average capacity of an open loop multiple antenna radio. (MAR) system is given ..... the receiver radio being driven around the campus area. The UCLA campus ...
Experiments in Space-Time Modulation Weijun Zhu, Daniel Liu, David Browne and Michael P. Fitz UnWiReD Laboratory at the University of California Los Angeles {zhuw,daniell,decibel,fitz}@ee.ucla.edu Abstract— This paper reports on some experiments with multiple antenna radios. Specifically this paper compares the performance between an experimental system with training and coherent demodulation and a system using noncoherent techniques of communication. The paper also examines robustness in performance across a variety of channel conditions.
I. I NTRODUCTION Over the past several years, there has been a great deal of research to improve performance of wireless communications in fading environments by exploiting transmitter and/or receiver diversity. The pioneering work by Telatar [1], Foschini and Gans [2] showed that multiple antennas in a wireless communication system can greatly improve performance. The average capacity of an open loop multiple antenna radio (MAR) system is given as HHh CA = E log det ILt + (1) N0 where H is the channel matrix, N0 is the noise spectral density, and the expected value is over the distribution of the channel matrix. For Lt transmit antennas and Lr receive antennas in Rayleigh fading, it was shown that, with spatial independenc, there are essentially Lt Lr levels of diversity available and there are min (Lt , Lr ) independent parallel channels that could be established. These information theoretic studies spawned two lines of work; one where the number of independent channels is large [3] and one where the number of independent channels is small [4], [5]. With eight years of intense engineering research and development effort after these insights, MAR techniques are starting to make a significant impact on how wireless services are provided. Examples include the 802.11n standard, 3G and 4G mobile telecommunications systems. A. Open Problems in Space-Time Signaling The open problems in MAR communications relate to situations where more sophisticated and detailed aspects of communication systems need to be modeled and understood. For example performance is not easily understood in channel models that are not well modeled as Gaussian/Rayleigh, or where the scattering is not rich or isotropic, or where system parameters are time-varying, or how system non-idealities impact system performance. These problems are not well addressed by simulation or analysis as the sophistication of the problem prohibits analysis in most cases and the utility of simulation is limited to the accuracy of the models used for simulation. Because of this trend in MAR research, our research team has decided that experimental MIMO communications will be important in advancing the technology.
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This paper examines a small subset of the open issues in the literature and reports on experiments that attempt to resolve these issues on real systems and real channels. The focus here is on the following systems 1) Land Mobile Wireless – Mobility and multipath typical of this environment will be the focus of the study presented in this paper. 2) Frequency flat channels – A vast majority of the work in space-time signaling has used frequency flat models. This corresponds to relatively narrowband transmission in a traditional land mobile wireless channels. 3) Linear Modulations – Only linear modulations will be the focus of the study presented in this paper. 4) Short Packet Communication – The packet lengths of the system presented in the paper will be approximately 300 symbols. This type of system is typical of speech communication systems or short packet data (paging). Within this fairly focused area, the following issues are open: 1) Trained Coherent versus Noncoherent – In general there are three types of communications paradigms for signal design: coherent, noncoherent, differentially coherent. The coherent system assumes that receiver perfectly knows the channel state information. This paradigm implies channel state information must be learned with training. Consequently a tradeoff exists between the bandwidth efficiency of coding schemes versus the performance in the presence of channel state estimation errors. This tradeoff is a function of the transmission rate and the channel characteristics. 2) Robustness Issues – Code performance is very much a function of the channel conditions [6] and channel models. Consequently it is useful to see if any interesting characteristics are produced in real wireless channels that impact the choice of coded modulations in practice. This paper is organized by having Section II overview the models, Section III presents the experimental system details, Section IV provides the experimental results, and Section V presents the take–away conclusions. II. S IGNAL M ODELS In our system, the signal on the ith antenna is modeled as Xi (t) =
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where u(t) is a Nyquist pulse shape. The sampled matched filter outputs are the sufficient statistics for the demodulation.
