Two-Stage Bit Loading Algorithm - Adaptive MIMO-OFDM Systems

4 Multiuser Adaptive MIMO-OFDM Systems

4.4 Adaptive MIMO-OFDM Systems

4.4.2 Two-Stage Bit Loading Algorithm

The capacity of a MIMO system is maximized by using simple singular value decomposition (SVD) weights combined with optimal power distribution over the transmit antennas which is known as the water filling (WF) algorithm. However, the WF algorithm requires infinite length codebook, continuous modulation order, and continuous power level. Thus, it isn’t possible to use the result directly in practice. A group of bit loading algorithms were proposed to approach the WF solution with the constraints of discrete modulation order. These bit loading algorithms distribute the available energy among a set of parallel AWGN channels as to maximize the overall bit rate for discrete loading problem in practice [34]-[37]. Therefore, on account of simplicity and capability, the Campllo’s loading criteria [35] is promoted that could be somewhat modified and extended to the V-BLAST based multiuser adaptive MIMO-OFDM system with reasonable computation complexity.

The modified ZF V-BLAST detection algorithm can generate a set of weighting vectors to perform spatial multiplexing and calculate the post-processing SNRs as in Equation (2.38). By simulation, the norm values of the weighting vectors are observed to change in an unpredictable manner when some transmit antennas turn off.

This undesirable result due to the nonlinear operations in the V-BLAST algorithm means that once some transmit antennas are chosen to turn off, the norm values will be recalculated according to the changed channel matrix. By this reason, an exhaustive search over all possible combinations of transmit antennas is required to find the optimal one subject to the constraint in Equation (4.4). By properly exploiting causality, the exhaustive search can be significantly mitigated.

The joint space-frequency bit loading problem in the V-BLAST based MIMO-OFDM system can be described as

1 1 the ith transmit antenna at the kth subcarrier respectively,, ε_error is the target BER, and

budget

P is the total power constraint. is normalized to 1 in the simulation to guarantee a fair comparison between systems equipped with different transmit antennas.

Considering the above observation, the joint loading problem should be taken apart into two separated subproblems by the following reasons:

budget

1. In order to avoid the unpredictable manner introduced by the V-BLAST detection algorithm, the active subchannels should be predetermined before a full search over all subchannels (Nc×Nt ).

2. The sorting complexity is significantly reduced by taking the joint bit loading problem apart into two smaller ones.

Therefore, the adaptive loading algorithm is applied to each subcarrier to obtain an optimal bit and power allocation over its Nt spatial channels at the first stage. At the second stage, the same loading algorithm is used over those active subchannels surviving from the first stage (at most _t N ). Through this two-stage processing, each subchannel’s condition will be precisely monitored and the unpredictable phenomenon happened in the V-BLAST detection algorithm won’t have to be worried about. The adaptive two-stage algorithm can be presented as follows:

Stage 1:

For each subband k containing spatial channels, the allocation problem can be stated as follows:

where is the distributed power at the kth subcarrier. It can be decided according to the ratio of the kth subcarrier channel gain and the sum of total subcarriers’ channel gains which would be presented as

distributed[ ]

When considering the practicability, the rate b should be restricted to an integer number.

Nevertheless, systems usually use a specified channel encoder along with different puncturing rate to make the rate b equivalent to some fraction numbers. For instance, if a convolution encoder is used to encode a sequence of source bits and puncture output bits to rate 2/3, and then use 16-QAM as modulation order, the information rate defined as b will be equivalent to 8/3. To assist the following statements, the case without channel coding will be described.

Initialization Step 1:

Defined q as the state of the Nt transmit antennas according to their active modes. For instance, assuming that four antennas are available at the transmitter side, two of them are selected, e.g. the 1st and 3rd antennas to be active, the state q will become 10, which is the result of converting the corresponding active mode vector [1, 0, 1, 0] to a decimal number. Let Rate 0= and Presidual final_{_} =Pdistributed[ ]k at first.

i active t active

t active

Calculate the post-processing SNR of each active layer according to Equation (2.38)

Clip the power of each layer to reduce its SNR in order to fit the nearest threshold below it by consulting the threshold table in table 4.1, and collect the residual power

( /10)

, [ ]

residual budget i active

The Power-Tighten Algorithm

A bit distribution is said to be power tighten if

1 1

The Power-Tighten algorithm can be described as Step 1:

Since the power-tighten algorithm would be employed for all subcarriers, the index k will be dropped for simplicity in following expressions. Assumed that ∆p b_i( )_i is the power required for ith layer to increase rate from b_i− to b . It can be defined as 1 _i to record the least amount of power needed to step from current transmission mode into the next high rate mode.

