How to pivot a DataFrame in PySpark on multiple columns?

I am having a data set in the following format:

import numpy as np
import pandas as pd

# Create the data set

np.random.seed(42)

records = list()
for i in range(2):
    for j in range(2):        
        for k in range(500):
            t = np.random.randint(pd.Timestamp('2000-01-01').value, pd.Timestamp('2018-01-01').value)
            if np.random.rand() > .95: continue                
            ts = pd.Timestamp(t).strftime('%Y-%m-%d %H:%M:%S.%f')
            records.append( (i, j, np.random.rand(), ts) )

df = pd.DataFrame.from_records(records)
df.columns =['a_id', 'b_id', 'value', 'time']

Which looks like this:

      a_id  b_id     value                        time
0        0     0  0.156019  2007-09-28 15:12:24.260596
1        0     0  0.601115  2015-09-08 01:59:18.043399
2        0     0  0.969910  2012-01-10 07:51:29.662492
3        0     0  0.181825  2011-08-28 19:58:33.281289
4        0     0  0.524756  2015-11-15 14:18:17.398715
5        0     0  0.611853  2015-01-07 23:44:37.034322
6        0     0  0.366362  2008-06-21 11:56:10.529679
7        0     0  0.199674  2010-11-08 18:24:18.794838
8        0     0  0.046450  2008-04-27 02:36:46.026876

Here a_id and b_id are the key for a sensor. This means the data frame has to be transformed as such:

df_ = pd.pivot_table(df, index='time', columns=['a_id', 'b_id'], values='value')
df_.index = [pd.to_datetime(v) for v in df_.index]
df_ = df_.resample('1W').mean().ffill().bfill()

After resampling and filling the gaps, the data is in the desired format:

a_id               0                   1          
b_id               0         1         0         1
2000-01-09  0.565028  0.560434  0.920740  0.458825
2000-01-16  0.565028  0.146963  0.920740  0.217588
2000-01-23  0.565028  0.840872  0.920740  0.209690
2000-01-30  0.565028  0.046852  0.920740  0.209690
2000-02-06  0.565028  0.046852  0.704871  0.209690

Each column contains now the data of a sensor.

The problem is, I do not know how to do this in PySpark.

df_test = spark.createDataFrame(df) \
    .withColumn('time', F.to_utc_timestamp('time', '%Y-%m-%d %H:%M:%S.%f'))
df_test.printSchema()

Having

root
 |-- a_id: long (nullable = true)
 |-- b_id: long (nullable = true)
 |-- value: double (nullable = true)
 |-- time: timestamp (nullable = true)

How can I transform df_test such that it has the same form as df_?