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If the fading is slow enough, the output samples of the matched filter for the k th symbol are given as a Lr × 1 vector (k) = H(k) Es X(k) (k) Y +N (3)
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where Xn , a Lt ×Nf matrix, is used to denote the transmitted codeword for transmitted word n, Y is the matched filter output matrix. If the modulation is defined on a trellis then the Viterbi algorithm can be used to find this minimum distance transmitted codeword and if the transmitted codeword is defined by a lattice then a suboptimal lattice search algorithm can be used to find the best codeword. B. Differentially Coherent Demodulation The core idea of differential modulation and demodulation is that unitary group codes have characteristics that enable a simple modulator and demodulator [7]. A unitary group code is characterized with a set of unitary matrices gn ∈ G of size Nb × Nb that satisfy the group property for matrix multiplication. Differential encoding generates a sequence of space-time block codes (STBC) of size Lt × Nb via x(k) = x(k − 1)g(k)
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where the value of g(k) = gn is determined by the bits that are transmitted a the k th block time. The supremum of the rate of the code is R = log2 (|G|) /Nb . The simplest differentially coherent demodulator uses two consecutive blocks of matched filter outputs to demodulate the signal with a form
(6) g(k) = arg max Tr gnH Y(k − 1)H Y(k) gn ∈G
where Y(k) is a block of matched filter outputs of size Lr × Nb . A couple comments are worth noting here: 1) If Y(k − 1) was replaced by H(k)x(k − 1) this demodulator would be exactly the coherent demodulator given in (4) for the unitary modulation. Hence an estimator–correlator interpretation of the demodulator is possible with Y(k − 1) being a channel estimate used in a coherent demodulation structure; 2) The demodulator is very simple but suffers two degradations: i) a 3dB performance loss compared to coherent demodulation due to the noisy channel estimate Y(k − 1); ii) an error floor when the channel is time varying.
IF signal 10.273MHz
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where Es is the energy per transmitted symbol; Hij (k) is the complex path gain from transmit antenna i to receive antenna j at time kT ; X(k) is the Lt ×1 vector of symbols transmitted (k) is the additive white Gaussian noise at symbol time k; N vector of size Lr × 1. The noise is modeled as independent circularly symmetric zero-mean complex Gaussian random variables with variance N0 /2 per dimension. A. Coherent Demodulation Coherent demodulation refers to the case of finding the most likely transmitted bit sequence when the channel is known. The optimum word demodulator denoted maximum likelihood (ML) word demodulator. For orthogonal modulations when H(k) = h (quasi-static channel), the optimum demodulator has a simpler form given as ˆ H (4) B = arg max Tr (Y − hXn ) (Y − hXn )
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The MAR system.
C. Noncoherent Demodulation The core idea of noncoherent modulation and demodulation is that a detector can be formed only based on the statistics of the fading channel and the observations. In the case of noncoherent detection it was shown by Hochwald and Marzetta [8] that a unitary constellation is capacity achieiving in the limit of large block lengths. A unitary noncoherent code is characterized with a set of unitary matrices xn ∈ X of size Lt × Nb . The rate of the code is R = log2 (|X |) /Nb . The noncoherent demodulator [9] uses the block of matched filter outputs to demodulate the signal with a form
ˆ (k) = arg max Tr xn Y(k)H Y(k)xH (7) x n xn ∈X
where Y(k) is a k th block of matched filter outputs of size Lr × Nb . The demodulator is very simple but suffers two degradations: 1) a performance loss compared to coherent demodulation; 2) an error floor in time varying channels. III. E XPERIMENTAL S YSTEM The experimental system that has been deployed for this experiment is a narrowband 3 × 4 MAR system. We have chosen a carrier frequency of 220MHz and a bandwidth of around 4kHz. All modulations are linear modulation with a spectral raised cosine pulse shape with an excess bandwidth of 0.2 and a symbol rate of 3.2kHz. This carrier frequency and bandwidth allow us to do realistic land mobile testing and still be confident that the frequency flat assumption will be valid. A. Radio System The UnWiReD narrowband testbed is a software defined real-time multi-antenna testbed. Fig. 1 shows the block diagram of the narrowband 3x4 MIMO real-time test system. Each box in the diagram represents a custom made building block of the testbed. The information bits are encoded and pulse shaped in the 3-TX modem by two Analog Devices (ADI) fixed point digital signal processors (DSP). The baseband signals are then digitally up converted to 10MHz IF signals. The 3-TX up converter radio further up converts the IF signals to the 220MHz RF and amplifies it for transmission with a maximum transmission power of 35dBm. The receiver chain provides a high performance system for narrowband MIMO processing. The received signals are down
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The superframe used in the field experiments.
