Interpreting CDMA Measurements

To properly evaluate CDMA systems, engineers need specialized test equipment, distinct measurements, and new ways of using traditional measurement techniques.

By Marcus da Silva, Business Development Manager, Hewlett-Packard Co. (HP)

The complexities of the IS-95 CDMA system has created the need for highly specialized test equipment, distinct measurements, and new ways of using traditional tests and measurement techniques. The particular characteristics of CDMA signals also require that measurements be interpreted with CDMA properties in mind.

The spectrum analyzer is one of the most common test and measurement instruments used in the wireless industry. When performing CDMA measurements, this instrument must be viewed with a different set of conditions in mind.

IS-95 CDMA systems distribute power over a 1.23 MHz bandwidth. As a result, power measurements using a marker on a spectrum analyzer must take into account the resolution bandwidth as well as the CDMA bandwidth (Figure 1).

Click here to see Figure 1.

A spectrum analyzer marker reads the power in its resolution bandwidth. The power in narrow band signals can be read directly from the marker. Since IS-95 CDMA's power is distributed over a 1.23 MHz bandwidth, the marker reading must be corrected for the ratio of bandwidths.

One should also note that the IS-95 CDMA spectrum is shaped by a modulation filter that has about +/-2 dB of ripple. This ripple must also be taken into account when computing power from a spectrum analyzer display

Non-Linearities in the Frequency Domain
When running spectrum analyzer measurements on CDMA products, engineers must closely look at non-linearities in these systems. Non-linearities can be created by overdriven power amplifiers, overdriven mixers, or even corrosion in metallic junctions at coaxial connectors or other interfaces. In CDMA systems, non-linearities often cause the intermodulation of signals (Figure 2).

Click here to see Figure 2.

For narrowband signals, the intermodulation products produced by non-linearities create spectral components at frequencies given by:

where:
N and M are integers and f₁ and f₂ are two frequencies present at the input of the non-linear device and fi is the frequency of the intermodulation products.

IS-95 CDMA signals can be thought of as many closely spaced spectral components. Intermodulation products of these spectral components form a shelf around the expected CDMA spectrum.

The creation of intermodulation products is exacerbated by the fact that IS-95 signals have a large crest factor (ratio of peak to average power). In CDMA systems, forward link signals can have crest factors in excess of 12 dB. This means that a transmitter capable of 10 W power must have a power amplifier with enough overhead to produce 158 W peak power.

Power Variability
In addition to high crest factors, IS-95 CDMA signals feature quite a bit of power variability. Power variability in forward link signals is affected by the total traffic on the channel and by forward link power control. Power variability in reverse link signals is primarily caused by mobile power control that adjusts power each 1.25 ms.

Due to the power variability in CDMA systems, accurate power measurements on CDMA signals require a measurement of the true average power. Power measurements on signals undergoing power control may also require triggering so that measurements encompass an entire frame or a power control group.

Power meters are used in conjunction with spectrum analyzers to perform power measurements on CDMA signals. When measuring CDMA power, engineers can either use broadband or frequency-selective power meters.

Broadband power meters respond to all signals present at the measurement input. They are highly accurate only when single signals are present. Their wide bandwidth also limits them to relatively high signal levels.

Frequency-selective power meters are needed when multiple signals are present or when low levels must be measured. In these situations, engineers are interested in power housed in the 1.23 MHz CDMA bandwidth.

Frequency-selective meters offer two methods to evaluate power. One mode works in the time domain while the other operates in the frequency domain.

In the time domain method, a 1.23 MHz bandpass filter is applied to the signal of interest. In this method, power is measured after it passes through a filter.

In the frequency domain method, the power spectral density of a signal is integrated over the bandwidth of interest. Once the signal is integrated over the bandwidth, the meter calculates the power contained in the entire bandwidth. This method, typically used with spectrum analyzers, is mathematically equivalent to the time domain method above.

Modulation Accuracy
All communications systems specify modulation accuracy. FM systems specify peak deviation and distortion. TDMA systems specify in error-vector magnitude (EVM). GSM systems specify in global phase trajectory.

