the performance of the V-BLAST based adaptive MIMO-OFDM system. Throughout the simulation, we only deal with the discrete time signal processing in the baseband, hence pulse-shaping and matched-filtering are removed from consideration for simulation simplicity. Also, channel estimation and timing synchronization are assumed to be perfect. Table 3.3 lists all parameters used in our simulation. The configuration we consider here is a MIMO-OFDM system with a bandwidth of 20 MHz and 64 subcarriers. The set of QAM constellation used in the simulation is {0, 2, 4, 8, 16, 32, and 64}, i.e. ∆ =b 1. Each link in MIMO is modeled as an exponential decay Rayleigh fading channel with
rms 50 sn
τ = .
Firstly, a look-up table that contains the SNR threshold values of each modulation mode should be established. These threshold values could be obtained from Figure 3.6 by consulting each BER curve to find the corresponding SNR value that meets the BER requirement (10-4 in our simulations).
Figure 3.10 shows the selection probability of each modulation mode at different SNRs. It’s obvious that higher order modulation modes are preferred as the average channel SNR increases. In the low SNR scenario, the adaptive loading procedure forces
some of transmit antennas to be blocked frequently to avoid inefficient or unreliable transmission in order to meet the target BER requirement.
In Figure 3.11, we record the unutilized power ratio after the two-stage loading procedure to give an insight into the system. It can be found that in both the low (< 2 dB) and high (> 30 dB) SNR environments, much power remains unused. This is because that at low SNR, most sub-channels suffer from ill conditions so that they are turned off to save power. On the other hand, at high SNR, most sub-channels are fully loaded with little power consumption, hence there is extra power remaining. The residual power could be effectively used to achieve a higher performance margin by uniformly assigning them to those active sub-channels. In Figure 3.12, we see a significant BER improvement benefiting from the residual power at high SNRs.
3.5 Summary
In this Chapter, we introduce an adaptive MIMO-OFDM system to present a new viewpoint in which SM and SD are complementary rather than competing approaches.
For instance, users closer to the transmitter are more likely to experience channel conditions preferring SM, assuming that scattering remains rich enough. For channels less suitable for SM, then the system will instead use SD. The flexibility in switching between SM and SD is realized by the use of adaptive modulation. In this system, the SD comes from the fact of more receive antennas than transmit antennas, under which the bit loading procedure can be deployed by excluding ill transmit antennas. In this case, more diversity gain could be extracted from the V-BLAST scheme. Moreover, by adjusting the transmission parameters to prevent ill-conditioned sub-channels from dominating the system performance, an indirect form of diversity is also drawn.
Serial
Figure 3.1: A digital implementation of appending cyclic prefix into OFDM signal in the transmitter.
Figure 3.2: V-BLAST based MIMO-OFDM transmitter architecture.
.
Encoder Bit Æ M-QAM DEMUX 1ÆNt
Encoder Bit Æ M-QAM DEMUX 1ÆNt
Figure 3.3: V-BLAST based MIMO-OFDM receiver architecture.
Figure 3.4: A typical time and frequency selective fading channel. (By assuming an exponential decay channel model with τrms =50 sn and a speed of 15
RX Antenna 1 Remove
CP FFT
RX Antenna 1 Remove
CP FFT
BPSK QPSK
Figure 3.5: BPSK, QPSK, 8-QAM, 16-QAM, 32-QAM, and 64-QAM constellation
000 100 001 100
000 000 001 000 000 001 001 001 000 101 001 101
000 111 001 111
000 110 001 110
000 010 001 010
000 011 001 011
i
100 001 101 001
100 010 101 010
100 011 101 011
i
000 100 001 100
000 000 001 000 000 001 001 001 000 101 001 101
000 111 001 111
000 110 001 110
000 010 001 010
000 011 001 011
i
100 001 101 001
100 010 101 010
100 011 101 011
i
-10 -5 0 5 10 15 20 25 30 10-5
10-4 10-3 10-2 10-1 100
SNR (dB)
BER
64-QAM 32-QAM 16-QAM 8-QAM QPSK BPSK
Figure 3.6: The average BER of various M-QAM modulation schemes over AWGN channel.