converted from RF to 10MHz IF signals by the down converter radio and then digitally down converted to baseband by the digital receiver. The digital receiver over–samples the input signals at 64MHz. Overall receiver dynamic range is greater than 80dB. The overall error vector magnitude through both the transmit and receive chains is less than 2%. The demodulation is performed by two floating point ADI DSPs. The demodulated data, as well as other important test information, is transferred to a laptop for data recording and displaying real-time test results. The collected data is the bit and frame error rate, signal power, noise power, channel amplitude gains, channel singular values, and vector diagrams at various points in the system in real-time. This data provides a near complete characterization of the system performance. B. Packet Format The frame for the transmitted signals of this experimental system was designed to allow many modulations to be tested in a rapidly time interleaved fashion. This structure is implemented at the transmitter with a superframe that is repeated about every 4 seconds. During this superframe, a preamble is sent and 42 different frames of space-time modulations (STM) can be transmitted. The preamble has a signal format that allows high performance symbol time estimation (a dotting pattern) so that accurate timing and a course frequency offset can be acquired. Each of the subsequent frames or data packets are 300 symbols in length (93.75ms). Modulations are independent from frame to frame for the experiments documented in this paper. At the end of the superframe there is a silence period of about 70 symbols. The noise power which can vary significantly at 220MHz in various scenarios due to man–made noise is measured every frame and averaged to get a good estimate of the SNR. C. Receiver Processing Overview All of the receiver functions are implemented in real-time in a digital signal processor. Time estimation is derived by using a nonlinear open loop timing estimator. Frequency estimation and frame synchronization are achieved during the first preamble portion of the frame during the decoding. Having a unique word for frame synchronization allows pilot symbols to be inserted and used for channel estimation and provides block boundary synchronization for all coded modulations during demodulation. Having a digital signal processing implementation allows a wide variety of different algorithms to be implemented in the same code. One of the powerful characteristics of the programmable implementation is that the same transmitted data can be used to compare decoding with a varying number of receive antennas. In almost all modulation formats, decoding for any number of receive antennas (from Lr = 1 to Lr = 4) can be accomplished in real time. IV. E XPERIMENTAL R ESULTS The experimentation was done in a variety of locations on the UCLA campus and the surronding West Los Angeles area.
The testing is divided into three types of testing 1) Indoor Stationary - This environment has both radios deployed in a building on the same floor (Boelter Hall at UCLA). The tests were run during both day and night time so foot traffic was typical of a campus building. Unless otherwise specified the receiver array was linear with a λ/2 spacing and the transmitter array was triangular also with a λ/2 spacing. 2) Outdoor Local - This environment has one radio (TX) deployed on the top of a 5 story building and one radio (RX) on a vehicle (a cart or a van). The test consisted of the receiver radio being driven around the campus area. The UCLA campus area is heavily urbanized. Unless otherwise specified the receiver array was square with a λ/2 spacing on each side and the transmitter array was linear with a 2λ spacing. 3) Outdoor High Speed - This environment has one radio (TX) deployed on the top of a 5 story building and one radio (RX) on a vehicle (a van). The test consisted of the receiver radio being driven on the 405 Freeway in West Los Angeles. The testing was done at times of relatively free flowing traffic so speeds of 5075MPH were maintained during the testing. The antenna geometries are the same as the outdoor local scenarios unless otherwise noted. A large amount of data was collected, of which, only a subset related to the questions posed will be reported in this paper. The complete data will be available upon request. The major findings reported will be the bit error rate and frame error frame versus Eb /N0 . The measured Eb /N0 reported in the experiments are computed by the averages over the entire superframe and all the receive antennas. This measure gives something closer to the average SNR in high mobility tests and something closer to the instantaneous SNR in static testing but the measurement was viewed as the best compromise in reporting the data. A. Trained Versus Noncoherent In this test, simple coherent demodulation with pilot symbol based channel estimation is compared with noncoherent modulation and demodulation techniques. Achieving the desired unitary form for the modulation placed a significant restriction on the constellations that can be used for noncoherent demodulation hence we limit our study to coding schemes that have small effective coding rates. To make a fair comparison for Lt = 2 the Alamouti code [10] (R = 2) using QPSK is compared with a R = 1.5 QPSK differentially coherent code of Hughes [7], a R = 1.5 and Nb = 4 noncoherent code of Kammoun and Belfiore [11], and a R = 1.5 and Nb = 4 Alamouti noncoherent code using 8PSK. The noncoherent Alamouti code has an identity matrix concatenated with a coherent Alamouti code. In the Alamouti code case, 448 bits are transmitted with 112 Alamouti block codes. For the differentially coherent code, 447 bits are transmitted with 150 block of length 2 symbols. The noncoherent codes use 75 blocks of length 4 symbols to send 450 bits.