( 1)

Find the active transmit antenna m requiring the least amount of power to step into the next high rate mode which can be defined as

{

1 ,

}

(d) arg

{

1 min [, ( 1)]

}

t active i i

m i N p

= ≤ ≤ ∆ b +

The Power-Efficientizing Algorithm

A bit distribution is said to be power efficient if max[ _i( )] min[_i _i( _i 1)]

i ∆p b ≤ ∆p b + (4.14)

The Power-Efficientizing algorithm can be described as Step 1:

Find the active transmit antenna m which requires the least amount of power to step into the next higher rate mode and the active transmit antenna n which releases the most amount of power to go back for the next lower rate mode. Both of them can be defined as

Comparing and Recording Step 1:

If all the predetermined active layers are assumed to remain surviving, the following process will be executed:

If P_residual >Presidual final_{_}

In this stage, a time-consuming exhaustive search is performed to determine which transmit antennas would be active to support the optimal bit and power allocation for every subcarrier. Fortunately, the needed effort can be reduced due to the causality between every possible combination. Fig. 4.8 shows the flow chart of the first stage adaptive bit loading algorithm.

Stage 2:

In this stage, the Power-Tighten algorithm and the Power-Efficientizing algorithm are reused for those surviving sub-channels from the first stage including both frequency and spatial channels to further exhaust the total residual power to get a rate enhancement.

The Power-Tighten Algorithm

The Power-Tighten algorithm would be employed according to the principle:

1 ;1

The Power-Efficientizing Algorithm

The Power-Efficientizing algorithm would be employed according to the principle:

; ;

max[ [ ]( [ ])] min[ [ ]( [ ] 1)]_i _i _i _i

i k p k b k ≤ i k p k b k + (4.17)

4.5 Computer Simulations

Computer simulations are conducted to evaluate the performance of the proposed V-BLAST based adaptive MIMO-OFDM system in this section. Channel estimation and timing synchronization are assumed to be perfect at first. The discrete time signal processing in the baseband is only dealt with throughout the simulation. Hence, pulse-shaping and matched-filtering are removed from consideration for simulation simplicity. Table 4.2 lists all parameters used in the following simulation. The configuration 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}. Each link in MIMO is modeled as an exponential decay Rayleigh fading channel with τ_rms =50 sn . The IEEE 802.11 Working Group suggests this channel profile as the baseline for predicting multipath in IEEE 802.11a (5 GHz). This model is ideal for software simulations in predicting performance results of a given implementation. The channel impulse response is illustrated in Fig. 3.11.

Before the simulation, a look-up table that contains the SNR threshold values of each modulation mode should be established at first. By consulting each BER curve to find the corresponding SNR vale that meets the BER requirement (10^-4 in our simulations), these threshold values could be obtained from Fig. 4.3.

Fig. 4.9 shows the selection probability of each modulation mode at different without considering the mobility issue. From the figure, higher order modulation modes are preferred as increases. In the low scenarios, the adaptive loading algorithm gives up adopting higher order modulation modes and turns to choose lower order modulation modes to meet the target BER requirement. The algorithm would force some of transmit antennas to be blocked frequently to avoid inefficient or unreliable transmission.

/ 0

E Ns

/ 0

E Ns E N_s/ ₀

Fig. 4.10 and Fig 4.11 shows BER versus with different detection criteria at different number of transmit and receive antennas. It is obvious that the ZF method always meets the BER requirement and the MMSE method exhibits performance degradation at low scenarios. By using the MMSE criterion, the actual post-processing SNR in Fig 4.3 doesn’t hold due to the bias of the signal component in the soft decision value. This is the reason why the MMSE method exhibits performance

/ 0

E Ns

/ 0

E Ns

degradation at low scenarios. However, at high scenarios, the MMSE method will approximate the ZF one and reaches the same performance.

/ 0

E Ns E N_s/ ₀

Fig 4.12 shows BER versus with ZF detection criteria at different number of transmit and receive antennas. The difference between Fig 4.10 and Fig 4.12 is that the system using residual power not only meets the BER requirement but also achieves a better BER performance. At high scenarios, most subchannels are fully loaded with little power consumption, hence there is extra power remaining. The residual power could be effectively used to achieve a significant BER improvement by uniformly assigning them to those active sub-channels.

