Research Article  Open Access
PAPR Reduction Performance by Active Constellation Extension for Diversity MIMOOFDM Systems
Abstract
The VBLAST wireless communication architecture, spacetime block code (STBC), and spacefrequency block code (SFBC) techniques are strong candidates for achieving very high data rates in 4G broadband wireless communications. This paper extends the efficient Active Constellation Extension Smart GradientProject (ACESGP) peaktoaverage power (PAPR) reduction method to STBC, SFBC, and VBLAST systems. Simulation results show 4.19 and 3.57 dB of PAPR reduction for the Alamouti STBC and SFBC, respectively.
1. Introduction
High peak power becomes a serious disadvantage when harnessing the power of MIMOOFDM systems. As the 4G wireless revolution is demanding higher speeds and increased reliability, transmit diversity and spatial multiplexing techniques in MIMO systems are becoming more popular. Of these techniques, spacetime block codes (STBCs), spacefrequency block codes (SFBCs), and the Vertical Bell Labs Layered SpaceTime (VBLAST) architecture have gained wide use in many wireless standards, such as WiMAX, IEEE 802.11n, and 3GPPLTE (3rd Generation Partnership Project—LongTerm Evolution). Spacetimefrequency (STF) block coding schemes take advantage of diversity at a transmitting station often without requiring any channelstate information (CSI); at the same time, when using orthogonal block codes, they allow simple decoding at the receiver station. However, they still have the high peaktoaverage power ratio (PAPR) of OFDM, which requires high power amplifier backoff and results in low efficiency [1].
A robust peak power reduction technique called active constellation extension (ACE) reduces the PAPR of singleinput singleoutput (SISO) OFDM signals by extending the outer constellation points in a way that minimizes the PAPR of an OFDM transmit signal, without reducing the bandwidth or increasing biterrorrate (BER) [1].
Recent work includes extensions of the concept of ACE using a modified smart gradientproject algorithm for MIMOOFDM systems [2]. In this letter, we extend the efficient ACESGP method to STBC, SFBC, and VBLAST OFDM systems. The proposed peak power reduction method can be applied to any STF block code, and its performance is bounded by the code structure.
2. PAPR Properties of OFDM Signals
OFDM modulation is performed by taking the inverse Discrete Fourier Transform (IDFT) of a block of QAMmodulated data symbols . The resulting baseband OFDM signal can be expressed as
The analog PAPR of an OFDM symbol block can be computed as
where and is the symbol period.
Oversampling the discretetime signal to a factor of is sufficient for capturing the continuoustime peaks, as discussed in [3], and to prevent large analog “peak regrowth” at the D/A converter. To statistically evaluate the PAR performance, the complementary cumulative distribution function (CCDF) of the PAPR of the OFDM time signals is used to describe the probability of exceeding a given threshold , that is,
3. ACESGP STBC MIMOOFDM Algorithm
3.1. STBC MIMOOFDM
The simplest STBC with full diversity was first introduced by Alamouti in [4]. The encoder takes a block of two QAM symbols and and assigns it to the two transmit antennas according to the following code matrix:
where the th row represents the th transmission period and the th column corresponds to the th antenna’s symbols.
In this letter, we also show simulation results for the following wellknown orthogonal codes designed for four transmit antennas [5], with code rates 1/2 and 3/4, respectively:
3.2. STBC MIMOOFDM GradientProject Algorithm
The solution to the PAPR reduction problem can be obtained with a fast gradientproject method, where only a couple of iterations are needed to considerably reduce the PAPR. A detailed discussion on the ACESGP algorithm can be found in [3].
Due to the structure of orthogonal spacetime block codes, the SISO ACESGP algorithm need only be applied for the first transmission period, since it can be proven that complex sequences and exhibit the same PAPR properties. Therefore, we only need to perform ACESGP processing on each SISO block independently, obtaining the minimum PAPR timedomain signal ready to transmit after adding the cyclic prefix for the first transmission period. To obtain the timedomain signals for the rest of the transmission periods, the scaling and conjugate DFT properties can be used to avoid the unnecessary IFFT operations for the remaining transmission periods across all transmit antennas:
This property is especially useful for lowerrate codes, such as .
4. ACESGP SFBC MIMOOFDM Algorithm
4.1. SFBC MIMOOFDM
Spacefrequency block coding is another way to obtain diversity in order to improve the performance when employing multiple antennas at the transmitter and the receiver, particularly when there is frequencyselective fading. Coding occurs across adjacent subcarriers of the same OFDM symbol rather than on the same subcarrier of subsequent OFDM symbols (i.e., STBC), thus, reducing the transmission delay.
4.2. SFBC MIMOOFDM GradientProject Algorithm
The main idea of the ACESGP algorithm is to look at the residual clippedoff signal and project it onto the space of allowable extension vectors. The result is a peakreduction signal scaled by an optimal step size subtracted from the timedomain signal. For STF block codes, to correctly decode the signal, we project the residual clippedoff signal into the space of allowable STFBC extensions, which depends on the code being used.
In general, the set of possible ACE vectors will be convex. The three convex sets are the following:
(1)the set , consisting of all vectors such that for some positive constant , (2)the set , an dimensional subspace of , consisting of all vectors with FFT that satisfy the datadependent ACE restrictions, (3)the set , a dimensional (, where is the number of transmission periods) subspace of , consisting of all vectors that yield the largest allowable ACE extension while maintaining the STFBC linear decoding properties.Below is a basic pseudocode for an STFBC OFDM algorithm based on the gradientproject method.