CDMA systems define modulation accuracy in terms of a correlation coefficient (r). r can be thought of as the fraction of power in a signal that correlates with a mathematically ideal signal when all frequency, phase, and time offsets are removed and amplitude is normalized.

A useful and intuitive simplification can be made for r when all sources of error are uncorrelated with the signal. If the CDMA signal is represented as the sum of an ideal signal and an error signal, r is then the ratio of ideal signal power to total signal power (See Equation).

Forward link r is defined for a pilot only signal. Reverse link r, on the other hand, is defined for an arbitrary mobile transmission.

Figures 3a and 3b show r, frequency error, pilot time offset, and carrier feedthrough for a forward signal channel containing only a pilot (Walsh code 0).

Click here to see Figure 3.

Figure 3a shows a signal that is well within specifications while Figure 3b highlights a signal where the frequency, pilot time offset, and carrier feedthrough have been degraded. It should be noted that the pilot time offset and frequency error do not degrade r. The entire degradation in this case was caused by the carrier feedthrough.

Using Figure 3a, engineers can calculate the effect of the carrier feedthrough as follows:

In Figure 3b, the total has been further increased by a local oscillator feedthrough of -20.7 dB or 0.00851. Therefore, carrier feedthrough can be calculated as:

Walsh Code Domain Power
CDMA forward links use Walsh codes to distinguish one traffic channel from all others. Walsh codes also identify pilot, synch, and paging signals. All of these signals occupy the same frequency band. The addition of a traffic channel does not change the spectrum shape, just its magnitude.

The IS-95 CDMA equivalent of spectrum analysis is Walsh code domain power. Walsh code domain power measurements display Walsh Codes 0 to 63 horizontally and the power in each Walsh code vertically (Figure 4).

Figure 4: The CDMA equivalent of spectrum analysis is Walsh code domain power.

Two Walsh code domain power measurement modes are available on most modern pieces of test equipment. In the first mode, Walsh code domain power is displayed in watts or dBm for each Walsh code. In the second, relative Walsh code domain power measurements display a fraction of total power in each Walsh code. In this second case, the sum of the measured values for all 64 Walsh codes adds to unity.

The Walsh code domain power measurement can be used to analyze and set the power in each active Walsh code (pilot, paging, synch, traffic, etc.). This measurement can also be used to evaluate the power in inactive Walsh codes.

As stated above, modulation quality (or r) for a forward link signal is defined for a pilot only transmission. Therefore, to directly measure r, the engineer must take a base station off the air. This procedure, however, is troublesome for a network operator. Taking a base station off the air can cause loss of service and, in turn, create loss of revenue.

r, however, can be estimated under most conditions from code domain power measurements made on an active base station without taking the base station off the air. To calculate r, engineers can use the following equation:

where
I denotes each of N active Walsh codes, and
j denotes each of 64-N inactive Walsh codes

In this equation, each active Walsh code contains an allotted power as well as a fraction of error power. If all errors are assumed to be equally distributed among all Walsh codes, the value of r can be estimated by:

CW Interference
CDMA systems are often degraded by CW interference. These CW signals can be caused by intermodulation between other carriers sharing the same antenna site.

CW signals are easily identified in the frequency domain. Figure 5a shows a CW interferer that has the same power as the CDMA signal.

Click here to see Figure 5a.

Note that the spectrum analyzer shows all of the CW power in one location. But as stated above, CDMA power is spread over a 1.23 MHz bandwidth. As a result, the CW signal looks like a bump on the Barthead. Interferers of a lower level may be totally hidden under the CDMA signal when observed in the frequency domain.

The pseudorandom noise (PN) spreading and de-spreading used in IS-95 CDMA takes the energy in the CW interference and spreads it equally among all Walsh codes. Therefore, 1/64th of the CW energy occupies each Walsh Code.

The CW spur has the same power as the CDMA signal. The total power (denominator) is therefore twice the power in the interference. Since, 1/64 of the interference power (numerator) occupies each Walsh code, the value of the average code domain floor in this case is -21 dB.

E_bN_t
Walsh code domain power measurements have the ability to separate signals into their Walsh code components. This ability can be used for a highly accurate measurement of the ratio of energy per bit to the power spectral density of noise and interference (also called E_bN_t). E_bN_t can be calculated as:

for 9 kb/s data rates, and

for 14.4 kb/s data rates.