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E Ns

In Fig 4.13 and Fig 4.14, the modulation mode selection probability and the transmission rate at different scenarios are compared for the two cases: space loading (without the second stage) and space-frequency loading (with the second stage).

The first stage is performed to select the active subchannels while the second stage is done over the subchannels surviving from the first stage to make a further use of the residual power. From Fig 4.13, it is obvious that the space-frequency loading will gain a higher peak in each modulation type at the second stage and lead to a rate enhancement which can be shown in Fig 4.14.

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E Ns

Fig 4.15 and Fig 4.16 show the modulation mode selection probability and the transmission rate at different scenarios. Both of them are compared with different number of transmit and receive antennas. The diversity gain in V-BLAST algorithm increases from an order of

/ 0

E Ns

r t 1

N −N + to Nr as the effective number of transmit signals decreases at each step of the SIC. Therefore, the systems with more receive antennas can always extract more diversity than those with fewer ones by assuming no error propagation problem. In the V-BLAST based adaptive MIMO-OFDM system, diversity gain can allow for the use of higher order modulation without degrading the BER performance. This feature proves why the transmission rate curve corresponding to the case of (Nt, Nr) = (5, 5) is steeper than the other curves in Fig. 4.16.

Fig 4.17 shows the unutilized power ratio after the two-stage adaptive loading algorithm. From the figure, it is evident that much power remains unused in both the low and high E N_s/ ₀ scenarios. The reason is that most subchannels suffer from ill

channel conditions to force them turning off to save power at low scenarios.

On the contrary, at high scenarios, most subchannels are employed higher order modulation modes with little power consumption, and there is extra power remaining. This residual power could be saved to reduce the total transmit power or effectively used to achieve a higher performance margin.

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/ 0

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Fig 4.18 shows the transmission bit rate versus with different loading algorithms including the rounding off WF algorithm, the QoS based WF algorithm [38], and the Chow’s algorithm. From the figure, it can be shown that the two-stage adaptive loading algorithm has the best performance than other loading algorithms. It is because that this algorithm uses the Power-Tighten algorithm and the Power- Efficientzing algorithm to achieve the maximum transmission rate efficiently.

/ 0

E Ns

Fig 4.19 shows BER versus with different detection criteria. In this simulation, a constant channel estimation error is assumed. The channel estimation error ΔH is defined to be equal to the noise power. From the figure, both methods exhibit significant performance degradation. This is because that the channel estimation error makes the chosen modulation mode not optimum with regards to the actual channel quality and hence degrades the BER performance.

/ 0

E Ns

In Fig 4.20, the proposed system is simulated in a realistic TDD system. In TDD system, the estimation of the channel quality priori to transmission is used to select the appropriate modulation mode for the next transmission. Hence a channel quality estimation delay is incurred in this scheme. During this delay, the fading channel quality varies according to the Doppler frequency and consequently, the channel quality estimates perceived priori to transmission may become antiquated. A delay time of one packet (0.4 ms) is assumed in this simulation. From the figure, it is obvious that the proposed system works well to meet the BER constraint. The proposed system only exhibits slight performance degradation even when the user moves with a high speed (120 m/s). The reason is that the estimation delay time is usually smaller than the channel coherence time. During the channel coherence time, the channel condition wouldn’t change severely. Therefore the chosen modulation mode would reflect to the current channel quality and doesn’t degrade the BER performance.

4.6 Summary

Due to the scarcity of radio spectrum, high spectral efficiency becomes a need requirement that encourages modern wireless modems toward this trend. An evolution of the V-BLAST supporting OFDM modulation seems to be a solution that can dramatically increase the capacity of wireless radio links with no additional power and bandwidth consumption. In Section 4.1, the V-BLAST based MIMO-OFDM system is introduced.

Adaptive modulation is also a promising technique to increase data rate that can be reliably transmitted over fading channels. This technique 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 which is introduced in Section 4.2 and Section 4.3.

From the analysis of MIMO channel capacity, the waterfilling distribution of power over channels with different SNR values achieves the optimal transmission scheme. 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. Therefore, a practical two-stage adaptive loading algorithm is presented 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. This two-stage adaptive loading algorithm is introduced in Section 4.4.

Encoder Bit Æ M-QAM DEMUX 1ÆN_t

Figure 4.1: V-BLAST based MIMO-OFDM transmitter architecture.

RX Antenna 1 Remove

CP FFT

RX Antenna 1 Remove

CP FFT

Figure 4.2: V-BLAST based MIMO-OFDM receiver architecture.

Figure 4.3: The average BER of various M-QAM modulation schemes over Rayleigh fading channel.

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