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Fig. 3. Comparison of effective R = 1.5 trained and noncoherent modulation performance in stationary tests. Lr = 4.
These tests and comparisons were completed both in a static and a mobile environment. The performance in the static environment is shown in Fig. 3. The differentially coherent and trained coherent results give about the same performance. The reason for this is that the higher rate code (R = 2 versus R = 1.5) and the nonperfect channel estimation causes enough degradation in coherent demodulation to give differentially coherent demodulation comparable performance even though theoretically the loss between using noncoherent and coherent is 3dB. The noncoherent modulations have about 3-4dB degradation compared to the others. The reason for this degradation is that the noncoherent coding schemes need to implicitely include training to demodulate in the presense of a random channel. Hence the constellation needs to be larger to keep the same average rate. The differentially coherent and trained coherent codes obtain this channel estimate in a more bandwidth efficient manner. Longer block length noncoherent codes might be able to recover this inefficiency but no codes of this type were tested. The performance in the high mobility environment is shown in Fig. 4. The results follow the same general trend of Fig. 3 except that trained coherent demodulation has a slightly better performance than differentially coherent demodulation and all modulations experience an error floor at high SNR. The slight performance improvement is probably due to the fact the pilot symbol aided channel estimation was designed to accomodate Doppler spread while differential demodulation was not. The error floor is expected and predicted by theory for the differential and noncoherent demodulators but the manifestation of an error floor for coherent demodulation was unexpected. The degradation of noncoherent codes in timevarying fading is more pronounced. B. Robustness Since the performance achieved by a space-time code is a function of the interaction of the code structure with the channel structure there have been a handful of papers looking
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Fig. 4. Comparison of effective R = 1.5 trained and noncoherent modulation performance in high mobility tests. Lr = 1.
at robustness in code design [12], [6]. As a first step toward quantifying this characteristic of STM, an experiment that implemented a wide variety of powerful trellis codes and compared performance was run. The code comparison that we will report here is between the Lt = 2 codes optimized for spatially white Rayleigh fading reported by Yan and Blum [13], the superorthogonal (SO) codes [14], [15], [16], [17] (specifically the codes of [14]) and the universal trellis codes of Kose and Wesel [6]. Typical results that were obtained are shown in Fig. 5 and Fig. 6. This figure shows the compilation of the outdoor local tests results for Lr = 2. Several conclusions can be drawn about these trellis codes’ performance in realistic channels. First, the bit error probability performance does not change dramatically between each of the powerful codes. The performance seems to vary significantly with SNR and this is probably due to a lack of acquiring statistically significant amount of data compared to the variability in the channel. Second, the powerful codes were also seen to demonstrate an error floor in the mobile environment. This leads us to believe that the error floor that occurs in our experimental system is not an aspect of the modulation but due to a some unforeseen aspect of channel estimation. An interesting characteristic of the SO codes is that they seem to produce worse bit error rate with with an increasing number of states in the code (as they do in simulation). In terms of frame error rate, the SO codes seem to hold a clear advantage. The more powerful codes perform better. Consequently it seems apparent that for short packet systems a SO code might be a good choice but in a system that concatenates an inner code with an outer code (like a Reed-Solomon code) the universal codes of Kose and Wesel [6] or the optimized trellis codes of Yan and Blum [13] might be be better choices. This concatenated experiment will be a subject of future work. Finally at least with this initial experiment a significant variation between simulation results and experimental results was not seen. A future experiment
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2) Robustness Issues – For the reported first order tests there appears to be no obvious issues with the robustness of space–time codes. It should be noted that a large number of other results and conclusions can be reported from this gathered data.