(1)Starting with the input bit stream, break it up into blocks of size for parallel transmission, where there are subchannels total. Consider transmission of OFDM blocks per antenna. Perform MQAM modulation to obtain the frequencydomain symbols, . (2)Add transmit diversity by performing spacetime block coding using an STFBC and determine the allowable extensions for each subchannel. (3)Take the IFFT for each antenna’s signal to construct the time signal, , for each antenna ( is the subchannel index, is the antenna index, and is the transmission period index). Set . (4)Clip any in magnitude for some clip level (i.e., project onto ) to obtain where (5)Compute the clipped signal portion (nonzero only at clipped samples): (6)Apply an FFT to each antenna’s clipped signal to obtain . (7)Keep only the components of which are acceptable extension directions for the given subchannel constellations and set all remaining elements to zero (i.e., project onto ). (8)Apply the STFBC constraint (i.e., project onto ) by taking the maximum ACE extension and enforcing it on each block according to the code matrix. (Note that this step ensures that the STFBC constraints are still satisfied; thus the optimal decoding methods associated with the STFBC are still optimal. For example, in the case of orthogonal SFBC, linear maximumlikelihood decoding is still optimal.)(9)Apply an IFFT to obtain .(10)Determine a step size according to the smart gradient criterion (i.e., for quick convergence, see [3]): (11)If an acceptable PAPR or a maximum iteration count has not been reached, update and return to Step . Otherwise, stop PAPR reduction.This algorithm’s complexity is (for each iteration) due to the oversampled IFFT/FFT operations. The algorithm converges sufficiently after 3 to 4 iterations. The algorithm described here can be applied to a general STF block code and it greatly simplifies for orthogonal STBC/SFBC’s (i.e., as in Section 3).
5. ACESGP VBLAST MIMOOFDM Algorithm
Unlike STBCs, VBLAST has a multiplexing gain but lacks a diversity gain [6]. Because independent data streams are sent on the different transmit antennas, the ACESGP algorithm can be applied on each antennas time signal independently, like in the SISO case described in great detail in [3].
6. Simulation Results
Results of the ACESGP algorithm for STBC and SFBC MIMOOFDM are shown in Figure 1. The algorithm was tested for a complexbaseband STBC OFDM twoantenna system with subchannels employing QPSK using randomly generated OFDM symbol blocks. A level of 4.0 dB above the average power was used to obtain the clipped signal to project onto the space of allowable extension vectors, and an upsampling factor of was used to approximate analog PAPR reduction. Failure to process oversampled digital signals leads to large peak regrowth at the D/A converter. Oversampling was performed by frequencydomain zeropadding and using oversampled IFFT operations.
As shown in Figure 1, for Alamouti STBC, looking at a symbol clip probability level, the third iteration achieves a PAPR reduction of approximately 4.19 dB. Further iterations provide negligible performance increases. Similarly, for Alamouti SFBC, a PAPR reduction of 3.57 dB is achieved in the third iteration. Due to the constellation extension, the average power of the transmit signal increases by 0.86 dB and by 1.08 dB (for each of the two antennas) under Alamouti STBC and SFBC, respectively. (The average power before any ACE processing is used in the PAPR calculation to avoid biasing of the results with the newly increased average power.)
Tables 1 and 2 summarize the PAPR reduction gains obtained using a 256subcarrier MIMOOFDM system when looking at a symbol clip probability. (In Tables 1, 2, and 3, denotes the reduction in PAPR for 4QAM, denotes the reduction in PAPR for 16QAM, denotes the reduction in PAPR for 64QAM, and denotes the initial PAPR) An upsampling factor and the clipping levels, , used were 4.0, 5.0, and 5.0 dB above the average power, for codes , , and , respectively.



Table 3 summarizes the PAPR reduction gains obtained for VBLAST, which are all obtained for a 256subcarrier MIMOOFDM system when looking at a symbol clip probability. A clipping levels of 4.0 and 6.0 dB above the average power were used for two and four transmit antennas, respectively (with ). Larger PAPR reduction gains were obtained for the VBLAST MIMOOFDM systems than the STBC/SFBC cases because there is no constraint across the signals being sent out from the antennas (i.e., independent streams).
Figure 2 evaluates the BER performance of a STBC MIMOOFDM system under QPSK modulation and ACESGP processing with and without amplifier saturation, assuming additive white Gaussian noise (AWGN) conditions. The nonlinear highpower amplifier model used was based on [7], with companding parameter of 6, saturation output amplitude corresponding to singlecarrier QPSK, and backoffs of 0 and 3 dB. The backoff was implemented by raising the saturation amplitude level. The required SNR to achieve a BER of is 2.2 dB less with ACE (versus without ACE) for 0 dB backoff and 1.0 dB less for a 3 dB backoff. Even without saturation, ACE slightly improves the BER due to increased margins on the extended symbols.
7. Conclusions
An extended method of ACE reduces the PAPR for spacetimefrequency blockcoded MIMOOFDM systems without compromising BER performance. Simulations showed that a PAPR reduction gain of 4.19 and 3.57 dB can be obtained under QPSK for Alamouti STBC and SFBC, respectively. On the other hand, gains above 4 dB were obtained for two and four antennas under QPSK for VBLAST. Results show that as the number of antennas increases, the block code constraint reduces the ACE PAPR reduction gain for spacetimefrequencycoded MIMOOFDM systems, due to the reduced number of degrees of freedom caused by structured redundancy. However, the ACE PAPR reduction gain increases with the number of antennas for uncoded MIMOOFDM systems (i.e., VBLAST). The PAPR reduction gains obtained are larger than those observed for the SISO case [3], and they seem most promising for small constellations (i.e., QPSK and 16QAM).
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Copyright
Copyright © 2010 Theodoros Tsiligkaridis and Douglas L. Jones. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.