Information coding rate to provide different protection ability
Assign different modulation mode to each subcarrier for each Tx antenna Demux the
information bits according to the CSI
Assign different power to each subcarrier for each Tx antenna coding rate to provide different protection ability
Assign different modulation mode to each subcarrier for each Tx antenna Demux the
information bits according to the CSI
Assign different power to each subcarrier for each Tx antenna
Figure 3.7: V-BLAST based adaptive MIMO-OFDM system transmitter architecture.
Figure 3.8: V-BLAST based adaptive MIMO-OFDM system receiver architecture.
SIC
Construct the
Clip each layer’s power to fit the
residual k budget i
i
Change the Tx’s mode from (4.11), Record b Pi, i
Change the Tx’s mode from (4.12),
Clip each layer’s power to fit the
residual k budget i
i
Change the Tx’s mode from (4.11), Record b Pi, i
Change the Tx’s mode from (4.12),
Figure 3.9: The first stage bit loading procedure flow chart.
-5 0 5 10 15 20 25 30 35 40 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Channel SNR (dB)
Mode Selection Probability
No TX BPSK QPSK 8-QAM 16-QAM 32-QAM 64-QAM
Figure 3.10: Simulated probabilities of each modulation mode utilized by the ZF V-BLAST based adaptive MIMO-OFDM system (with space loading) in the exponentially decay Rayleigh fading channel with τrms =50 ns.
d 0 Hz
f = . ( ,N Nt r) (4, 4)= . Other simulation parameters are listed in Table 3.3.
-5 0 5 10 15 20 25 30 35 40 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Unutilized Power Ratio
Channel SNR (dB)
(4,5) SF loading - ZF (4,4) SF loading - ZF (3,3) SF loading - ZF
Figure 3.11: Unutilized power ratio in the V-BLAST based adaptive MIMO-OFDM system (with space-time loading) at different channel SNRs. Exponential decay Rayleigh fading channel with τrms =50 sn . 0 fd = Hz .
( ,N Nt r) (4,5), (4,4), and (3,3)= . Other parameters are listed in Table 3.3.
-5 0 5 10 15 20 25 30 35 40 10-8
10-7 10-6 10-5 10-4 10-3 10-2 10-1
Channel SNR (dB)
BER
(4,4) SF loading - ZF (3,3) SF loading - ZF (4,5) SF loading - ZF
Figure 3.12: BER versus average channel SNR for the ZF V-BLAST based adaptive MIMO-OFDM system (with space-frequency loading) in an exponential decay Rayleigh fading channel with τrms =50 sn . 0 fd = Hz .
( ,N Nt r) (4,5), (4,4), and (3,3)= . Other parameters are listed in Table 3.3.
Table 3.1: Simulation parameters of the V-BLAST based OFDM system.
Table 3.2: SNR threshold table for various M-QAM at the target BER=10-4.
Table 3.3: Simulation parameters for the proposed V-BLAST based adaptive MIMO- OFDM system.
Number of transmit/receive antennas 3/3, 4/4, and 4/5
Carrier frequency 5 GHz
Modulation QPSK
Number of FFT points 64
Guard interval 16 samples
Channel model Exponential decay Rayleigh fading
Delay spread τrms =50 sn
Bandwidth 20 MHz
No TX BPSK QPSK 8-QAM 16-QAM 32-QAM 64-QAM
s
−∞ 8.41 11.37 15.51 18.53 21.63 24.82Number of transmit/receive antennas 3/3, 4/4, 4/5
Carrier frequency 5 GHz
Bandwidth 20 MHz
Number of carriers, FFT size 64
OFDM symbol duration 3.2µs
Guard interval 0.8µs
M-QAM available 0,1,2,3,4,5,6
M-QAM available 0,1,2,3,4,5,6