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VI. ACKNOWLEDGEMENTS A great deal of work has gone into this project that needs to be acknowledged. Past UnWiReD Laboratory members who partcipated in the project are Parul Gupta, Shingwa Wong, and Sunder Venkateswaran. A portion of the software implemented in the experiments was the result of class work in the Wireless Communication Theory course that is taught by Prof. Fitz at UCLA and people whose project contributed to the results reported in this paper are Cenk Kose, Maryam Owrang and Scott Enserink. Prof. Belfiore also gave us an unpublished noncoherent R = 1.5 code based on the results in [11]
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Fig. 5. Comparison of the bit error rate of R = 2 trellis codes in mobile outdoor tests. Lr = 2.
which specifically characterizes the performance versus the gain conditions is planned and might generate different results than this aggregation of all the data. Error performance in outdoor mobile tests 2BRX Antennas
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V. C ONCLUSIONS The following conclusion result form these experiments: 1) Trained Coherent versus Noncoherent – The experiments presented in this paper show that for low rates ≤ R = 2, differentially coherent demodulation has good performance and low complexity. The loss in rate due to training and noisy channel estimates in trained coherent system cause these systems have comparable performance. Error floors for all modulations occur at high mobility. Short block length noncoherent codes do not provide competitive performance but perhaps longer codes would give better performance.
R EFERENCES [1] E. Teletar. Capacity of multi-antenna Gaussian channels. Technical report, AT&T–Bell Labs, June 1995. [2] G. J. Foschini and M. Gans. On the limits of wireless communication in a fading environment. Wireless Personal Comm., 6:311–355, March 1998. [3] G. J. Foschini. Layered space-time architecture for wireless communications in a fading environment when using multiple antennass. Bell Labs Technical Journal, pages 41–59, Autumn 1996. [4] V. Tarokh, N. Seshadri, and A.R. Calderbank. Space-time codes for high data rate wireless communication: Performance criterion and code construction. IEEE Info. Theory, vol. IT-44:744–765, March 1998. [5] J.-C. Guey, M. P. Fitz, M. R. Bell, and W.-Y. Kuo. Signal design for transmitter diversity wireless communication systems over Rayleigh fading channels. In 1996 IEEE Vehicular Technology Conference, pages 136–140, Atlanta, GA, 1996. [6] C. Kose and R.D. Wesel. Universal space-time trellis codes. IEEE Transactions on Information Theory, 49:2717 – 2727, Oct. 2003. [7] B.L. Hughes. Differential space-time modulation. IEEE Transactions on Information Theory, 46:2567 – 2578, Nov. 2000. [8] B. M. Hochwald and T. L. Marzetta. Unitary space-time modulation for multiple-antenna communications in rayleigh flat fading. IEEE Transactions on Information Theory, 46:543–564, March 2000. [9] B. M. Hochwald, T. L. Marzetta, T. J. Richardson, W. Sweldens, and R. Urbanke. Systematic design of unitary space-time constellations. IEEE Transactions on Information Theory, 46:1962–1973, September 2000. [10] S. M. Alamouti. A simple transmit diversity technique for wireless communications. IEEE J. Select. Areas Commun., 16:1451–1458, October 1998. [11] I. Kammoun and J.-C Belfiore. A new family of grassmann space-time codes for non-coherent MIMO systems. IEEE Communications Letters, 7:528–530, Nov. 2003. [12] S. Siwamogsatam and M.P. Fitz. Robust space–time coding for correlated Rayleigh fading channels. IEEE Trans. Signal Processing, pages 2408 –2416, October 2002. [13] Q. Yan and R.S. Blum. Optimum space-time convolutional codes. In IEEE Wireless Communications and Networking Confernce, pages 1351– 1355, September 2000. [14] S. Siwamogsatam and M.P. Fitz. Improved high rate space–time TCM via orthogonality and set partitioning. In International Symposium on Wireless Personal Multimedia Communications, Alborg, Denmark, September 2001. [15] S. Siwamogsatam and M.P. Fitz. Improved high rate space–time TCM via concatenation of expanded orthogonal block codes and MTCM. In IEEE International Conference on Communication, New York, April 2002. [16] M. Ionescu, K. K. Mukkavilli, Z. Yan, and J. Lilleberg. Improved 8state and 16-state space time codes for 4-PSK with two transmit antennas. IEEE Communications Letters, pages 301–303, July 2001. [17] H. Jafarkhani and N. Seshadri. Super orthogonal space-time trellis codes. In IEEE Int. Conf. on Commun., New York, April 2002.
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