In CDMA systems, two symbols out of every active power control group are dedicated to a punctured power control bit. As a result, engineers must account for this power control bit when performing CDMA measurements.

Figure 5b highlights a situation where power control bits were not accounted for.

Click here to see Figure 5b.

In this figure, the display shows a CDMA forward link with a single traffic channel at Walsh Code 42. The signal is known to be a full rate 9600 b/s signal. The code domain power coefficient for Walsh Code 42 is -13.15 dB. The average Code Domain noise floor is -22.5 dB.

If engineers calculate E_bN_t using the numbers provided in Figure 5, they will arrive at an E_bN_t of 11.85 dB. But, this calculation is inaccurate because it ignores the power control subchannel. If the power control bits are transmitted with the same power as the traffic bits, only 11 of 12 b in each power control group are dedicated to traffic. The other bit is dedicated to the power control subchannel. Therefore, the correction for the power control subchannel is equal to 11/12 or - 0.378 dB and the value of E_bN_t really is:

E_bN_t = 11.85 dB - 0.378 dB = 11.47 dB.

Walsh Code Domain Timing
Walsh codes are useful to distinguish forward link traffic channels. A Walsh Code's orthogonal nature prevents one code from interfering with other Walsh codes.

The orthogonal nature of Walsh codes is lost when they are not time aligned. As a result, a loss of time alignment can cause interference between forward link traffic channels.

To prevent alignment problems, engineers must perform Walsh code domain timing measurements on forward link traffic channels. A Walsh code domain timing measurement displays codes 0 to 63 horizontally and the time offset between each Walsh Channel and the pilot vertically. Typically, only the timing for active Walsh codes is shown.

To avoid timing problems, the time alignment between Walsh channels is also carefully determined by design. There are several adjustments included in CDMA application-specific ICs (ASICs) employed in base stations which ensure that timing is properly aligned when all of the Walsh codes reach the antenna.

Timing problems are not the only cause of misalignment in the forward link channels. Interference problems can also occur when there is a phase misalignment between the transmitted pilot and other Walsh channels. The IS-95 CDMA forward link uses separate and distinct in-phase (I) and quadrature (Q) PN spreading sequences. The same sequences are used for the pilot and all the Walsh Channels. The mobile receiver uses the received pilot to synchronize its spreading sequences and phase align its local oscillator. The local oscillator is then assumed to also be phase aligned with each of the different Walsh codes.

Any phase misalignment between the receiver local oscillator and its Walsh channel results in interference from I to Q and from Q to I. Phase errors are essentially a loss of orthogonality between I and Q. These phase errors can result from cross talk between I and Q in the base station baseband processing section, misaligned local oscillators, or intermodulation between Walsh codes.

PN Offset Domain Measurements
While FDMA systems use frequency to distinguish between all transmitters, the channelization in the IS-95 CDMA system uses several different kinds of codes. Walsh codes are used to define the communication channel from a base station to each of the several mobiles with which it is linked. The long code mask is used to define the reverse link transmissions from each mobile to base stations. PN offset is used to identify the forward link transmitter. PN offsets identify individual sectors of base stations. Each pilot has a unique PN offset which can be one of 512 possible codes.

PN offset domain measurements are shown in Figures 6a and 6b.

Click here to see Figures 6a and 6b.

Figure 6a shows a measurement of the ratio of pilot energy per chip to the power spectral density of noise and interference (E_c/I_o) as a function of PN offset. Figure 6b shows the five largest pilots received at a particular location. The pilots are identified by their PN offset assignment, their strength is indicated by the bar height, and their delay relative to the ideal GPS timing is shown as a number on top of the bar.

Many other parameters can be studied in the PN offset domain. The measurements shown in Figures 6a and 6b are caused by the pilot E_c/I_o. In principle, Walsh code domain measurements can also be combined with PN offset domain measurements to measure traffic E_c/I_o.

Marcus da Silva, Business Development Manager, HP, East 24001 Mission Ave, Liberty Lake, WA 99019; 509-921-3488; Fax: 509-921-4332.